From: Thomas Pornin <pornin@bolet.org>
Date: Sun, 5 Aug 2018 22:02:36 +0000 (+0200)
Subject: Added support code for RSA and EC key encoding (including reconstruction of all publi... 
X-Git-Tag: v0.6~4
X-Git-Url: https://bearssl.org/gitweb//home/git/?a=commitdiff_plain;h=d8fa415fcabecb7d7c8461d8edbe2f265911e72c;p=BearSSL

Added support code for RSA and EC key encoding (including reconstruction of all public and private key elements from the private key structure), with raw and PKCS#8 formats, both in DER and PEM.
---

diff --git a/inc/bearssl_ec.h b/inc/bearssl_ec.h
index 533296d..db22692 100644
--- a/inc/bearssl_ec.h
+++ b/inc/bearssl_ec.h
@@ -28,6 +28,8 @@
 #include <stddef.h>
 #include <stdint.h>
 
+#include "bearssl_rand.h"
+
 #ifdef __cplusplus
 extern "C" {
 #endif
@@ -797,6 +799,83 @@ br_ecdsa_vrfy br_ecdsa_vrfy_asn1_get_default(void);
  */
 br_ecdsa_vrfy br_ecdsa_vrfy_raw_get_default(void);
 
+/**
+ * \brief Maximum size for EC private key element buffer.
+ *
+ * This is the largest number of bytes that `br_ec_keygen()` may need or
+ * ever return.
+ */
+#define BR_EC_KBUF_PRIV_MAX_SIZE   72
+
+/**
+ * \brief Maximum size for EC public key element buffer.
+ *
+ * This is the largest number of bytes that `br_ec_compute_public()` may
+ * need or ever return.
+ */
+#define BR_EC_KBUF_PUB_MAX_SIZE    145
+
+/**
+ * \brief Generate a new EC private key.
+ *
+ * If the specified `curve` is not supported by the elliptic curve
+ * implementation (`impl`), then this function returns zero.
+ *
+ * The `sk` structure fields are set to the new private key data. In
+ * particular, `sk.x` is made to point to the provided key buffer (`kbuf`),
+ * in which the actual private key data is written. That buffer is assumed
+ * to be large enough. The `BR_EC_KBUF_PRIV_MAX_SIZE` defines the maximum
+ * size for all supported curves.
+ *
+ * The number of bytes used in `kbuf` is returned. If `kbuf` is `NULL`, then
+ * the private key is not actually generated, and `sk` may also be `NULL`;
+ * the minimum length for `kbuf` is still computed and returned.
+ *
+ * If `sk` is `NULL` but `kbuf` is not `NULL`, then the private key is
+ * still generated and stored in `kbuf`.
+ *
+ * \param rng_ctx   source PRNG context (already initialized).
+ * \param impl      the elliptic curve implementation.
+ * \param sk        the private key structure to fill, or `NULL`.
+ * \param kbuf      the key element buffer, or `NULL`.
+ * \param curve     the curve identifier.
+ * \return  the key data length (in bytes), or zero.
+ */
+size_t br_ec_keygen(const br_prng_class **rng_ctx,
+	const br_ec_impl *impl, br_ec_private_key *sk,
+	void *kbuf, int curve);
+
+/**
+ * \brief Compute EC public key from EC private key.
+ *
+ * This function uses the provided elliptic curve implementation (`impl`)
+ * to compute the public key corresponding to the private key held in `sk`.
+ * The public key point is written into `kbuf`, which is then linked from
+ * the `*pk` structure. The size of the public key point, i.e. the number
+ * of bytes used in `kbuf`, is returned.
+ *
+ * If `kbuf` is `NULL`, then the public key point is NOT computed, and
+ * the public key structure `*pk` is unmodified (`pk` may be `NULL` in
+ * that case). The size of the public key point is still returned.
+ *
+ * If `pk` is `NULL` but `kbuf` is not `NULL`, then the public key
+ * point is computed and stored in `kbuf`, and its size is returned.
+ *
+ * If the curve used by the private key is not supported by the curve
+ * implementation, then this function returns zero.
+ *
+ * The private key MUST be valid. An off-range private key value is not
+ * necessarily detected, and leads to unpredictable results.
+ *
+ * \param impl   the elliptic curve implementation.
+ * \param pk     the public key structure to fill (or `NULL`).
+ * \param kbuf   the public key point buffer (or `NULL`).
+ * \param sk     the source private key.
+ * \return  the public key point length (in bytes), or zero.
+ */
+size_t br_ec_compute_pub(const br_ec_impl *impl, br_ec_public_key *pk,
+	void *kbuf, const br_ec_private_key *sk);
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/inc/bearssl_pem.h b/inc/bearssl_pem.h
index 5e466bc..8dba582 100644
--- a/inc/bearssl_pem.h
+++ b/inc/bearssl_pem.h
@@ -236,6 +236,57 @@ br_pem_decoder_name(br_pem_decoder_context *ctx)
 	return ctx->name;
 }
 
+/**
+ * \brief Encode an object in PEM.
+ *
+ * This function encodes the provided binary object (`data`, of length `len`
+ * bytes) into PEM. The `banner` text will be included in the header and
+ * footer (e.g. use `"CERTIFICATE"` to get a `"BEGIN CERTIFICATE"` header).
+ *
+ * The length (in characters) of the PEM output is returned; that length
+ * does NOT include the terminating zero, that this function nevertheless
+ * adds. If using the returned value for allocation purposes, the allocated
+ * buffer size MUST be at least one byte larger than the returned size.
+ *
+ * If `dest` is `NULL`, then the encoding does not happen; however, the
+ * length of the encoded object is still computed and returned.
+ *
+ * The `data` pointer may be `NULL` only if `len` is zero (when encoding
+ * an object of length zero, which is not very useful), or when `dest`
+ * is `NULL` (in that case, source data bytes are ignored).
+ *
+ * Some `flags` can be specified to alter the encoding behaviour:
+ *
+ *   - If `BR_PEM_LINE64` is set, then line-breaking will occur after
+ *     every 64 characters of output, instead of the default of 76.
+ *
+ *   - If `BR_PEM_CRLF` is set, then end-of-line sequence will use
+ *     CR+LF instead of a single LF.
+ *
+ * The `data` and `dest` buffers may overlap, in which case the source
+ * binary data is destroyed in the process. Note that the PEM-encoded output
+ * is always larger than the source binary.
+ *
+ * \param dest     the destination buffer (or `NULL`).
+ * \param data     the source buffer (can be `NULL` in some cases).
+ * \param len      the source length (in bytes).
+ * \param banner   the PEM banner expression.
+ * \param flags    the behavioural flags.
+ * \return  the PEM object length (in characters), EXCLUDING the final zero.
+ */
+size_t br_pem_encode(void *dest, const void *data, size_t len,
+	const char *banner, unsigned flags);
+
+/**
+ * \brief PEM encoding flag: split lines at 64 characters.
+ */
+#define BR_PEM_LINE64   0x0001
+
+/**
+ * \brief PEM encoding flag: use CR+LF line endings.
+ */
+#define BR_PEM_CRLF     0x0002
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/inc/bearssl_rsa.h b/inc/bearssl_rsa.h
index 7c79d33..f3825d1 100644
--- a/inc/bearssl_rsa.h
+++ b/inc/bearssl_rsa.h
@@ -28,6 +28,8 @@
 #include <stddef.h>
 #include <stdint.h>
 
+#include "bearssl_rand.h"
+
 #ifdef __cplusplus
 extern "C" {
 #endif
@@ -1068,7 +1070,7 @@ uint32_t br_rsa_i62_oaep_decrypt(
  * Similarly, the public key elements are written in `kbuf_pub`, with
  * pointers and lengths set in `pk`.
  *
- * If `sk` is `NULL`, then `kbuf_pub` may be `NULL`, and only the
+ * If `pk` is `NULL`, then `kbuf_pub` may be `NULL`, and only the
  * private key is set.
  *
  * If `pubexp` is not zero, then its value will be used as public
@@ -1098,8 +1100,8 @@ uint32_t br_rsa_i62_oaep_decrypt(
  */
 typedef uint32_t (*br_rsa_keygen)(
 	const br_prng_class **rng_ctx,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp);
 
 /**
@@ -1118,8 +1120,8 @@ typedef uint32_t (*br_rsa_keygen)(
  */
 uint32_t br_rsa_i15_keygen(
 	const br_prng_class **rng_ctx,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp);
 
 /**
@@ -1138,8 +1140,8 @@ uint32_t br_rsa_i15_keygen(
  */
 uint32_t br_rsa_i31_keygen(
 	const br_prng_class **rng_ctx,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp);
 
 /**
@@ -1162,8 +1164,8 @@ uint32_t br_rsa_i31_keygen(
  */
 uint32_t br_rsa_i62_keygen(
 	const br_prng_class **rng_ctx,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp);
 
 /**
@@ -1184,6 +1186,176 @@ br_rsa_keygen br_rsa_i62_keygen_get(void);
  */
 br_rsa_keygen br_rsa_keygen_get_default(void);
 
+/**
+ * \brief Type for a modulus computing function.
+ *
+ * Such a function computes the public modulus from the private key. The
+ * encoded modulus (unsigned big-endian) is written on `n`, and the size
+ * (in bytes) is returned. If `n` is `NULL`, then the size is returned but
+ * the modulus itself is not computed.
+ *
+ * If the key size exceeds an internal limit, 0 is returned.
+ *
+ * \param n    destination buffer (or `NULL`).
+ * \param sk   RSA private key.
+ * \return  the modulus length (in bytes), or 0.
+ */
+typedef size_t (*br_rsa_compute_modulus)(void *n, const br_rsa_private_key *sk);
+
+/**
+ * \brief Recompute RSA modulus ("i15" engine).
+ *
+ * \see br_rsa_compute_modulus
+ *
+ * \param n    destination buffer (or `NULL`).
+ * \param sk   RSA private key.
+ * \return  the modulus length (in bytes), or 0.
+ */
+size_t br_rsa_i15_compute_modulus(void *n, const br_rsa_private_key *sk);
+
+/**
+ * \brief Recompute RSA modulus ("i31" engine).
+ *
+ * \see br_rsa_compute_modulus
+ *
+ * \param n    destination buffer (or `NULL`).
+ * \param sk   RSA private key.
+ * \return  the modulus length (in bytes), or 0.
+ */
+size_t br_rsa_i31_compute_modulus(void *n, const br_rsa_private_key *sk);
+
+/**
+ * \brief Get "default" RSA implementation (recompute modulus).
+ *
+ * This returns the preferred implementation of RSA (recompute modulus)
+ * on the current system.
+ *
+ * \return  the default implementation.
+ */
+br_rsa_compute_modulus br_rsa_compute_modulus_get_default(void);
+
+/**
+ * \brief Type for a public exponent computing function.
+ *
+ * Such a function recomputes the public exponent from the private key.
+ * 0 is returned if any of the following occurs:
+ *
+ *   - Either `p` or `q` is not equal to 3 modulo 4.
+ *
+ *   - The public exponent does not fit on 32 bits.
+ *
+ *   - An internal limit is exceeded.
+ *
+ *   - The private key is invalid in some way.
+ *
+ * For all private keys produced by the key generator functions
+ * (`br_rsa_keygen` type), this function succeeds and returns the true
+ * public exponent. The public exponent is always an odd integer greater
+ * than 1.
+ *
+ * \return  the public exponent, or 0.
+ */
+typedef uint32_t (*br_rsa_compute_pubexp)(const br_rsa_private_key *sk);
+
+/**
+ * \brief Recompute RSA public exponent ("i15" engine).
+ *
+ * \see br_rsa_compute_pubexp
+ *
+ * \return  the public exponent, or 0.
+ */
+uint32_t br_rsa_i15_compute_pubexp(const br_rsa_private_key *sk);
+
+/**
+ * \brief Recompute RSA public exponent ("i31" engine).
+ *
+ * \see br_rsa_compute_pubexp
+ *
+ * \return  the public exponent, or 0.
+ */
+uint32_t br_rsa_i31_compute_pubexp(const br_rsa_private_key *sk);
+
+/**
+ * \brief Get "default" RSA implementation (recompute public exponent).
+ *
+ * This returns the preferred implementation of RSA (recompute public
+ * exponent) on the current system.
+ *
+ * \return  the default implementation.
+ */
+br_rsa_compute_pubexp br_rsa_compute_pubexp_get_default(void);
+
+/**
+ * \brief Type for a private exponent computing function.
+ *
+ * An RSA private key (`br_rsa_private_key`) contains two reduced
+ * private exponents, which are sufficient to perform private key
+ * operations. However, standard encoding formats for RSA private keys
+ * require also a copy of the complete private exponent (non-reduced),
+ * which this function recomputes.
+ *
+ * This function suceeds if all the following conditions hold:
+ *
+ *   - Both private factors `p` and `q` are equal to 3 modulo 4.
+ *
+ *   - The provided public exponent `pubexp` is correct, and, in particular,
+ *     is odd, relatively prime to `p-1` and `q-1`, and greater than 1.
+ *
+ *   - No internal storage limit is exceeded.
+ *
+ * For all private keys produced by the key generator functions
+ * (`br_rsa_keygen` type), this function succeeds. Note that the API
+ * restricts the public exponent to a maximum size of 32 bits.
+ *
+ * The encoded private exponent is written in `d` (unsigned big-endian
+ * convention), and the length (in bytes) is returned. If `d` is `NULL`,
+ * then the exponent is not written anywhere, but the length is still
+ * returned. On error, 0 is returned.
+ *
+ * Not all error conditions are detected when `d` is `NULL`; therefore, the
+ * returned value shall be checked also when actually producing the value.
+ *
+ * \param d    destination buffer (or `NULL`).
+ * \param sk   RSA private key.
+ * \return  the private exponent length (in bytes), or 0.
+ */
+typedef size_t (*br_rsa_compute_privexp)(void *d,
+	const br_rsa_private_key *sk, uint32_t pubexp);
+
+/**
+ * \brief Recompute RSA private exponent ("i15" engine).
+ *
+ * \see br_rsa_compute_privexp
+ *
+ * \param d    destination buffer (or `NULL`).
+ * \param sk   RSA private key.
+ * \return  the private exponent length (in bytes), or 0.
+ */
+size_t br_rsa_i15_compute_privexp(void *d,
+	const br_rsa_private_key *sk, uint32_t pubexp);
+
+/**
+ * \brief Recompute RSA private exponent ("i31" engine).
+ *
+ * \see br_rsa_compute_privexp
+ *
+ * \param d    destination buffer (or `NULL`).
+ * \param sk   RSA private key.
+ * \return  the private exponent length (in bytes), or 0.
+ */
+size_t br_rsa_i31_compute_privexp(void *d,
+	const br_rsa_private_key *sk, uint32_t pubexp);
+
+/**
+ * \brief Get "default" RSA implementation (recompute private exponent).
+ *
+ * This returns the preferred implementation of RSA (recompute private
+ * exponent) on the current system.
+ *
+ * \return  the default implementation.
+ */
+br_rsa_compute_privexp br_rsa_compute_privexp_get_default(void);
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/inc/bearssl_x509.h b/inc/bearssl_x509.h
index 10e3510..49d2fba 100644
--- a/inc/bearssl_x509.h
+++ b/inc/bearssl_x509.h
@@ -1249,6 +1249,147 @@ br_skey_decoder_get_ec(const br_skey_decoder_context *ctx)
 	}
 }
 
+/**
+ * \brief Encode an RSA private key (raw DER format).
+ *
+ * This function encodes the provided key into the "raw" format specified
+ * in PKCS#1 (RFC 8017, Appendix C, type `RSAPrivateKey`), with DER
+ * encoding rules.
+ *
+ * The key elements are:
+ *
+ *  - `sk`: the private key (`p`, `q`, `dp`, `dq` and `iq`)
+ *
+ *  - `pk`: the public key (`n` and `e`)
+ *
+ *  - `d` (size: `dlen` bytes): the private exponent
+ *
+ * The public key elements, and the private exponent `d`, can be
+ * recomputed from the private key (see `br_rsa_compute_modulus()`,
+ * `br_rsa_compute_pubexp()` and `br_rsa_compute_privexp()`).
+ *
+ * If `dest` is not `NULL`, then the encoded key is written at that
+ * address, and the encoded length (in bytes) is returned. If `dest` is
+ * `NULL`, then nothing is written, but the encoded length is still
+ * computed and returned.
+ *
+ * \param dest   the destination buffer (or `NULL`).
+ * \param sk     the RSA private key.
+ * \param pk     the RSA public key.
+ * \param d      the RSA private exponent.
+ * \param dlen   the RSA private exponent length (in bytes).
+ * \return  the encoded key length (in bytes).
+ */
+size_t br_encode_rsa_raw_der(void *dest, const br_rsa_private_key *sk,
+	const br_rsa_public_key *pk, const void *d, size_t dlen);
+
+/**
+ * \brief Encode an RSA private key (PKCS#8 DER format).
+ *
+ * This function encodes the provided key into the PKCS#8 format
+ * (RFC 5958, type `OneAsymmetricKey`). It wraps around the "raw DER"
+ * format for the RSA key, as implemented by `br_encode_rsa_raw_der()`.
+ *
+ * The key elements are:
+ *
+ *  - `sk`: the private key (`p`, `q`, `dp`, `dq` and `iq`)
+ *
+ *  - `pk`: the public key (`n` and `e`)
+ *
+ *  - `d` (size: `dlen` bytes): the private exponent
+ *
+ * The public key elements, and the private exponent `d`, can be
+ * recomputed from the private key (see `br_rsa_compute_modulus()`,
+ * `br_rsa_compute_pubexp()` and `br_rsa_compute_privexp()`).
+ *
+ * If `dest` is not `NULL`, then the encoded key is written at that
+ * address, and the encoded length (in bytes) is returned. If `dest` is
+ * `NULL`, then nothing is written, but the encoded length is still
+ * computed and returned.
+ *
+ * \param dest   the destination buffer (or `NULL`).
+ * \param sk     the RSA private key.
+ * \param pk     the RSA public key.
+ * \param d      the RSA private exponent.
+ * \param dlen   the RSA private exponent length (in bytes).
+ * \return  the encoded key length (in bytes).
+ */
+size_t br_encode_rsa_pkcs8_der(void *dest, const br_rsa_private_key *sk,
+	const br_rsa_public_key *pk, const void *d, size_t dlen);
+
+/**
+ * \brief Encode an EC private key (raw DER format).
+ *
+ * This function encodes the provided key into the "raw" format specified
+ * in RFC 5915 (type `ECPrivateKey`), with DER encoding rules.
+ *
+ * The private key is provided in `sk`, the public key being `pk`. If
+ * `pk` is `NULL`, then the encoded key will not include the public key
+ * in its `publicKey` field (which is nominally optional).
+ *
+ * If `dest` is not `NULL`, then the encoded key is written at that
+ * address, and the encoded length (in bytes) is returned. If `dest` is
+ * `NULL`, then nothing is written, but the encoded length is still
+ * computed and returned.
+ *
+ * If the key cannot be encoded (e.g. because there is no known OBJECT
+ * IDENTIFIER for the used curve), then 0 is returned.
+ *
+ * \param dest   the destination buffer (or `NULL`).
+ * \param sk     the EC private key.
+ * \param pk     the EC public key (or `NULL`).
+ * \return  the encoded key length (in bytes), or 0.
+ */
+size_t br_encode_ec_raw_der(void *dest,
+	const br_ec_private_key *sk, const br_ec_public_key *pk);
+
+/**
+ * \brief Encode an EC private key (PKCS#8 DER format).
+ *
+ * This function encodes the provided key into the PKCS#8 format
+ * (RFC 5958, type `OneAsymmetricKey`). The curve is identified
+ * by an OID provided as parameters to the `privateKeyAlgorithm`
+ * field. The private key value (contents of the `privateKey` field)
+ * contains the DER encoding of the `ECPrivateKey` type defined in
+ * RFC 5915, without the `parameters` field (since they would be
+ * redundant with the information in `privateKeyAlgorithm`).
+ *
+ * The private key is provided in `sk`, the public key being `pk`. If
+ * `pk` is not `NULL`, then the encoded public key is included in the
+ * `publicKey` field of the private key value (but not in the `publicKey`
+ * field of the PKCS#8 `OneAsymmetricKey` wrapper).
+ *
+ * If `dest` is not `NULL`, then the encoded key is written at that
+ * address, and the encoded length (in bytes) is returned. If `dest` is
+ * `NULL`, then nothing is written, but the encoded length is still
+ * computed and returned.
+ *
+ * If the key cannot be encoded (e.g. because there is no known OBJECT
+ * IDENTIFIER for the used curve), then 0 is returned.
+ *
+ * \param dest   the destination buffer (or `NULL`).
+ * \param sk     the EC private key.
+ * \param pk     the EC public key (or `NULL`).
+ * \return  the encoded key length (in bytes), or 0.
+ */
+size_t br_encode_ec_pkcs8_der(void *dest,
+	const br_ec_private_key *sk, const br_ec_public_key *pk);
+
+/**
+ * \brief PEM banner for RSA private key (raw).
+ */
+#define BR_ENCODE_PEM_RSA_RAW      "RSA PRIVATE KEY"
+
+/**
+ * \brief PEM banner for EC private key (raw).
+ */
+#define BR_ENCODE_PEM_EC_RAW       "EC PRIVATE KEY"
+
+/**
+ * \brief PEM banner for an RSA or EC private key in PKCS#8 format.
+ */
+#define BR_ENCODE_PEM_PKCS8        "PRIVATE KEY"
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/mk/Rules.mk b/mk/Rules.mk
index 88195fd..fd55dfd 100644
--- a/mk/Rules.mk
+++ b/mk/Rules.mk
@@ -19,6 +19,7 @@ OBJ = \
  $(OBJDIR)$Penc64be$O \
  $(OBJDIR)$Penc64le$O \
  $(OBJDIR)$Ppemdec$O \
+ $(OBJDIR)$Ppemenc$O \
  $(OBJDIR)$Pec_all_m15$O \
  $(OBJDIR)$Pec_all_m31$O \
  $(OBJDIR)$Pec_c25519_i15$O \
@@ -27,10 +28,12 @@ OBJ = \
  $(OBJDIR)$Pec_c25519_m31$O \
  $(OBJDIR)$Pec_curve25519$O \
  $(OBJDIR)$Pec_default$O \
+ $(OBJDIR)$Pec_keygen$O \
  $(OBJDIR)$Pec_p256_m15$O \
  $(OBJDIR)$Pec_p256_m31$O \
  $(OBJDIR)$Pec_prime_i15$O \
  $(OBJDIR)$Pec_prime_i31$O \
+ $(OBJDIR)$Pec_pubkey$O \
  $(OBJDIR)$Pec_secp256r1$O \
  $(OBJDIR)$Pec_secp384r1$O \
  $(OBJDIR)$Pec_secp521r1$O \
@@ -126,27 +129,36 @@ OBJ = \
  $(OBJDIR)$Phmac_drbg$O \
  $(OBJDIR)$Psysrng$O \
  $(OBJDIR)$Prsa_default_keygen$O \
+ $(OBJDIR)$Prsa_default_modulus$O \
  $(OBJDIR)$Prsa_default_oaep_decrypt$O \
  $(OBJDIR)$Prsa_default_oaep_encrypt$O \
  $(OBJDIR)$Prsa_default_pkcs1_sign$O \
  $(OBJDIR)$Prsa_default_pkcs1_vrfy$O \
  $(OBJDIR)$Prsa_default_priv$O \
+ $(OBJDIR)$Prsa_default_privexp$O \
  $(OBJDIR)$Prsa_default_pub$O \
+ $(OBJDIR)$Prsa_default_pubexp$O \
  $(OBJDIR)$Prsa_i15_keygen$O \
+ $(OBJDIR)$Prsa_i15_modulus$O \
  $(OBJDIR)$Prsa_i15_oaep_decrypt$O \
  $(OBJDIR)$Prsa_i15_oaep_encrypt$O \
  $(OBJDIR)$Prsa_i15_pkcs1_sign$O \
  $(OBJDIR)$Prsa_i15_pkcs1_vrfy$O \
  $(OBJDIR)$Prsa_i15_priv$O \
+ $(OBJDIR)$Prsa_i15_privexp$O \
  $(OBJDIR)$Prsa_i15_pub$O \
+ $(OBJDIR)$Prsa_i15_pubexp$O \
  $(OBJDIR)$Prsa_i31_keygen$O \
  $(OBJDIR)$Prsa_i31_keygen_inner$O \
+ $(OBJDIR)$Prsa_i31_modulus$O \
  $(OBJDIR)$Prsa_i31_oaep_decrypt$O \
  $(OBJDIR)$Prsa_i31_oaep_encrypt$O \
  $(OBJDIR)$Prsa_i31_pkcs1_sign$O \
  $(OBJDIR)$Prsa_i31_pkcs1_vrfy$O \
  $(OBJDIR)$Prsa_i31_priv$O \
+ $(OBJDIR)$Prsa_i31_privexp$O \
  $(OBJDIR)$Prsa_i31_pub$O \
+ $(OBJDIR)$Prsa_i31_pubexp$O \
  $(OBJDIR)$Prsa_i32_oaep_decrypt$O \
  $(OBJDIR)$Prsa_i32_oaep_encrypt$O \
  $(OBJDIR)$Prsa_i32_pkcs1_sign$O \
@@ -254,6 +266,11 @@ OBJ = \
  $(OBJDIR)$Ppoly1305_ctmul32$O \
  $(OBJDIR)$Ppoly1305_ctmulq$O \
  $(OBJDIR)$Ppoly1305_i15$O \
+ $(OBJDIR)$Pasn1enc$O \
+ $(OBJDIR)$Pencode_ec_pk8der$O \
+ $(OBJDIR)$Pencode_ec_rawder$O \
+ $(OBJDIR)$Pencode_rsa_pk8der$O \
+ $(OBJDIR)$Pencode_rsa_rawder$O \
  $(OBJDIR)$Pskey_decoder$O \
  $(OBJDIR)$Px509_decoder$O \
  $(OBJDIR)$Px509_knownkey$O \
@@ -393,6 +410,9 @@ $(OBJDIR)$Penc64le$O: src$Pcodec$Penc64le.c $(HEADERSPRIV)
 $(OBJDIR)$Ppemdec$O: src$Pcodec$Ppemdec.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Ppemdec$O src$Pcodec$Ppemdec.c
 
+$(OBJDIR)$Ppemenc$O: src$Pcodec$Ppemenc.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Ppemenc$O src$Pcodec$Ppemenc.c
+
 $(OBJDIR)$Pec_all_m15$O: src$Pec$Pec_all_m15.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pec_all_m15$O src$Pec$Pec_all_m15.c
 
@@ -417,6 +437,9 @@ $(OBJDIR)$Pec_curve25519$O: src$Pec$Pec_curve25519.c $(HEADERSPRIV)
 $(OBJDIR)$Pec_default$O: src$Pec$Pec_default.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pec_default$O src$Pec$Pec_default.c
 
+$(OBJDIR)$Pec_keygen$O: src$Pec$Pec_keygen.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pec_keygen$O src$Pec$Pec_keygen.c
+
 $(OBJDIR)$Pec_p256_m15$O: src$Pec$Pec_p256_m15.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pec_p256_m15$O src$Pec$Pec_p256_m15.c
 
@@ -429,6 +452,9 @@ $(OBJDIR)$Pec_prime_i15$O: src$Pec$Pec_prime_i15.c $(HEADERSPRIV)
 $(OBJDIR)$Pec_prime_i31$O: src$Pec$Pec_prime_i31.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pec_prime_i31$O src$Pec$Pec_prime_i31.c
 
+$(OBJDIR)$Pec_pubkey$O: src$Pec$Pec_pubkey.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pec_pubkey$O src$Pec$Pec_pubkey.c
+
 $(OBJDIR)$Pec_secp256r1$O: src$Pec$Pec_secp256r1.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pec_secp256r1$O src$Pec$Pec_secp256r1.c
 
@@ -714,6 +740,9 @@ $(OBJDIR)$Psysrng$O: src$Prand$Psysrng.c $(HEADERSPRIV)
 $(OBJDIR)$Prsa_default_keygen$O: src$Prsa$Prsa_default_keygen.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_keygen$O src$Prsa$Prsa_default_keygen.c
 
+$(OBJDIR)$Prsa_default_modulus$O: src$Prsa$Prsa_default_modulus.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_modulus$O src$Prsa$Prsa_default_modulus.c
+
 $(OBJDIR)$Prsa_default_oaep_decrypt$O: src$Prsa$Prsa_default_oaep_decrypt.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_oaep_decrypt$O src$Prsa$Prsa_default_oaep_decrypt.c
 
@@ -729,12 +758,21 @@ $(OBJDIR)$Prsa_default_pkcs1_vrfy$O: src$Prsa$Prsa_default_pkcs1_vrfy.c $(HEADER
 $(OBJDIR)$Prsa_default_priv$O: src$Prsa$Prsa_default_priv.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_priv$O src$Prsa$Prsa_default_priv.c
 
+$(OBJDIR)$Prsa_default_privexp$O: src$Prsa$Prsa_default_privexp.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_privexp$O src$Prsa$Prsa_default_privexp.c
+
 $(OBJDIR)$Prsa_default_pub$O: src$Prsa$Prsa_default_pub.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_pub$O src$Prsa$Prsa_default_pub.c
 
+$(OBJDIR)$Prsa_default_pubexp$O: src$Prsa$Prsa_default_pubexp.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_pubexp$O src$Prsa$Prsa_default_pubexp.c
+
 $(OBJDIR)$Prsa_i15_keygen$O: src$Prsa$Prsa_i15_keygen.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_keygen$O src$Prsa$Prsa_i15_keygen.c
 
+$(OBJDIR)$Prsa_i15_modulus$O: src$Prsa$Prsa_i15_modulus.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_modulus$O src$Prsa$Prsa_i15_modulus.c
+
 $(OBJDIR)$Prsa_i15_oaep_decrypt$O: src$Prsa$Prsa_i15_oaep_decrypt.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_oaep_decrypt$O src$Prsa$Prsa_i15_oaep_decrypt.c
 
@@ -750,15 +788,24 @@ $(OBJDIR)$Prsa_i15_pkcs1_vrfy$O: src$Prsa$Prsa_i15_pkcs1_vrfy.c $(HEADERSPRIV)
 $(OBJDIR)$Prsa_i15_priv$O: src$Prsa$Prsa_i15_priv.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_priv$O src$Prsa$Prsa_i15_priv.c
 
+$(OBJDIR)$Prsa_i15_privexp$O: src$Prsa$Prsa_i15_privexp.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_privexp$O src$Prsa$Prsa_i15_privexp.c
+
 $(OBJDIR)$Prsa_i15_pub$O: src$Prsa$Prsa_i15_pub.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_pub$O src$Prsa$Prsa_i15_pub.c
 
+$(OBJDIR)$Prsa_i15_pubexp$O: src$Prsa$Prsa_i15_pubexp.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_pubexp$O src$Prsa$Prsa_i15_pubexp.c
+
 $(OBJDIR)$Prsa_i31_keygen$O: src$Prsa$Prsa_i31_keygen.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_keygen$O src$Prsa$Prsa_i31_keygen.c
 
 $(OBJDIR)$Prsa_i31_keygen_inner$O: src$Prsa$Prsa_i31_keygen_inner.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_keygen_inner$O src$Prsa$Prsa_i31_keygen_inner.c
 
+$(OBJDIR)$Prsa_i31_modulus$O: src$Prsa$Prsa_i31_modulus.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_modulus$O src$Prsa$Prsa_i31_modulus.c
+
 $(OBJDIR)$Prsa_i31_oaep_decrypt$O: src$Prsa$Prsa_i31_oaep_decrypt.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_oaep_decrypt$O src$Prsa$Prsa_i31_oaep_decrypt.c
 
@@ -774,9 +821,15 @@ $(OBJDIR)$Prsa_i31_pkcs1_vrfy$O: src$Prsa$Prsa_i31_pkcs1_vrfy.c $(HEADERSPRIV)
 $(OBJDIR)$Prsa_i31_priv$O: src$Prsa$Prsa_i31_priv.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_priv$O src$Prsa$Prsa_i31_priv.c
 
+$(OBJDIR)$Prsa_i31_privexp$O: src$Prsa$Prsa_i31_privexp.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_privexp$O src$Prsa$Prsa_i31_privexp.c
+
 $(OBJDIR)$Prsa_i31_pub$O: src$Prsa$Prsa_i31_pub.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_pub$O src$Prsa$Prsa_i31_pub.c
 
+$(OBJDIR)$Prsa_i31_pubexp$O: src$Prsa$Prsa_i31_pubexp.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_pubexp$O src$Prsa$Prsa_i31_pubexp.c
+
 $(OBJDIR)$Prsa_i32_oaep_decrypt$O: src$Prsa$Prsa_i32_oaep_decrypt.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i32_oaep_decrypt$O src$Prsa$Prsa_i32_oaep_decrypt.c
 
@@ -1098,6 +1151,21 @@ $(OBJDIR)$Ppoly1305_ctmulq$O: src$Psymcipher$Ppoly1305_ctmulq.c $(HEADERSPRIV)
 $(OBJDIR)$Ppoly1305_i15$O: src$Psymcipher$Ppoly1305_i15.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Ppoly1305_i15$O src$Psymcipher$Ppoly1305_i15.c
 
+$(OBJDIR)$Pasn1enc$O: src$Px509$Pasn1enc.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pasn1enc$O src$Px509$Pasn1enc.c
+
+$(OBJDIR)$Pencode_ec_pk8der$O: src$Px509$Pencode_ec_pk8der.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pencode_ec_pk8der$O src$Px509$Pencode_ec_pk8der.c
+
+$(OBJDIR)$Pencode_ec_rawder$O: src$Px509$Pencode_ec_rawder.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pencode_ec_rawder$O src$Px509$Pencode_ec_rawder.c
+
+$(OBJDIR)$Pencode_rsa_pk8der$O: src$Px509$Pencode_rsa_pk8der.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pencode_rsa_pk8der$O src$Px509$Pencode_rsa_pk8der.c
+
+$(OBJDIR)$Pencode_rsa_rawder$O: src$Px509$Pencode_rsa_rawder.c $(HEADERSPRIV)
+	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pencode_rsa_rawder$O src$Px509$Pencode_rsa_rawder.c
+
 $(OBJDIR)$Pskey_decoder$O: src$Px509$Pskey_decoder.c $(HEADERSPRIV)
 	$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pskey_decoder$O src$Px509$Pskey_decoder.c
 
diff --git a/mk/mkrules.sh b/mk/mkrules.sh
index 0e3895e..16f16ab 100755
--- a/mk/mkrules.sh
+++ b/mk/mkrules.sh
@@ -67,6 +67,7 @@ coresrc=" \
 	src/codec/enc64be.c \
 	src/codec/enc64le.c \
 	src/codec/pemdec.c \
+	src/codec/pemenc.c \
 	src/ec/ec_all_m15.c \
 	src/ec/ec_all_m31.c \
 	src/ec/ec_c25519_i15.c \
@@ -75,10 +76,12 @@ coresrc=" \
 	src/ec/ec_c25519_m31.c \
 	src/ec/ec_curve25519.c \
 	src/ec/ec_default.c \
+	src/ec/ec_keygen.c \
 	src/ec/ec_p256_m15.c \
 	src/ec/ec_p256_m31.c \
 	src/ec/ec_prime_i15.c \
 	src/ec/ec_prime_i31.c \
+	src/ec/ec_pubkey.c \
 	src/ec/ec_secp256r1.c \
 	src/ec/ec_secp384r1.c \
 	src/ec/ec_secp521r1.c \
@@ -174,27 +177,36 @@ coresrc=" \
 	src/rand/hmac_drbg.c \
 	src/rand/sysrng.c \
 	src/rsa/rsa_default_keygen.c \
+	src/rsa/rsa_default_modulus.c \
 	src/rsa/rsa_default_oaep_decrypt.c \
 	src/rsa/rsa_default_oaep_encrypt.c \
 	src/rsa/rsa_default_pkcs1_sign.c \
 	src/rsa/rsa_default_pkcs1_vrfy.c \
 	src/rsa/rsa_default_priv.c \
+	src/rsa/rsa_default_privexp.c \
 	src/rsa/rsa_default_pub.c \
+	src/rsa/rsa_default_pubexp.c \
 	src/rsa/rsa_i15_keygen.c \
+	src/rsa/rsa_i15_modulus.c \
 	src/rsa/rsa_i15_oaep_decrypt.c \
 	src/rsa/rsa_i15_oaep_encrypt.c \
 	src/rsa/rsa_i15_pkcs1_sign.c \
 	src/rsa/rsa_i15_pkcs1_vrfy.c \
 	src/rsa/rsa_i15_priv.c \
+	src/rsa/rsa_i15_privexp.c \
 	src/rsa/rsa_i15_pub.c \
+	src/rsa/rsa_i15_pubexp.c \
 	src/rsa/rsa_i31_keygen.c \
 	src/rsa/rsa_i31_keygen_inner.c \
+	src/rsa/rsa_i31_modulus.c \
 	src/rsa/rsa_i31_oaep_decrypt.c \
 	src/rsa/rsa_i31_oaep_encrypt.c \
 	src/rsa/rsa_i31_pkcs1_sign.c \
 	src/rsa/rsa_i31_pkcs1_vrfy.c \
 	src/rsa/rsa_i31_priv.c \
+	src/rsa/rsa_i31_privexp.c \
 	src/rsa/rsa_i31_pub.c \
+	src/rsa/rsa_i31_pubexp.c \
 	src/rsa/rsa_i32_oaep_decrypt.c \
 	src/rsa/rsa_i32_oaep_encrypt.c \
 	src/rsa/rsa_i32_pkcs1_sign.c \
@@ -302,6 +314,11 @@ coresrc=" \
 	src/symcipher/poly1305_ctmul32.c \
 	src/symcipher/poly1305_ctmulq.c \
 	src/symcipher/poly1305_i15.c \
+	src/x509/asn1enc.c \
+	src/x509/encode_ec_pk8der.c \
+	src/x509/encode_ec_rawder.c \
+	src/x509/encode_rsa_pk8der.c \
+	src/x509/encode_rsa_rawder.c \
 	src/x509/skey_decoder.c \
 	src/x509/x509_decoder.c \
 	src/x509/x509_knownkey.c \
diff --git a/src/codec/pemenc.c b/src/codec/pemenc.c
new file mode 100644
index 0000000..236601e
--- /dev/null
+++ b/src/codec/pemenc.c
@@ -0,0 +1,173 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/*
+ * Get the appropriate Base64 character for a numeric value in the
+ * 0..63 range. This is constant-time.
+ */
+static char
+b64char(uint32_t x)
+{
+	/*
+	 * Values 0 to 25 map to 0x41..0x5A ('A' to 'Z')
+	 * Values 26 to 51 map to 0x61..0x7A ('a' to 'z')
+	 * Values 52 to 61 map to 0x30..0x39 ('0' to '9')
+	 * Value 62 maps to 0x2B ('+')
+	 * Value 63 maps to 0x2F ('/')
+	 */
+	uint32_t a, b, c;
+
+	a = x - 26;
+	b = x - 52;
+	c = x - 62;
+
+	/*
+	 * Looking at bits 8..15 of values a, b and c:
+	 *
+	 *     x       a   b   c
+	 *  ---------------------
+	 *   0..25    FF  FF  FF
+	 *   26..51   00  FF  FF
+	 *   52..61   00  00  FF
+	 *   62..63   00  00  00
+	 */
+	return (char)(((x + 0x41) & ((a & b & c) >> 8))
+		| ((x + (0x61 - 26)) & ((~a & b & c) >> 8))
+		| ((x - (52 - 0x30)) & ((~a & ~b & c) >> 8))
+		| ((0x2B + ((x & 1) << 2)) & (~(a | b | c) >> 8)));
+}
+
+/* see bearssl_pem.h */
+size_t
+br_pem_encode(void *dest, const void *data, size_t len,
+	const char *banner, unsigned flags)
+{
+	size_t dlen, banner_len, lines;
+	char *d;
+	unsigned char *buf;
+	size_t u;
+	int off, lim;
+
+	banner_len = strlen(banner);
+	/* FIXME: try to avoid divisions here, as they may pull
+	   an extra libc function. */
+	if ((flags & BR_PEM_LINE64) != 0) {
+		lines = (len + 47) / 48;
+	} else {
+		lines = (len + 56) / 57;
+	}
+	dlen = (banner_len << 1) + 30 + (((len + 2) / 3) << 2)
+		+ lines + 2;
+	if ((flags & BR_PEM_CRLF) != 0) {
+		dlen += lines + 2;
+	}
+
+	if (dest == NULL) {
+		return dlen;
+	}
+
+	d = dest;
+
+	/*
+	 * We always move the source data to the end of output buffer;
+	 * the encoding process never "catches up" except at the very
+	 * end. This also handles all conditions of partial or total
+	 * overlap.
+	 */
+	buf = (unsigned char *)d + dlen - len;
+	memmove(buf, data, len);
+
+	memcpy(d, "-----BEGIN ", 11);
+	d += 11;
+	memcpy(d, banner, banner_len);
+	d += banner_len;
+	memcpy(d, "-----", 5);
+	d += 5;
+	if ((flags & BR_PEM_CRLF) != 0) {
+		*d ++ = 0x0D;
+	}
+	*d ++ = 0x0A;
+
+	off = 0;
+	lim = (flags & BR_PEM_LINE64) != 0 ? 16 : 19;
+	for (u = 0; (u + 2) < len; u += 3) {
+		uint32_t w;
+
+		w = ((uint32_t)buf[u] << 16)
+			| ((uint32_t)buf[u + 1] << 8)
+			| (uint32_t)buf[u + 2];
+		*d ++ = b64char(w >> 18);
+		*d ++ = b64char((w >> 12) & 0x3F);
+		*d ++ = b64char((w >> 6) & 0x3F);
+		*d ++ = b64char(w & 0x3F);
+		if (++ off == lim) {
+			off = 0;
+			if ((flags & BR_PEM_CRLF) != 0) {
+				*d ++ = 0x0D;
+			}
+			*d ++ = 0x0A;
+		}
+	}
+	if (u < len) {
+		uint32_t w;
+
+		w = (uint32_t)buf[u] << 16;
+		if (u + 1 < len) {
+			w |= (uint32_t)buf[u + 1] << 8;
+		}
+		*d ++ = b64char(w >> 18);
+		*d ++ = b64char((w >> 12) & 0x3F);
+		if (u + 1 < len) {
+			*d ++ = b64char((w >> 6) & 0x3F);
+		} else {
+			*d ++ = 0x3D;
+		}
+		*d ++ = 0x3D;
+		off ++;
+	}
+	if (off != 0) {
+		if ((flags & BR_PEM_CRLF) != 0) {
+			*d ++ = 0x0D;
+		}
+		*d ++ = 0x0A;
+	}
+
+	memcpy(d, "-----END ", 9);
+	d += 9;
+	memcpy(d, banner, banner_len);
+	d += banner_len;
+	memcpy(d, "-----", 5);
+	d += 5;
+	if ((flags & BR_PEM_CRLF) != 0) {
+		*d ++ = 0x0D;
+	}
+	*d ++ = 0x0A;
+
+	/* Final zero, not counted in returned length. */
+	*d ++ = 0x00;
+
+	return dlen;
+}
diff --git a/src/ec/ec_keygen.c b/src/ec/ec_keygen.c
new file mode 100644
index 0000000..02a3096
--- /dev/null
+++ b/src/ec/ec_keygen.c
@@ -0,0 +1,86 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_ec.h */
+size_t
+br_ec_keygen(const br_prng_class **rng_ctx,
+	const br_ec_impl *impl, br_ec_private_key *sk,
+	void *kbuf, int curve)
+{
+	const unsigned char *order;
+	unsigned char *buf;
+	size_t len;
+	unsigned mask;
+
+	if (curve < 0 || curve >= 32
+		|| ((impl->supported_curves >> curve) & 1) == 0)
+	{
+		return 0;
+	}
+	order = impl->order(curve, &len);
+	while (len > 0 && *order == 0) {
+		order ++;
+		len --;
+	}
+	if (kbuf == NULL || len == 0) {
+		return len;
+	}
+	mask = order[0];
+	mask |= (mask >> 1);
+	mask |= (mask >> 2);
+	mask |= (mask >> 4);
+
+	/*
+	 * We generate sequences of random bits of the right size, until
+	 * the value is strictly lower than the curve order (we also
+	 * check for all-zero values, which are invalid).
+	 */
+	buf = kbuf;
+	for (;;) {
+		size_t u;
+		unsigned cc, zz;
+
+		(*rng_ctx)->generate(rng_ctx, buf, len);
+		buf[0] &= mask;
+		cc = 0;
+		u = len;
+		zz = 0;
+		while (u -- > 0) {
+			cc = ((unsigned)(buf[u] - order[u] - cc) >> 8) & 1;
+			zz |= buf[u];
+		}
+		if (cc != 0 && zz != 0) {
+			break;
+		}
+	}
+
+	if (sk != NULL) {
+		sk->curve = curve;
+		sk->x = buf;
+		sk->xlen = len;
+	}
+	return len;
+}
diff --git a/src/ec/ec_pubkey.c b/src/ec/ec_pubkey.c
new file mode 100644
index 0000000..383ff28
--- /dev/null
+++ b/src/ec/ec_pubkey.c
@@ -0,0 +1,85 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+static const unsigned char POINT_LEN[] = {
+	  0,   /* 0: not a valid curve ID */
+	 43,   /* sect163k1 */
+	 43,   /* sect163r1 */
+	 43,   /* sect163r2 */
+	 51,   /* sect193r1 */
+	 51,   /* sect193r2 */
+	 61,   /* sect233k1 */
+	 61,   /* sect233r1 */
+	 61,   /* sect239k1 */
+	 73,   /* sect283k1 */
+	 73,   /* sect283r1 */
+	105,   /* sect409k1 */
+	105,   /* sect409r1 */
+	145,   /* sect571k1 */
+	145,   /* sect571r1 */
+	 41,   /* secp160k1 */
+	 41,   /* secp160r1 */
+	 41,   /* secp160r2 */
+	 49,   /* secp192k1 */
+	 49,   /* secp192r1 */
+	 57,   /* secp224k1 */
+	 57,   /* secp224r1 */
+	 65,   /* secp256k1 */
+	 65,   /* secp256r1 */
+	 97,   /* secp384r1 */
+	133,   /* secp521r1 */
+	 65,   /* brainpoolP256r1 */
+	 97,   /* brainpoolP384r1 */
+	129,   /* brainpoolP512r1 */
+	 32,   /* curve25519 */
+	 56,   /* curve448 */
+};
+
+/* see bearssl_ec.h */
+size_t
+br_ec_compute_pub(const br_ec_impl *impl, br_ec_public_key *pk,
+	void *kbuf, const br_ec_private_key *sk)
+{
+	int curve;
+	size_t len;
+
+	curve = sk->curve;
+	if (curve < 0 || curve >= 32 || curve >= (int)(sizeof POINT_LEN)
+		|| ((impl->supported_curves >> curve) & 1) == 0)
+	{
+		return 0;
+	}
+	if (kbuf == NULL) {
+		return POINT_LEN[curve];
+	}
+	len = impl->mulgen(kbuf, sk->x, sk->xlen, curve);
+	if (pk != NULL) {
+		pk->curve = curve;
+		pk->q = kbuf;
+		pk->qlen = len;
+	}
+	return len;
+}
diff --git a/src/inner.h b/src/inner.h
index c507102..d7e4091 100644
--- a/src/inner.h
+++ b/src/inner.h
@@ -1973,8 +1973,8 @@ void br_mgf1_xor(void *data, size_t len,
  * implementations.
  */
 uint32_t br_rsa_i31_keygen_inner(const br_prng_class **rng,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp, br_i31_modpow_opt_type mp31);
 
 /* ==================================================================== */
@@ -2027,6 +2027,72 @@ void br_ecdsa_i31_bits2int(uint32_t *x,
 void br_ecdsa_i15_bits2int(uint16_t *x,
 	const void *src, size_t len, uint32_t ebitlen);
 
+/* ==================================================================== */
+/*
+ * ASN.1 support functions.
+ */
+
+/*
+ * A br_asn1_uint structure contains encoding information about an
+ * INTEGER nonnegative value: pointer to the integer contents (unsigned
+ * big-endian representation), length of the integer contents,
+ * and length of the encoded value. The data shall have minimal length:
+ *  - If the integer value is zero, then 'len' must be zero.
+ *  - If the integer value is not zero, then data[0] must be non-zero.
+ *
+ * Under these conditions, 'asn1len' is necessarily equal to either len
+ * or len+1.
+ */
+typedef struct {
+	const unsigned char *data;
+	size_t len;
+	size_t asn1len;
+} br_asn1_uint;
+
+/*
+ * Given an encoded integer (unsigned big-endian, with possible leading
+ * bytes of value 0), returned the "prepared INTEGER" structure.
+ */
+br_asn1_uint br_asn1_uint_prepare(const void *xdata, size_t xlen);
+
+/*
+ * Encode an ASN.1 length. The length of the encoded length is returned.
+ * If 'dest' is NULL, then no encoding is performed, but the length of
+ * the encoded length is still computed and returned.
+ */
+size_t br_asn1_encode_length(void *dest, size_t len);
+
+/*
+ * Convenient macro for computing lengths of lengths.
+ */
+#define len_of_len(len)   br_asn1_encode_length(NULL, len)
+
+/*
+ * Encode a (prepared) ASN.1 INTEGER. The encoded length is returned.
+ * If 'dest' is NULL, then no encoding is performed, but the length of
+ * the encoded integer is still computed and returned.
+ */
+size_t br_asn1_encode_uint(void *dest, br_asn1_uint pp);
+
+/*
+ * Get the OID that identifies an elliptic curve. Returned value is
+ * the DER-encoded OID, with the length (always one byte) but without
+ * the tag. Thus, the first byte of the returned buffer contains the
+ * number of subsequent bytes in the value. If the curve is not
+ * recognised, NULL is returned.
+ */
+const unsigned char *br_get_curve_OID(int curve);
+
+/*
+ * Inner function for EC private key encoding. This is equivalent to
+ * the API function br_encode_ec_raw_der(), except for an extra
+ * parameter: if 'include_curve_oid' is zero, then the curve OID is
+ * _not_ included in the output blob (this is for PKCS#8 support).
+ */
+size_t br_encode_ec_raw_der_inner(void *dest,
+	const br_ec_private_key *sk, const br_ec_public_key *pk,
+	int include_curve_oid);
+
 /* ==================================================================== */
 /*
  * SSL/TLS support functions.
diff --git a/src/rsa/rsa_default_modulus.c b/src/rsa/rsa_default_modulus.c
new file mode 100644
index 0000000..57d4be5
--- /dev/null
+++ b/src/rsa/rsa_default_modulus.c
@@ -0,0 +1,36 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_rsa.h */
+br_rsa_compute_modulus
+br_rsa_compute_modulus_get_default(void)
+{
+#if BR_LOMUL
+	return &br_rsa_i15_compute_modulus;
+#else
+	return &br_rsa_i31_compute_modulus;
+#endif
+}
diff --git a/src/rsa/rsa_default_privexp.c b/src/rsa/rsa_default_privexp.c
new file mode 100644
index 0000000..cda4555
--- /dev/null
+++ b/src/rsa/rsa_default_privexp.c
@@ -0,0 +1,36 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_rsa.h */
+br_rsa_compute_privexp
+br_rsa_compute_privexp_get_default(void)
+{
+#if BR_LOMUL
+	return &br_rsa_i15_compute_privexp;
+#else
+	return &br_rsa_i31_compute_privexp;
+#endif
+}
diff --git a/src/rsa/rsa_default_pubexp.c b/src/rsa/rsa_default_pubexp.c
new file mode 100644
index 0000000..47bc000
--- /dev/null
+++ b/src/rsa/rsa_default_pubexp.c
@@ -0,0 +1,36 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_rsa.h */
+br_rsa_compute_pubexp
+br_rsa_compute_pubexp_get_default(void)
+{
+#if BR_LOMUL
+	return &br_rsa_i15_compute_pubexp;
+#else
+	return &br_rsa_i31_compute_pubexp;
+#endif
+}
diff --git a/src/rsa/rsa_i15_keygen.c b/src/rsa/rsa_i15_keygen.c
index 0f4435f..1c011fe 100644
--- a/src/rsa/rsa_i15_keygen.c
+++ b/src/rsa/rsa_i15_keygen.c
@@ -435,8 +435,8 @@ bufswap(void *b1, void *b2, size_t len)
 /* see bearssl_rsa.h */
 uint32_t
 br_rsa_i15_keygen(const br_prng_class **rng,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp)
 {
 	uint32_t esize_p, esize_q;
diff --git a/src/rsa/rsa_i15_modulus.c b/src/rsa/rsa_i15_modulus.c
new file mode 100644
index 0000000..d61c794
--- /dev/null
+++ b/src/rsa/rsa_i15_modulus.c
@@ -0,0 +1,99 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_rsa.h */
+size_t
+br_rsa_i15_compute_modulus(void *n, const br_rsa_private_key *sk)
+{
+	uint16_t tmp[2 * ((BR_MAX_RSA_SIZE + 14) / 15) + 5];
+	uint16_t *t, *p, *q;
+	const unsigned char *pbuf, *qbuf;
+	size_t nlen, plen, qlen, tlen;
+
+	/*
+	 * Compute actual byte and lengths for p and q.
+	 */
+	pbuf = sk->p;
+	plen = sk->plen;
+	while (plen > 0 && *pbuf == 0) {
+		pbuf ++;
+		plen --;
+	}
+	qbuf = sk->q;
+	qlen = sk->qlen;
+	while (qlen > 0 && *qbuf == 0) {
+		qbuf ++;
+		qlen --;
+	}
+
+	t = tmp;
+	tlen = (sizeof tmp) / (sizeof tmp[0]);
+
+	/*
+	 * Decode p.
+	 */
+	if ((15 * tlen) < (plen << 3) + 15) {
+		return 0;
+	}
+	br_i15_decode(t, pbuf, plen);
+	p = t;
+	plen = (p[0] + 31) >> 4;
+	t += plen;
+	tlen -= plen;
+
+	/*
+	 * Decode q.
+	 */
+	if ((15 * tlen) < (qlen << 3) + 15) {
+		return 0;
+	}
+	br_i15_decode(t, qbuf, qlen);
+	q = t;
+	qlen = (q[0] + 31) >> 4;
+	t += qlen;
+	tlen -= qlen;
+
+	/*
+	 * Computation can proceed only if we have enough room for the
+	 * modulus.
+	 */
+	if (tlen < (plen + qlen + 1)) {
+		return 0;
+	}
+
+	/*
+	 * Private key already contains the modulus bit length, from which
+	 * we can infer the output length. Even if n is NULL, we still had
+	 * to decode p and q to make sure that the product can be computed.
+	 */
+	nlen = (sk->n_bitlen + 7) >> 3;
+	if (n != NULL) {
+		br_i15_zero(t, p[0]);
+		br_i15_mulacc(t, p, q);
+		br_i15_encode(n, nlen, t);
+	}
+	return nlen;
+}
diff --git a/src/rsa/rsa_i15_privexp.c b/src/rsa/rsa_i15_privexp.c
new file mode 100644
index 0000000..57d6918
--- /dev/null
+++ b/src/rsa/rsa_i15_privexp.c
@@ -0,0 +1,320 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_rsa.h */
+size_t
+br_rsa_i15_compute_privexp(void *d,
+	const br_rsa_private_key *sk, uint32_t e)
+{
+	/*
+	 * We want to invert e modulo phi = (p-1)(q-1). This first
+	 * requires computing phi, which is easy since we have the factors
+	 * p and q in the private key structure.
+	 *
+	 * Since p = 3 mod 4 and q = 3 mod 4, phi/4 is an odd integer.
+	 * We could invert e modulo phi/4 then patch the result to
+	 * modulo phi, but this would involve assembling three modulus-wide
+	 * values (phi/4, 1 and e) and calling moddiv, that requires
+	 * three more temporaries, for a total of six big integers, or
+	 * slightly more than 3 kB of stack space for RSA-4096. This
+	 * exceeds our stack requirements.
+	 *
+	 * Instead, we first use one step of the extended GCD:
+	 *
+	 *   - We compute phi = k*e + r  (Euclidean division of phi by e).
+	 *     If public exponent e is correct, then r != 0 (e must be
+	 *     invertible modulo phi). We also have k != 0 since we
+	 *     enforce non-ridiculously-small factors.
+	 *
+	 *   - We find small u, v such that u*e - v*r = 1  (using a
+	 *     binary GCD; we can arrange for u < r and v < e, i.e. all
+	 *     values fit on 32 bits).
+	 *
+	 *   - Solution is: d = u + v*k
+	 *     This last computation is exact: since u < r and v < e,
+	 *     the above implies d < r + e*((phi-r)/e) = phi
+	 */
+
+	uint16_t tmp[4 * ((BR_MAX_RSA_FACTOR + 14) / 15) + 12];
+	uint16_t *p, *q, *k, *m, *z, *phi;
+	const unsigned char *pbuf, *qbuf;
+	size_t plen, qlen, u, len, dlen;
+	uint32_t r, a, b, u0, v0, u1, v1, he, hr;
+	int i;
+
+	/*
+	 * Check that e is correct.
+	 */
+	if (e < 3 || (e & 1) == 0) {
+		return 0;
+	}
+
+	/*
+	 * Check lengths of p and q, and that they are both odd.
+	 */
+	pbuf = sk->p;
+	plen = sk->plen;
+	while (plen > 0 && *pbuf == 0) {
+		pbuf ++;
+		plen --;
+	}
+	if (plen < 5 || plen > (BR_MAX_RSA_FACTOR / 8)
+		|| (pbuf[plen - 1] & 1) != 1)
+	{
+		return 0;
+	}
+	qbuf = sk->q;
+	qlen = sk->qlen;
+	while (qlen > 0 && *qbuf == 0) {
+		qbuf ++;
+		qlen --;
+	}
+	if (qlen < 5 || qlen > (BR_MAX_RSA_FACTOR / 8)
+		|| (qbuf[qlen - 1] & 1) != 1)
+	{
+		return 0;
+	}
+
+	/*
+	 * Output length is that of the modulus.
+	 */
+	dlen = (sk->n_bitlen + 7) >> 3;
+	if (d == NULL) {
+		return dlen;
+	}
+
+	p = tmp;
+	br_i15_decode(p, pbuf, plen);
+	plen = (p[0] + 15) >> 4;
+	q = p + 1 + plen;
+	br_i15_decode(q, qbuf, qlen);
+	qlen = (q[0] + 15) >> 4;
+
+	/*
+	 * Compute phi = (p-1)*(q-1), then move it over p-1 and q-1 (that
+	 * we do not need anymore). The mulacc function sets the announced
+	 * bit length of t to be the sum of the announced bit lengths of
+	 * p-1 and q-1, which is usually exact but may overshoot by one 1
+	 * bit in some cases; we readjust it to its true length.
+	 */
+	p[1] --;
+	q[1] --;
+	phi = q + 1 + qlen;
+	br_i15_zero(phi, p[0]);
+	br_i15_mulacc(phi, p, q);
+	len = (phi[0] + 15) >> 4;
+	memmove(tmp, phi, (1 + len) * sizeof *phi);
+	phi = tmp;
+	phi[0] = br_i15_bit_length(phi + 1, len);
+	len = (phi[0] + 15) >> 4;
+
+	/*
+	 * Divide phi by public exponent e. The final remainder r must be
+	 * non-zero (otherwise, the key is invalid). The quotient is k,
+	 * which we write over phi, since we don't need phi after that.
+	 */
+	r = 0;
+	for (u = len; u >= 1; u --) {
+		/*
+		 * Upon entry, r < e, and phi[u] < 2^15; hence,
+		 * hi:lo < e*2^15. Thus, the produced word k[u]
+		 * must be lower than 2^15, and the new remainder r
+		 * is lower than e.
+		 */
+		uint32_t hi, lo;
+
+		hi = r >> 17;
+		lo = (r << 15) + phi[u];
+		phi[u] = br_divrem(hi, lo, e, &r);
+	}
+	if (r == 0) {
+		return 0;
+	}
+	k = phi;
+
+	/*
+	 * Compute u and v such that u*e - v*r = GCD(e,r). We use
+	 * a binary GCD algorithm, with 6 extra integers a, b,
+	 * u0, u1, v0 and v1. Initial values are:
+	 *   a = e    u0 = 1   v0 = 0
+	 *   b = r    u1 = r   v1 = e-1
+	 * The following invariants are maintained:
+	 *   a = u0*e - v0*r
+	 *   b = u1*e - v1*r
+	 *   0 < a <= e
+	 *   0 < b <= r
+	 *   0 <= u0 <= r
+	 *   0 <= v0 <= e
+	 *   0 <= u1 <= r
+	 *   0 <= v1 <= e
+	 *
+	 * At each iteration, we reduce either a or b by one bit, and
+	 * adjust u0, u1, v0 and v1 to maintain the invariants:
+	 *  - if a is even, then a <- a/2
+	 *  - otherwise, if b is even, then b <- b/2
+	 *  - otherwise, if a > b, then a <- (a-b)/2
+	 *  - otherwise, if b > a, then b <- (b-a)/2
+	 * Algorithm stops when a = b. At that point, the common value
+	 * is the GCD of e and r; it must be 1 (otherwise, the private
+	 * key or public exponent is not valid). The (u0,v0) or (u1,v1)
+	 * pairs are the solution we are looking for.
+	 *
+	 * Since either a or b is reduced by at least 1 bit at each
+	 * iteration, 62 iterations are enough to reach the end
+	 * condition.
+	 *
+	 * To maintain the invariants, we must compute the same operations
+	 * on the u* and v* values that we do on a and b:
+	 *  - When a is divided by 2, u0 and v0 must be divided by 2.
+	 *  - When b is divided by 2, u1 and v1 must be divided by 2.
+	 *  - When b is subtracted from a, u1 and v1 are subtracted from
+	 *    u0 and v0, respectively.
+	 *  - When a is subtracted from b, u0 and v0 are subtracted from
+	 *    u1 and v1, respectively.
+	 *
+	 * However, we want to keep the u* and v* values in their proper
+	 * ranges. The following remarks apply:
+	 *
+	 *  - When a is divided by 2, then a is even. Therefore:
+	 *
+	 *     * If r is odd, then u0 and v0 must have the same parity;
+	 *       if they are both odd, then adding r to u0 and e to v0
+	 *       makes them both even, and the division by 2 brings them
+	 *       back to the proper range.
+	 *
+	 *     * If r is even, then u0 must be even; if v0 is odd, then
+	 *       adding r to u0 and e to v0 makes them both even, and the
+	 *       division by 2 brings them back to the proper range.
+	 *
+	 *    Thus, all we need to do is to look at the parity of v0,
+	 *    and add (r,e) to (u0,v0) when v0 is odd. In order to avoid
+	 *    a 32-bit overflow, we can add ((r+1)/2,(e/2)+1) after the
+	 *    division (r+1 does not overflow since r < e; and (e/2)+1
+	 *    is equal to (e+1)/2 since e is odd).
+	 *
+	 *  - When we subtract b from a, three cases may occur:
+	 *
+	 *     * u1 <= u0 and v1 <= v0: just do the subtractions
+	 *
+	 *     * u1 > u0 and v1 > v0: compute:
+	 *         (u0, v0) <- (u0 + r - u1, v0 + e - v1)
+	 *
+	 *     * u1 <= u0 and v1 > v0: compute:
+	 *         (u0, v0) <- (u0 + r - u1, v0 + e - v1)
+	 *
+	 *    The fourth case (u1 > u0 and v1 <= v0) is not possible
+	 *    because it would contradict "b < a" (which is the reason
+	 *    why we subtract b from a).
+	 *
+	 *    The tricky case is the third one: from the equations, it
+	 *    seems that u0 may go out of range. However, the invariants
+	 *    and ranges of other values imply that, in that case, the
+	 *    new u0 does not actually exceed the range.
+	 *
+	 *    We can thus handle the subtraction by adding (r,e) based
+	 *    solely on the comparison between v0 and v1.
+	 */
+	a = e;
+	b = r;
+	u0 = 1;
+	v0 = 0;
+	u1 = r;
+	v1 = e - 1;
+	hr = (r + 1) >> 1;
+	he = (e >> 1) + 1;
+	for (i = 0; i < 62; i ++) {
+		uint32_t oa, ob, agtb, bgta;
+		uint32_t sab, sba, da, db;
+		uint32_t ctl;
+
+		oa = a & 1;                  /* 1 if a is odd */
+		ob = b & 1;                  /* 1 if b is odd */
+		agtb = GT(a, b);             /* 1 if a > b */
+		bgta = GT(b, a);             /* 1 if b > a */
+
+		sab = oa & ob & agtb;        /* 1 if a <- a-b */
+		sba = oa & ob & bgta;        /* 1 if b <- b-a */
+
+		/* a <- a-b, u0 <- u0-u1, v0 <- v0-v1 */
+		ctl = GT(v1, v0);
+		a -= b & -sab;
+		u0 -= (u1 - (r & -ctl)) & -sab;
+		v0 -= (v1 - (e & -ctl)) & -sab;
+
+		/* b <- b-a, u1 <- u1-u0 mod r, v1 <- v1-v0 mod e */
+		ctl = GT(v0, v1);
+		b -= a & -sba;
+		u1 -= (u0 - (r & -ctl)) & -sba;
+		v1 -= (v0 - (e & -ctl)) & -sba;
+
+		da = NOT(oa) | sab;          /* 1 if a <- a/2 */
+		db = (oa & NOT(ob)) | sba;   /* 1 if b <- b/2 */
+
+		/* a <- a/2, u0 <- u0/2, v0 <- v0/2 */
+		ctl = v0 & 1;
+		a ^= (a ^ (a >> 1)) & -da;
+		u0 ^= (u0 ^ ((u0 >> 1) + (hr & -ctl))) & -da;
+		v0 ^= (v0 ^ ((v0 >> 1) + (he & -ctl))) & -da;
+
+		/* b <- b/2, u1 <- u1/2 mod r, v1 <- v1/2 mod e */
+		ctl = v1 & 1;
+		b ^= (b ^ (b >> 1)) & -db;
+		u1 ^= (u1 ^ ((u1 >> 1) + (hr & -ctl))) & -db;
+		v1 ^= (v1 ^ ((v1 >> 1) + (he & -ctl))) & -db;
+	}
+
+	/*
+	 * Check that the GCD is indeed 1. If not, then the key is invalid
+	 * (and there's no harm in leaking that piece of information).
+	 */
+	if (a != 1) {
+		return 0;
+	}
+
+	/*
+	 * Now we have u0*e - v0*r = 1. Let's compute the result as:
+	 *   d = u0 + v0*k
+	 * We still have k in the tmp[] array, and its announced bit
+	 * length is that of phi.
+	 */
+	m = k + 1 + len;
+	m[0] = (2 << 4) + 2;  /* bit length is 32 bits, encoded */
+	m[1] = v0 & 0x7FFF;
+	m[2] = (v0 >> 15) & 0x7FFF;
+	m[3] = v0 >> 30;
+	z = m + 4;
+	br_i15_zero(z, k[0]);
+	z[1] = u0 & 0x7FFF;
+	z[2] = (u0 >> 15) & 0x7FFF;
+	z[3] = u0 >> 30;
+	br_i15_mulacc(z, k, m);
+
+	/*
+	 * Encode the result.
+	 */
+	br_i15_encode(d, dlen, z);
+	return dlen;
+}
diff --git a/src/rsa/rsa_i15_pubexp.c b/src/rsa/rsa_i15_pubexp.c
new file mode 100644
index 0000000..803bff7
--- /dev/null
+++ b/src/rsa/rsa_i15_pubexp.c
@@ -0,0 +1,152 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/*
+ * Recompute public exponent, based on factor p and reduced private
+ * exponent dp.
+ */
+static uint32_t
+get_pubexp(const unsigned char *pbuf, size_t plen,
+	const unsigned char *dpbuf, size_t dplen)
+{
+	/*
+	 * dp is the inverse of e modulo p-1. If p = 3 mod 4, then
+	 * p-1 = 2*((p-1)/2). Taken modulo 2, e is odd and has inverse 1;
+	 * thus, dp must be odd.
+	 *
+	 * We compute the inverse of dp modulo (p-1)/2. This requires
+	 * first reducing dp modulo (p-1)/2 (this can be done with a
+	 * conditional subtract, no need to use the generic modular
+	 * reduction function); then, we use moddiv.
+	 */
+
+	uint16_t tmp[6 * ((BR_MAX_RSA_FACTOR + 29) / 15)];
+	uint16_t *p, *dp, *x;
+	size_t len;
+	uint32_t e;
+
+	/*
+	 * Compute actual factor length (in bytes) and check that it fits
+	 * under our size constraints.
+	 */
+	while (plen > 0 && *pbuf == 0) {
+		pbuf ++;
+		plen --;
+	}
+	if (plen == 0 || plen < 5 || plen > (BR_MAX_RSA_FACTOR / 8)) {
+		return 0;
+	}
+
+	/*
+	 * Compute actual reduced exponent length (in bytes) and check that
+	 * it is not longer than p.
+	 */
+	while (dplen > 0 && *dpbuf == 0) {
+		dpbuf ++;
+		dplen --;
+	}
+	if (dplen > plen || dplen == 0
+		|| (dplen == plen && dpbuf[0] > pbuf[0]))
+	{
+		return 0;
+	}
+
+	/*
+	 * Verify that p = 3 mod 4 and that dp is odd.
+	 */
+	if ((pbuf[plen - 1] & 3) != 3 || (dpbuf[dplen - 1] & 1) != 1) {
+		return 0;
+	}
+
+	/*
+	 * Decode p and compute (p-1)/2.
+	 */
+	p = tmp;
+	br_i15_decode(p, pbuf, plen);
+	len = (p[0] + 31) >> 4;
+	br_i15_rshift(p, 1);
+
+	/*
+	 * Decode dp and make sure its announced bit length matches that of
+	 * p (we already know that the size of dp, in bits, does not exceed
+	 * the size of p, so we just have to copy the header word).
+	 */
+	dp = p + len;
+	memset(dp, 0, len * sizeof *dp);
+	br_i15_decode(dp, dpbuf, dplen);
+	dp[0] = p[0];
+
+	/*
+	 * Subtract (p-1)/2 from dp if necessary.
+	 */
+	br_i15_sub(dp, p, NOT(br_i15_sub(dp, p, 0)));
+
+	/*
+	 * If another subtraction is needed, then this means that the
+	 * value was invalid. We don't care to leak information about
+	 * invalid keys.
+	 */
+	if (br_i15_sub(dp, p, 0) == 0) {
+		return 0;
+	}
+
+	/*
+	 * Invert dp modulo (p-1)/2. If the inversion fails, then the
+	 * key value was invalid.
+	 */
+	x = dp + len;
+	br_i15_zero(x, p[0]);
+	x[1] = 1;
+	if (br_i15_moddiv(x, dp, p, br_i15_ninv15(p[1]), x + len) == 0) {
+		return 0;
+	}
+
+	/*
+	 * We now have an inverse. We must set it to zero (error) if its
+	 * length is greater than 32 bits and/or if it is an even integer.
+	 * Take care that the bit_length function returns an encoded
+	 * bit length.
+	 */
+	e = (uint32_t)x[1] | ((uint32_t)x[2] << 15) | ((uint32_t)x[3] << 30);
+	e &= -LT(br_i15_bit_length(x + 1, len - 1), 35);
+	e &= -(e & 1);
+	return e;
+}
+
+/* see bearssl_rsa.h */
+uint32_t
+br_rsa_i15_compute_pubexp(const br_rsa_private_key *sk)
+{
+	/*
+	 * Get the public exponent from both p and q. This is the right
+	 * exponent if we get twice the same value.
+	 */
+	uint32_t ep, eq;
+
+	ep = get_pubexp(sk->p, sk->plen, sk->dp, sk->dplen);
+	eq = get_pubexp(sk->q, sk->qlen, sk->dq, sk->dqlen);
+	return ep & -EQ(ep, eq);
+}
diff --git a/src/rsa/rsa_i31_keygen.c b/src/rsa/rsa_i31_keygen.c
index 0e26246..77708f8 100644
--- a/src/rsa/rsa_i31_keygen.c
+++ b/src/rsa/rsa_i31_keygen.c
@@ -27,8 +27,8 @@
 /* see bearssl_rsa.h */
 uint32_t
 br_rsa_i31_keygen(const br_prng_class **rng,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp)
 {
 	return br_rsa_i31_keygen_inner(rng,
diff --git a/src/rsa/rsa_i31_keygen_inner.c b/src/rsa/rsa_i31_keygen_inner.c
index 69120e7..9ec881b 100644
--- a/src/rsa/rsa_i31_keygen_inner.c
+++ b/src/rsa/rsa_i31_keygen_inner.c
@@ -456,8 +456,8 @@ bufswap(void *b1, void *b2, size_t len)
 /* see inner.h */
 uint32_t
 br_rsa_i31_keygen_inner(const br_prng_class **rng,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp, br_i31_modpow_opt_type mp31)
 {
 	uint32_t esize_p, esize_q;
diff --git a/src/rsa/rsa_i31_modulus.c b/src/rsa/rsa_i31_modulus.c
new file mode 100644
index 0000000..c469cf3
--- /dev/null
+++ b/src/rsa/rsa_i31_modulus.c
@@ -0,0 +1,99 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_rsa.h */
+size_t
+br_rsa_i31_compute_modulus(void *n, const br_rsa_private_key *sk)
+{
+	uint32_t tmp[2 * ((BR_MAX_RSA_SIZE + 30) / 31) + 5];
+	uint32_t *t, *p, *q;
+	const unsigned char *pbuf, *qbuf;
+	size_t nlen, plen, qlen, tlen;
+
+	/*
+	 * Compute actual byte and lengths for p and q.
+	 */
+	pbuf = sk->p;
+	plen = sk->plen;
+	while (plen > 0 && *pbuf == 0) {
+		pbuf ++;
+		plen --;
+	}
+	qbuf = sk->q;
+	qlen = sk->qlen;
+	while (qlen > 0 && *qbuf == 0) {
+		qbuf ++;
+		qlen --;
+	}
+
+	t = tmp;
+	tlen = (sizeof tmp) / (sizeof tmp[0]);
+
+	/*
+	 * Decode p.
+	 */
+	if ((31 * tlen) < (plen << 3) + 31) {
+		return 0;
+	}
+	br_i31_decode(t, pbuf, plen);
+	p = t;
+	plen = (p[0] + 63) >> 5;
+	t += plen;
+	tlen -= plen;
+
+	/*
+	 * Decode q.
+	 */
+	if ((31 * tlen) < (qlen << 3) + 31) {
+		return 0;
+	}
+	br_i31_decode(t, qbuf, qlen);
+	q = t;
+	qlen = (q[0] + 63) >> 5;
+	t += qlen;
+	tlen -= qlen;
+
+	/*
+	 * Computation can proceed only if we have enough room for the
+	 * modulus.
+	 */
+	if (tlen < (plen + qlen + 1)) {
+		return 0;
+	}
+
+	/*
+	 * Private key already contains the modulus bit length, from which
+	 * we can infer the output length. Even if n is NULL, we still had
+	 * to decode p and q to make sure that the product can be computed.
+	 */
+	nlen = (sk->n_bitlen + 7) >> 3;
+	if (n != NULL) {
+		br_i31_zero(t, p[0]);
+		br_i31_mulacc(t, p, q);
+		br_i31_encode(n, nlen, t);
+	}
+	return nlen;
+}
diff --git a/src/rsa/rsa_i31_privexp.c b/src/rsa/rsa_i31_privexp.c
new file mode 100644
index 0000000..eee62a0
--- /dev/null
+++ b/src/rsa/rsa_i31_privexp.c
@@ -0,0 +1,318 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_rsa.h */
+size_t
+br_rsa_i31_compute_privexp(void *d,
+	const br_rsa_private_key *sk, uint32_t e)
+{
+	/*
+	 * We want to invert e modulo phi = (p-1)(q-1). This first
+	 * requires computing phi, which is easy since we have the factors
+	 * p and q in the private key structure.
+	 *
+	 * Since p = 3 mod 4 and q = 3 mod 4, phi/4 is an odd integer.
+	 * We could invert e modulo phi/4 then patch the result to
+	 * modulo phi, but this would involve assembling three modulus-wide
+	 * values (phi/4, 1 and e) and calling moddiv, that requires
+	 * three more temporaries, for a total of six big integers, or
+	 * slightly more than 3 kB of stack space for RSA-4096. This
+	 * exceeds our stack requirements.
+	 *
+	 * Instead, we first use one step of the extended GCD:
+	 *
+	 *   - We compute phi = k*e + r  (Euclidean division of phi by e).
+	 *     If public exponent e is correct, then r != 0 (e must be
+	 *     invertible modulo phi). We also have k != 0 since we
+	 *     enforce non-ridiculously-small factors.
+	 *
+	 *   - We find small u, v such that u*e - v*r = 1  (using a
+	 *     binary GCD; we can arrange for u < r and v < e, i.e. all
+	 *     values fit on 32 bits).
+	 *
+	 *   - Solution is: d = u + v*k
+	 *     This last computation is exact: since u < r and v < e,
+	 *     the above implies d < r + e*((phi-r)/e) = phi
+	 */
+
+	uint32_t tmp[4 * ((BR_MAX_RSA_FACTOR + 30) / 31) + 12];
+	uint32_t *p, *q, *k, *m, *z, *phi;
+	const unsigned char *pbuf, *qbuf;
+	size_t plen, qlen, u, len, dlen;
+	uint32_t r, a, b, u0, v0, u1, v1, he, hr;
+	int i;
+
+	/*
+	 * Check that e is correct.
+	 */
+	if (e < 3 || (e & 1) == 0) {
+		return 0;
+	}
+
+	/*
+	 * Check lengths of p and q, and that they are both odd.
+	 */
+	pbuf = sk->p;
+	plen = sk->plen;
+	while (plen > 0 && *pbuf == 0) {
+		pbuf ++;
+		plen --;
+	}
+	if (plen < 5 || plen > (BR_MAX_RSA_FACTOR / 8)
+		|| (pbuf[plen - 1] & 1) != 1)
+	{
+		return 0;
+	}
+	qbuf = sk->q;
+	qlen = sk->qlen;
+	while (qlen > 0 && *qbuf == 0) {
+		qbuf ++;
+		qlen --;
+	}
+	if (qlen < 5 || qlen > (BR_MAX_RSA_FACTOR / 8)
+		|| (qbuf[qlen - 1] & 1) != 1)
+	{
+		return 0;
+	}
+
+	/*
+	 * Output length is that of the modulus.
+	 */
+	dlen = (sk->n_bitlen + 7) >> 3;
+	if (d == NULL) {
+		return dlen;
+	}
+
+	p = tmp;
+	br_i31_decode(p, pbuf, plen);
+	plen = (p[0] + 31) >> 5;
+	q = p + 1 + plen;
+	br_i31_decode(q, qbuf, qlen);
+	qlen = (q[0] + 31) >> 5;
+
+	/*
+	 * Compute phi = (p-1)*(q-1), then move it over p-1 and q-1 (that
+	 * we do not need anymore). The mulacc function sets the announced
+	 * bit length of t to be the sum of the announced bit lengths of
+	 * p-1 and q-1, which is usually exact but may overshoot by one 1
+	 * bit in some cases; we readjust it to its true length.
+	 */
+	p[1] --;
+	q[1] --;
+	phi = q + 1 + qlen;
+	br_i31_zero(phi, p[0]);
+	br_i31_mulacc(phi, p, q);
+	len = (phi[0] + 31) >> 5;
+	memmove(tmp, phi, (1 + len) * sizeof *phi);
+	phi = tmp;
+	phi[0] = br_i31_bit_length(phi + 1, len);
+	len = (phi[0] + 31) >> 5;
+
+	/*
+	 * Divide phi by public exponent e. The final remainder r must be
+	 * non-zero (otherwise, the key is invalid). The quotient is k,
+	 * which we write over phi, since we don't need phi after that.
+	 */
+	r = 0;
+	for (u = len; u >= 1; u --) {
+		/*
+		 * Upon entry, r < e, and phi[u] < 2^31; hence,
+		 * hi:lo < e*2^31. Thus, the produced word k[u]
+		 * must be lower than 2^31, and the new remainder r
+		 * is lower than e.
+		 */
+		uint32_t hi, lo;
+
+		hi = r >> 1;
+		lo = (r << 31) + phi[u];
+		phi[u] = br_divrem(hi, lo, e, &r);
+	}
+	if (r == 0) {
+		return 0;
+	}
+	k = phi;
+
+	/*
+	 * Compute u and v such that u*e - v*r = GCD(e,r). We use
+	 * a binary GCD algorithm, with 6 extra integers a, b,
+	 * u0, u1, v0 and v1. Initial values are:
+	 *   a = e    u0 = 1   v0 = 0
+	 *   b = r    u1 = r   v1 = e-1
+	 * The following invariants are maintained:
+	 *   a = u0*e - v0*r
+	 *   b = u1*e - v1*r
+	 *   0 < a <= e
+	 *   0 < b <= r
+	 *   0 <= u0 <= r
+	 *   0 <= v0 <= e
+	 *   0 <= u1 <= r
+	 *   0 <= v1 <= e
+	 *
+	 * At each iteration, we reduce either a or b by one bit, and
+	 * adjust u0, u1, v0 and v1 to maintain the invariants:
+	 *  - if a is even, then a <- a/2
+	 *  - otherwise, if b is even, then b <- b/2
+	 *  - otherwise, if a > b, then a <- (a-b)/2
+	 *  - otherwise, if b > a, then b <- (b-a)/2
+	 * Algorithm stops when a = b. At that point, the common value
+	 * is the GCD of e and r; it must be 1 (otherwise, the private
+	 * key or public exponent is not valid). The (u0,v0) or (u1,v1)
+	 * pairs are the solution we are looking for.
+	 *
+	 * Since either a or b is reduced by at least 1 bit at each
+	 * iteration, 62 iterations are enough to reach the end
+	 * condition.
+	 *
+	 * To maintain the invariants, we must compute the same operations
+	 * on the u* and v* values that we do on a and b:
+	 *  - When a is divided by 2, u0 and v0 must be divided by 2.
+	 *  - When b is divided by 2, u1 and v1 must be divided by 2.
+	 *  - When b is subtracted from a, u1 and v1 are subtracted from
+	 *    u0 and v0, respectively.
+	 *  - When a is subtracted from b, u0 and v0 are subtracted from
+	 *    u1 and v1, respectively.
+	 *
+	 * However, we want to keep the u* and v* values in their proper
+	 * ranges. The following remarks apply:
+	 *
+	 *  - When a is divided by 2, then a is even. Therefore:
+	 *
+	 *     * If r is odd, then u0 and v0 must have the same parity;
+	 *       if they are both odd, then adding r to u0 and e to v0
+	 *       makes them both even, and the division by 2 brings them
+	 *       back to the proper range.
+	 *
+	 *     * If r is even, then u0 must be even; if v0 is odd, then
+	 *       adding r to u0 and e to v0 makes them both even, and the
+	 *       division by 2 brings them back to the proper range.
+	 *
+	 *    Thus, all we need to do is to look at the parity of v0,
+	 *    and add (r,e) to (u0,v0) when v0 is odd. In order to avoid
+	 *    a 32-bit overflow, we can add ((r+1)/2,(e/2)+1) after the
+	 *    division (r+1 does not overflow since r < e; and (e/2)+1
+	 *    is equal to (e+1)/2 since e is odd).
+	 *
+	 *  - When we subtract b from a, three cases may occur:
+	 *
+	 *     * u1 <= u0 and v1 <= v0: just do the subtractions
+	 *
+	 *     * u1 > u0 and v1 > v0: compute:
+	 *         (u0, v0) <- (u0 + r - u1, v0 + e - v1)
+	 *
+	 *     * u1 <= u0 and v1 > v0: compute:
+	 *         (u0, v0) <- (u0 + r - u1, v0 + e - v1)
+	 *
+	 *    The fourth case (u1 > u0 and v1 <= v0) is not possible
+	 *    because it would contradict "b < a" (which is the reason
+	 *    why we subtract b from a).
+	 *
+	 *    The tricky case is the third one: from the equations, it
+	 *    seems that u0 may go out of range. However, the invariants
+	 *    and ranges of other values imply that, in that case, the
+	 *    new u0 does not actually exceed the range.
+	 *
+	 *    We can thus handle the subtraction by adding (r,e) based
+	 *    solely on the comparison between v0 and v1.
+	 */
+	a = e;
+	b = r;
+	u0 = 1;
+	v0 = 0;
+	u1 = r;
+	v1 = e - 1;
+	hr = (r + 1) >> 1;
+	he = (e >> 1) + 1;
+	for (i = 0; i < 62; i ++) {
+		uint32_t oa, ob, agtb, bgta;
+		uint32_t sab, sba, da, db;
+		uint32_t ctl;
+
+		oa = a & 1;                  /* 1 if a is odd */
+		ob = b & 1;                  /* 1 if b is odd */
+		agtb = GT(a, b);             /* 1 if a > b */
+		bgta = GT(b, a);             /* 1 if b > a */
+
+		sab = oa & ob & agtb;        /* 1 if a <- a-b */
+		sba = oa & ob & bgta;        /* 1 if b <- b-a */
+
+		/* a <- a-b, u0 <- u0-u1, v0 <- v0-v1 */
+		ctl = GT(v1, v0);
+		a -= b & -sab;
+		u0 -= (u1 - (r & -ctl)) & -sab;
+		v0 -= (v1 - (e & -ctl)) & -sab;
+
+		/* b <- b-a, u1 <- u1-u0 mod r, v1 <- v1-v0 mod e */
+		ctl = GT(v0, v1);
+		b -= a & -sba;
+		u1 -= (u0 - (r & -ctl)) & -sba;
+		v1 -= (v0 - (e & -ctl)) & -sba;
+
+		da = NOT(oa) | sab;          /* 1 if a <- a/2 */
+		db = (oa & NOT(ob)) | sba;   /* 1 if b <- b/2 */
+
+		/* a <- a/2, u0 <- u0/2, v0 <- v0/2 */
+		ctl = v0 & 1;
+		a ^= (a ^ (a >> 1)) & -da;
+		u0 ^= (u0 ^ ((u0 >> 1) + (hr & -ctl))) & -da;
+		v0 ^= (v0 ^ ((v0 >> 1) + (he & -ctl))) & -da;
+
+		/* b <- b/2, u1 <- u1/2 mod r, v1 <- v1/2 mod e */
+		ctl = v1 & 1;
+		b ^= (b ^ (b >> 1)) & -db;
+		u1 ^= (u1 ^ ((u1 >> 1) + (hr & -ctl))) & -db;
+		v1 ^= (v1 ^ ((v1 >> 1) + (he & -ctl))) & -db;
+	}
+
+	/*
+	 * Check that the GCD is indeed 1. If not, then the key is invalid
+	 * (and there's no harm in leaking that piece of information).
+	 */
+	if (a != 1) {
+		return 0;
+	}
+
+	/*
+	 * Now we have u0*e - v0*r = 1. Let's compute the result as:
+	 *   d = u0 + v0*k
+	 * We still have k in the tmp[] array, and its announced bit
+	 * length is that of phi.
+	 */
+	m = k + 1 + len;
+	m[0] = (1 << 5) + 1;  /* bit length is 32 bits, encoded */
+	m[1] = v0 & 0x7FFFFFFF;
+	m[2] = v0 >> 31;
+	z = m + 3;
+	br_i31_zero(z, k[0]);
+	z[1] = u0 & 0x7FFFFFFF;
+	z[2] = u0 >> 31;
+	br_i31_mulacc(z, k, m);
+
+	/*
+	 * Encode the result.
+	 */
+	br_i31_encode(d, dlen, z);
+	return dlen;
+}
diff --git a/src/rsa/rsa_i31_pubexp.c b/src/rsa/rsa_i31_pubexp.c
new file mode 100644
index 0000000..f26537d
--- /dev/null
+++ b/src/rsa/rsa_i31_pubexp.c
@@ -0,0 +1,152 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/*
+ * Recompute public exponent, based on factor p and reduced private
+ * exponent dp.
+ */
+static uint32_t
+get_pubexp(const unsigned char *pbuf, size_t plen,
+	const unsigned char *dpbuf, size_t dplen)
+{
+	/*
+	 * dp is the inverse of e modulo p-1. If p = 3 mod 4, then
+	 * p-1 = 2*((p-1)/2). Taken modulo 2, e is odd and has inverse 1;
+	 * thus, dp must be odd.
+	 *
+	 * We compute the inverse of dp modulo (p-1)/2. This requires
+	 * first reducing dp modulo (p-1)/2 (this can be done with a
+	 * conditional subtract, no need to use the generic modular
+	 * reduction function); then, we use moddiv.
+	 */
+
+	uint32_t tmp[6 * ((BR_MAX_RSA_FACTOR + 61) / 31)];
+	uint32_t *p, *dp, *x;
+	size_t len;
+	uint32_t e;
+
+	/*
+	 * Compute actual factor length (in bytes) and check that it fits
+	 * under our size constraints.
+	 */
+	while (plen > 0 && *pbuf == 0) {
+		pbuf ++;
+		plen --;
+	}
+	if (plen == 0 || plen < 5 || plen > (BR_MAX_RSA_FACTOR / 8)) {
+		return 0;
+	}
+
+	/*
+	 * Compute actual reduced exponent length (in bytes) and check that
+	 * it is not longer than p.
+	 */
+	while (dplen > 0 && *dpbuf == 0) {
+		dpbuf ++;
+		dplen --;
+	}
+	if (dplen > plen || dplen == 0
+		|| (dplen == plen && dpbuf[0] > pbuf[0]))
+	{
+		return 0;
+	}
+
+	/*
+	 * Verify that p = 3 mod 4 and that dp is odd.
+	 */
+	if ((pbuf[plen - 1] & 3) != 3 || (dpbuf[dplen - 1] & 1) != 1) {
+		return 0;
+	}
+
+	/*
+	 * Decode p and compute (p-1)/2.
+	 */
+	p = tmp;
+	br_i31_decode(p, pbuf, plen);
+	len = (p[0] + 63) >> 5;
+	br_i31_rshift(p, 1);
+
+	/*
+	 * Decode dp and make sure its announced bit length matches that of
+	 * p (we already know that the size of dp, in bits, does not exceed
+	 * the size of p, so we just have to copy the header word).
+	 */
+	dp = p + len;
+	memset(dp, 0, len * sizeof *dp);
+	br_i31_decode(dp, dpbuf, dplen);
+	dp[0] = p[0];
+
+	/*
+	 * Subtract (p-1)/2 from dp if necessary.
+	 */
+	br_i31_sub(dp, p, NOT(br_i31_sub(dp, p, 0)));
+
+	/*
+	 * If another subtraction is needed, then this means that the
+	 * value was invalid. We don't care to leak information about
+	 * invalid keys.
+	 */
+	if (br_i31_sub(dp, p, 0) == 0) {
+		return 0;
+	}
+
+	/*
+	 * Invert dp modulo (p-1)/2. If the inversion fails, then the
+	 * key value was invalid.
+	 */
+	x = dp + len;
+	br_i31_zero(x, p[0]);
+	x[1] = 1;
+	if (br_i31_moddiv(x, dp, p, br_i31_ninv31(p[1]), x + len) == 0) {
+		return 0;
+	}
+
+	/*
+	 * We now have an inverse. We must set it to zero (error) if its
+	 * length is greater than 32 bits and/or if it is an even integer.
+	 * Take care that the bit_length function returns an encoded
+	 * bit length.
+	 */
+	e = (uint32_t)x[1] | ((uint32_t)x[2] << 31);
+	e &= -LT(br_i31_bit_length(x + 1, len - 1), 34);
+	e &= -(e & 1);
+	return e;
+}
+
+/* see bearssl_rsa.h */
+uint32_t
+br_rsa_i31_compute_pubexp(const br_rsa_private_key *sk)
+{
+	/*
+	 * Get the public exponent from both p and q. This is the right
+	 * exponent if we get twice the same value.
+	 */
+	uint32_t ep, eq;
+
+	ep = get_pubexp(sk->p, sk->plen, sk->dp, sk->dplen);
+	eq = get_pubexp(sk->q, sk->qlen, sk->dq, sk->dqlen);
+	return ep & -EQ(ep, eq);
+}
diff --git a/src/rsa/rsa_i62_keygen.c b/src/rsa/rsa_i62_keygen.c
index 7d60af9..8f55c37 100644
--- a/src/rsa/rsa_i62_keygen.c
+++ b/src/rsa/rsa_i62_keygen.c
@@ -29,8 +29,8 @@
 /* see bearssl_rsa.h */
 uint32_t
 br_rsa_i62_keygen(const br_prng_class **rng,
-	br_rsa_private_key *sk, unsigned char *kbuf_priv,
-	br_rsa_public_key *pk, unsigned char *kbuf_pub,
+	br_rsa_private_key *sk, void *kbuf_priv,
+	br_rsa_public_key *pk, void *kbuf_pub,
 	unsigned size, uint32_t pubexp)
 {
 	return br_rsa_i31_keygen_inner(rng,
diff --git a/src/x509/asn1enc.c b/src/x509/asn1enc.c
new file mode 100644
index 0000000..7a74963
--- /dev/null
+++ b/src/x509/asn1enc.c
@@ -0,0 +1,93 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see inner.h */
+br_asn1_uint
+br_asn1_uint_prepare(const void *xdata, size_t xlen)
+{
+	const unsigned char *x;
+	br_asn1_uint t;
+
+	x = xdata;
+	while (xlen > 0 && *x == 0) {
+		x ++;
+		xlen --;
+	}
+	t.data = x;
+	t.len = xlen;
+	t.asn1len = xlen;
+	if (xlen == 0 || x[0] >= 0x80) {
+		t.asn1len ++;
+	}
+	return t;
+}
+
+/* see inner.h */
+size_t
+br_asn1_encode_length(void *dest, size_t len)
+{
+	unsigned char *buf;
+	size_t z;
+	int i, j;
+
+	buf = dest;
+	if (len < 0x80) {
+		if (buf != NULL) {
+			*buf = len;
+		}
+		return 1;
+	}
+	i = 0;
+	for (z = len; z != 0; z >>= 8) {
+		i ++;
+	}
+	if (buf != NULL) {
+		*buf ++ = 0x80 + i;
+		for (j = i - 1; j >= 0; j --) {
+			*buf ++ = len >> (j << 3);
+		}
+	}
+	return i + 1;
+}
+
+/* see inner.h */
+size_t
+br_asn1_encode_uint(void *dest, br_asn1_uint pp)
+{
+	unsigned char *buf;
+	size_t lenlen;
+
+	if (dest == NULL) {
+		return 1 + br_asn1_encode_length(NULL, pp.asn1len) + pp.asn1len;
+	}
+	buf = dest;
+	*buf ++ = 0x02;
+	lenlen = br_asn1_encode_length(buf, pp.asn1len);
+	buf += lenlen;
+	*buf = 0x00;
+	memcpy(buf + pp.asn1len - pp.len, pp.data, pp.len);
+	return 1 + lenlen + pp.asn1len;
+}
diff --git a/src/x509/encode_ec_pk8der.c b/src/x509/encode_ec_pk8der.c
new file mode 100644
index 0000000..53717ce
--- /dev/null
+++ b/src/x509/encode_ec_pk8der.c
@@ -0,0 +1,110 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_x509.h */
+size_t
+br_encode_ec_pkcs8_der(void *dest,
+	const br_ec_private_key *sk, const br_ec_public_key *pk)
+{
+	/*
+	 * ASN.1 format:
+	 *
+	 *   OneAsymmetricKey ::= SEQUENCE {
+	 *     version                   Version,
+	 *     privateKeyAlgorithm       PrivateKeyAlgorithmIdentifier,
+	 *     privateKey                PrivateKey,
+	 *     attributes            [0] Attributes OPTIONAL,
+	 *     ...,
+	 *     [[2: publicKey        [1] PublicKey OPTIONAL ]],
+	 *     ...
+	 *   }
+	 *
+	 * We don't include attributes or public key (the public key
+	 * is included in the private key value instead). The
+	 * 'version' field is an INTEGER that we will set to 0
+	 * (meaning 'v1', compatible with previous versions of PKCS#8).
+	 * The 'privateKeyAlgorithm' structure is an AlgorithmIdentifier
+	 * whose OID should be id-ecPublicKey, with, as parameters, the
+	 * curve OID. The 'privateKey' is an OCTET STRING, whose value
+	 * is the "raw DER" encoding of the key pair.
+	 */
+
+	/*
+	 * OID id-ecPublicKey (1.2.840.10045.2.1), DER-encoded (with
+	 * the tag).
+	 */
+	static const unsigned char OID_ECPUBKEY[] = {
+		0x06, 0x07, 0x2a, 0x86, 0x48, 0xce, 0x3d, 0x02, 0x01
+	};
+
+	size_t len_version, len_privateKeyAlgorithm, len_privateKeyValue;
+	size_t len_privateKey, len_seq;
+	const unsigned char *oid;
+
+	oid = br_get_curve_OID(sk->curve);
+	if (oid == NULL) {
+		return 0;
+	}
+	len_version = 3;
+	len_privateKeyAlgorithm = 2 + sizeof OID_ECPUBKEY + 2 + oid[0];
+	len_privateKeyValue = br_encode_ec_raw_der_inner(NULL, sk, pk, 0);
+	len_privateKey = 1 + len_of_len(len_privateKeyValue)
+		+ len_privateKeyValue;
+	len_seq = len_version + len_privateKeyAlgorithm + len_privateKey;
+
+	if (dest == NULL) {
+		return 1 + len_of_len(len_seq) + len_seq;
+	} else {
+		unsigned char *buf;
+		size_t lenlen;
+
+		buf = dest;
+		*buf ++ = 0x30;  /* SEQUENCE tag */
+		lenlen = br_asn1_encode_length(buf, len_seq);
+		buf += lenlen;
+
+		/* version */
+		*buf ++ = 0x02;
+		*buf ++ = 0x01;
+		*buf ++ = 0x00;
+
+		/* privateKeyAlgorithm */
+		*buf ++ = 0x30;
+		*buf ++ = (sizeof OID_ECPUBKEY) + 2 + oid[0];
+		memcpy(buf, OID_ECPUBKEY, sizeof OID_ECPUBKEY);
+		buf += sizeof OID_ECPUBKEY;
+		*buf ++ = 0x06;
+		memcpy(buf, oid, 1 + oid[0]);
+		buf += 1 + oid[0];
+
+		/* privateKey */
+		*buf ++ = 0x04;
+		buf += br_asn1_encode_length(buf, len_privateKeyValue);
+		br_encode_ec_raw_der_inner(buf, sk, pk, 0);
+
+		return 1 + lenlen + len_seq;
+	}
+}
diff --git a/src/x509/encode_ec_rawder.c b/src/x509/encode_ec_rawder.c
new file mode 100644
index 0000000..5985909
--- /dev/null
+++ b/src/x509/encode_ec_rawder.c
@@ -0,0 +1,161 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see inner.h */
+const unsigned char *
+br_get_curve_OID(int curve)
+{
+	static const unsigned char OID_secp256r1[] = {
+		0x08, 0x2a, 0x86, 0x48, 0xce, 0x3d, 0x03, 0x01, 0x07
+	};
+	static const unsigned char OID_secp384r1[] = {
+		0x05, 0x2b, 0x81, 0x04, 0x00, 0x22
+	};
+	static const unsigned char OID_secp521r1[] = {
+		0x05, 0x2b, 0x81, 0x04, 0x00, 0x23
+	};
+
+	switch (curve) {
+	case BR_EC_secp256r1:  return OID_secp256r1;
+	case BR_EC_secp384r1:  return OID_secp384r1;
+	case BR_EC_secp521r1:  return OID_secp521r1;
+	default:
+		return NULL;
+	}
+}
+
+/* see inner.h */
+size_t
+br_encode_ec_raw_der_inner(void *dest,
+	const br_ec_private_key *sk, const br_ec_public_key *pk,
+	int include_curve_oid)
+{
+	/*
+	 * ASN.1 format:
+	 *
+	 *   ECPrivateKey ::= SEQUENCE {
+	 *     version        INTEGER { ecPrivkeyVer1(1) } (ecPrivkeyVer1),
+	 *     privateKey     OCTET STRING,
+	 *     parameters [0] ECParameters {{ NamedCurve }} OPTIONAL,
+	 *     publicKey  [1] BIT STRING OPTIONAL
+	 *   }
+	 *
+	 * The tages '[0]' and '[1]' are explicit. The 'ECParameters'
+	 * is a CHOICE; in our case, it will always be an OBJECT IDENTIFIER
+	 * that identifies the curve.
+	 *
+	 * The value of the 'privateKey' field is the raw unsigned big-endian
+	 * encoding of the private key (integer modulo the curve subgroup
+	 * order); there is no INTEGER tag, and the leading bit may be 1.
+	 * Also, leading bytes of value 0x00 are _not_ removed.
+	 *
+	 * The 'publicKey' contents are the raw encoded public key point,
+	 * normally uncompressed (leading byte of value 0x04, followed
+	 * by the unsigned big-endian encodings of the X and Y coordinates,
+	 * padded to the full field length if necessary).
+	 */
+
+	size_t len_version, len_privateKey, len_parameters, len_publicKey;
+	size_t len_publicKey_bits, len_seq;
+	const unsigned char *oid;
+
+	if (include_curve_oid) {
+		oid = br_get_curve_OID(sk->curve);
+		if (oid == NULL) {
+			return 0;
+		}
+	} else {
+		oid = NULL;
+	}
+	len_version = 3;
+	len_privateKey = 1 + len_of_len(sk->xlen) + sk->xlen;
+	if (include_curve_oid) {
+		len_parameters = 4 + oid[0];
+	} else {
+		len_parameters = 0;
+	}
+	if (pk == NULL) {
+		len_publicKey = 0;
+		len_publicKey_bits = 0;
+	} else {
+		len_publicKey_bits = 2 + len_of_len(pk->qlen) + pk->qlen;
+		len_publicKey = 1 + len_of_len(len_publicKey_bits)
+			+ len_publicKey_bits;
+	}
+	len_seq = len_version + len_privateKey + len_parameters + len_publicKey;
+	if (dest == NULL) {
+		return 1 + len_of_len(len_seq) + len_seq;
+	} else {
+		unsigned char *buf;
+		size_t lenlen;
+
+		buf = dest;
+		*buf ++ = 0x30;  /* SEQUENCE tag */
+		lenlen = br_asn1_encode_length(buf, len_seq);
+		buf += lenlen;
+
+		/* version */
+		*buf ++ = 0x02;
+		*buf ++ = 0x01;
+		*buf ++ = 0x01;
+
+		/* privateKey */
+		*buf ++ = 0x04;
+		buf += br_asn1_encode_length(buf, sk->xlen);
+		memcpy(buf, sk->x, sk->xlen);
+		buf += sk->xlen;
+
+		/* parameters */
+		if (include_curve_oid) {
+			*buf ++ = 0xA0;
+			*buf ++ = oid[0] + 2;
+			*buf ++ = 0x06;
+			memcpy(buf, oid, oid[0] + 1);
+			buf += oid[0] + 1;
+		}
+
+		/* publicKey */
+		if (pk != NULL) {
+			*buf ++ = 0xA1;
+			buf += br_asn1_encode_length(buf, len_publicKey_bits);
+			*buf ++ = 0x03;
+			buf += br_asn1_encode_length(buf, pk->qlen + 1);
+			*buf ++ = 0x00;
+			memcpy(buf, pk->q, pk->qlen);
+			/* buf += pk->qlen; */
+		}
+
+		return 1 + lenlen + len_seq;
+	}
+}
+
+/* see bearssl_x509.h */
+size_t
+br_encode_ec_raw_der(void *dest,
+	const br_ec_private_key *sk, const br_ec_public_key *pk)
+{
+	return br_encode_ec_raw_der_inner(dest, sk, pk, 1);
+}
diff --git a/src/x509/encode_rsa_pk8der.c b/src/x509/encode_rsa_pk8der.c
new file mode 100644
index 0000000..c053503
--- /dev/null
+++ b/src/x509/encode_rsa_pk8der.c
@@ -0,0 +1,97 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_x509.h */
+size_t
+br_encode_rsa_pkcs8_der(void *dest, const br_rsa_private_key *sk,
+	const br_rsa_public_key *pk, const void *d, size_t dlen)
+{
+	/*
+	 * ASN.1 format:
+	 *
+	 *   OneAsymmetricKey ::= SEQUENCE {
+	 *     version                   Version,
+	 *     privateKeyAlgorithm       PrivateKeyAlgorithmIdentifier,
+	 *     privateKey                PrivateKey,
+	 *     attributes            [0] Attributes OPTIONAL,
+	 *     ...,
+	 *     [[2: publicKey        [1] PublicKey OPTIONAL ]],
+	 *     ...
+	 *   }
+	 *
+	 * We don't include attributes or public key. The 'version' field
+	 * is an INTEGER that we will set to 0 (meaning 'v1', compatible
+	 * with previous versions of PKCS#8). The 'privateKeyAlgorithm'
+	 * structure is an AlgorithmIdentifier whose OID should be
+	 * rsaEncryption, with NULL parameters. The 'privateKey' is an
+	 * OCTET STRING, whose value is the "raw DER" encoding of the
+	 * key pair.
+	 *
+	 * Since the private key value comes last, this function really
+	 * adds a header, which is mostly fixed (only some lengths have
+	 * to be modified.
+	 */
+
+	/*
+	 * Concatenation of:
+	 *  - DER encoding of an INTEGER of value 0 (the 'version' field)
+	 *  - DER encoding of a PrivateKeyAlgorithmIdentifier that uses
+	 *    the rsaEncryption OID, and NULL parameters
+	 *  - An OCTET STRING tag
+	 */
+	static const unsigned char PK8_HEAD[] = {
+		0x02, 0x01, 0x00,
+		0x30, 0x0d, 0x06, 0x09, 0x2a, 0x86, 0x48, 0x86,
+		0xf7, 0x0d, 0x01, 0x01, 0x01, 0x05, 0x00,
+		0x04
+	};
+
+	size_t len_raw, len_seq;
+
+	len_raw = br_encode_rsa_raw_der(NULL, sk, pk, d, dlen);
+	len_seq = (sizeof PK8_HEAD) + len_of_len(len_raw) + len_raw;
+	if (dest == NULL) {
+		return 1 + len_of_len(len_seq) + len_seq;
+	} else {
+		unsigned char *buf;
+		size_t lenlen;
+
+		buf = dest;
+		*buf ++ = 0x30;  /* SEQUENCE tag */
+		lenlen = br_asn1_encode_length(buf, len_seq);
+		buf += lenlen;
+
+		/* version, privateKeyAlgorithm, privateKey tag */
+		memcpy(buf, PK8_HEAD, sizeof PK8_HEAD);
+		buf += sizeof PK8_HEAD;
+
+		/* privateKey */
+		buf += br_asn1_encode_length(buf, len_raw);
+		br_encode_rsa_raw_der(buf, sk, pk, d, dlen);
+
+		return 1 + lenlen + len_seq;
+	}
+}
diff --git a/src/x509/encode_rsa_rawder.c b/src/x509/encode_rsa_rawder.c
new file mode 100644
index 0000000..1a8052b
--- /dev/null
+++ b/src/x509/encode_rsa_rawder.c
@@ -0,0 +1,96 @@
+/*
+ * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* see bearssl_x509.h */
+size_t
+br_encode_rsa_raw_der(void *dest, const br_rsa_private_key *sk,
+	const br_rsa_public_key *pk, const void *d, size_t dlen)
+{
+	/*
+	 * ASN.1 format:
+	 *
+	 *   RSAPrivateKey ::= SEQUENCE {
+	 *       version           Version,
+	 *       modulus           INTEGER,  -- n
+	 *       publicExponent    INTEGER,  -- e
+	 *       privateExponent   INTEGER,  -- d
+	 *       prime1            INTEGER,  -- p
+	 *       prime2            INTEGER,  -- q
+	 *       exponent1         INTEGER,  -- d mod (p-1)
+	 *       exponent2         INTEGER,  -- d mod (q-1)
+	 *       coefficient       INTEGER,  -- (inverse of q) mod p
+	 *       otherPrimeInfos   OtherPrimeInfos OPTIONAL
+	 *   }
+	 *
+	 * The 'version' field is an INTEGER of value 0 (meaning: there
+	 * are exactly two prime factors), and 'otherPrimeInfos' will
+	 * be absent (because there are exactly two prime factors).
+	 */
+
+	br_asn1_uint num[9];
+	size_t u, slen;
+
+	/*
+	 * For all INTEGER values, get the pointer and length for the
+	 * data bytes.
+	 */
+	num[0] = br_asn1_uint_prepare(NULL, 0);
+	num[1] = br_asn1_uint_prepare(pk->n, pk->nlen);
+	num[2] = br_asn1_uint_prepare(pk->e, pk->elen);
+	num[3] = br_asn1_uint_prepare(d, dlen);
+	num[4] = br_asn1_uint_prepare(sk->p, sk->plen);
+	num[5] = br_asn1_uint_prepare(sk->q, sk->qlen);
+	num[6] = br_asn1_uint_prepare(sk->dp, sk->dplen);
+	num[7] = br_asn1_uint_prepare(sk->dq, sk->dqlen);
+	num[8] = br_asn1_uint_prepare(sk->iq, sk->iqlen);
+
+	/*
+	 * Get the length of the SEQUENCE contents.
+	 */
+	slen = 0;
+	for (u = 0; u < 9; u ++) {
+		uint32_t ilen;
+
+		ilen = num[u].asn1len;
+		slen += 1 + len_of_len(ilen) + ilen;
+	}
+
+	if (dest == NULL) {
+		return 1 + len_of_len(slen) + slen;
+	} else {
+		unsigned char *buf;
+		size_t lenlen;
+
+		buf = dest;
+		*buf ++ = 0x30;  /* SEQUENCE tag */
+		lenlen = br_asn1_encode_length(buf, slen);
+		buf += lenlen;
+		for (u = 0; u < 9; u ++) {
+			buf += br_asn1_encode_uint(buf, num[u]);
+		}
+		return 1 + lenlen + slen;
+	}
+}
diff --git a/test/test_crypto.c b/test/test_crypto.c
index 60a431c..70029b3 100644
--- a/test/test_crypto.c
+++ b/test/test_crypto.c
@@ -5721,8 +5721,9 @@ test_RSA_OAEP(const char *name,
 }
 
 static void
-test_RSA_keygen(const char *name, br_rsa_keygen kg,
-	br_rsa_pkcs1_sign sign, br_rsa_pkcs1_vrfy vrfy)
+test_RSA_keygen(const char *name, br_rsa_keygen kg, br_rsa_compute_modulus cm,
+	br_rsa_compute_pubexp ce, br_rsa_compute_privexp cd,
+	br_rsa_public pub, br_rsa_pkcs1_sign sign, br_rsa_pkcs1_vrfy vrfy)
 {
 	br_hmac_drbg_context rng;
 	int i;
@@ -5732,25 +5733,30 @@ test_RSA_keygen(const char *name, br_rsa_keygen kg,
 
 	br_hmac_drbg_init(&rng, &br_sha256_vtable, "seed for RSA keygen", 19);
 
-	for (i = 0; i < 40; i ++) {
+	for (i = 0; i <= 42; i ++) {
 		unsigned size;
-		uint32_t pubexp;
+		uint32_t pubexp, z;
 		br_rsa_private_key sk;
-		br_rsa_public_key pk;
+		br_rsa_public_key pk, pk2;
 		unsigned char kbuf_priv[BR_RSA_KBUF_PRIV_SIZE(2048)];
 		unsigned char kbuf_pub[BR_RSA_KBUF_PUB_SIZE(2048)];
+		unsigned char n2[256], d[256], msg1[256], msg2[256];
 		uint32_t mod[256];
 		uint32_t cc;
 		size_t u, v;
 		unsigned char sig[257], hv[32], hv2[sizeof hv];
 		unsigned mask1, mask2;
+		int j;
 
 		if (i <= 35) {
 			size = 1024 + i;
 			pubexp = 17;
-		} else {
+		} else if (i <= 40) {
 			size = 2048;
 			pubexp = (i << 1) - 69;
+		} else {
+			size = 2048;
+			pubexp = 0xFFFFFFFF;
 		}
 
 		if (!kg(&rng.vtable,
@@ -5760,14 +5766,15 @@ test_RSA_keygen(const char *name, br_rsa_keygen kg,
 			exit(EXIT_FAILURE);
 		}
 
+		z = pubexp;
 		for (u = pk.elen; u > 0; u --) {
-			if (pk.e[u - 1] != (pubexp & 0xFF)) {
+			if (pk.e[u - 1] != (z & 0xFF)) {
 				fprintf(stderr, "wrong public exponent\n");
 				exit(EXIT_FAILURE);
 			}
-			pubexp >>= 8;
+			z >>= 8;
 		}
-		if (pubexp != 0) {
+		if (z != 0) {
 			fprintf(stderr, "truncated public exponent\n");
 			exit(EXIT_FAILURE);
 		}
@@ -5806,28 +5813,86 @@ test_RSA_keygen(const char *name, br_rsa_keygen kg,
 			exit(EXIT_FAILURE);
 		}
 
-		rng.vtable->generate(&rng.vtable, hv, sizeof hv);
-		memset(sig, 0, sizeof sig);
-		sig[pk.nlen] = 0x00;
-		if (!sign(BR_HASH_OID_SHA256, hv, sizeof hv, &sk, sig)) {
-			fprintf(stderr, "signature error\n");
+		if (cm(NULL, &sk) != pk.nlen) {
+			fprintf(stderr, "wrong recomputed modulus length\n");
 			exit(EXIT_FAILURE);
 		}
-		if (sig[pk.nlen] != 0x00) {
-			fprintf(stderr, "signature length error\n");
+		if (cm(n2, &sk) != pk.nlen || memcmp(pk.n, n2, pk.nlen) != 0) {
+			fprintf(stderr, "wrong recomputed modulus value\n");
 			exit(EXIT_FAILURE);
 		}
-		if (!vrfy(sig, pk.nlen, BR_HASH_OID_SHA256, sizeof hv,
-			&pk, hv2))
-		{
-			fprintf(stderr, "signature verification error (1)\n");
+
+		z = ce(&sk);
+		if (z != pubexp) {
+			fprintf(stderr,
+				"wrong recomputed pubexp: %lu (exp: %lu)\n",
+				(unsigned long)z, (unsigned long)pubexp);
 			exit(EXIT_FAILURE);
 		}
-		if (memcmp(hv, hv2, sizeof hv) != 0) {
-			fprintf(stderr, "signature verification error (2)\n");
+
+		if (cd(NULL, &sk, pubexp) != pk.nlen) {
+			fprintf(stderr,
+				"wrong recomputed privexp length (1)\n");
+			exit(EXIT_FAILURE);
+		}
+		if (cd(d, &sk, pubexp) != pk.nlen) {
+			fprintf(stderr,
+				"wrong recomputed privexp length (2)\n");
+			exit(EXIT_FAILURE);
+		}
+		/*
+		 * To check that the private exponent is correct, we make
+		 * it into a _public_ key, and use the public-key operation
+		 * to perform the modular exponentiation.
+		 */
+		pk2 = pk;
+		pk2.e = d;
+		pk2.elen = pk.nlen;
+		rng.vtable->generate(&rng.vtable, msg1, pk.nlen);
+		msg1[0] = 0x00;
+		memcpy(msg2, msg1, pk.nlen);
+		if (!pub(msg2, pk.nlen, &pk2) || !pub(msg2, pk.nlen, &pk)) {
+			fprintf(stderr, "public-key operation error\n");
+			exit(EXIT_FAILURE);
+		}
+		if (memcmp(msg1, msg2, pk.nlen) != 0) {
+			fprintf(stderr, "wrong recomputed privexp\n");
 			exit(EXIT_FAILURE);
 		}
 
+		/*
+		 * We test the RSA operation over a some random messages.
+		 */
+		for (j = 0; j < 20; j ++) {
+			rng.vtable->generate(&rng.vtable, hv, sizeof hv);
+			memset(sig, 0, sizeof sig);
+			sig[pk.nlen] = 0x00;
+			if (!sign(BR_HASH_OID_SHA256,
+				hv, sizeof hv, &sk, sig))
+			{
+				fprintf(stderr,
+					"signature error (%d)\n", j);
+				exit(EXIT_FAILURE);
+			}
+			if (sig[pk.nlen] != 0x00) {
+				fprintf(stderr,
+					"signature length error (%d)\n", j);
+				exit(EXIT_FAILURE);
+			}
+			if (!vrfy(sig, pk.nlen, BR_HASH_OID_SHA256, sizeof hv,
+				&pk, hv2))
+			{
+				fprintf(stderr,
+					"signature verif error (%d)\n", j);
+				exit(EXIT_FAILURE);
+			}
+			if (memcmp(hv, hv2, sizeof hv) != 0) {
+				fprintf(stderr,
+					"signature extract error (%d)\n", j);
+				exit(EXIT_FAILURE);
+			}
+		}
+
 		printf(".");
 		fflush(stdout);
 	}
@@ -5845,6 +5910,8 @@ test_RSA_i15(void)
 	test_RSA_OAEP("RSA i15 OAEP",
 		&br_rsa_i15_oaep_encrypt, &br_rsa_i15_oaep_decrypt);
 	test_RSA_keygen("RSA i15 keygen", &br_rsa_i15_keygen,
+		&br_rsa_i15_compute_modulus, &br_rsa_i15_compute_pubexp,
+		&br_rsa_i15_compute_privexp, &br_rsa_i15_public,
 		&br_rsa_i15_pkcs1_sign, &br_rsa_i15_pkcs1_vrfy);
 }
 
@@ -5857,6 +5924,8 @@ test_RSA_i31(void)
 	test_RSA_OAEP("RSA i31 OAEP",
 		&br_rsa_i31_oaep_encrypt, &br_rsa_i31_oaep_decrypt);
 	test_RSA_keygen("RSA i31 keygen", &br_rsa_i31_keygen,
+		&br_rsa_i31_compute_modulus, &br_rsa_i31_compute_pubexp,
+		&br_rsa_i31_compute_privexp, &br_rsa_i31_public,
 		&br_rsa_i31_pkcs1_sign, &br_rsa_i31_pkcs1_vrfy);
 }
 
@@ -5896,7 +5965,10 @@ test_RSA_i62(void)
 		test_RSA_core("RSA i62 core", pub, priv);
 		test_RSA_sign("RSA i62 sign", priv, sign, vrfy);
 		test_RSA_OAEP("RSA i62 OAEP", menc, mdec);
-		test_RSA_keygen("RSA i62 keygen", kgen, sign, vrfy);
+		test_RSA_keygen("RSA i62 keygen", kgen,
+			&br_rsa_i31_compute_modulus, &br_rsa_i31_compute_pubexp,
+			&br_rsa_i31_compute_privexp, pub,
+			sign, vrfy);
 	} else {
 		if (priv || sign || vrfy || menc || mdec || kgen) {
 			fprintf(stderr, "Inconsistent i62 availability\n");
@@ -7209,7 +7281,6 @@ test_EC_P256_carry(const br_ec_impl *impl)
 static void
 test_EC_KAT(const char *name, const br_ec_impl *impl, uint32_t curve_mask)
 {
-
 	printf("Test %s: ", name);
 	fflush(stdout);
 
@@ -7237,6 +7308,155 @@ test_EC_KAT(const char *name, const br_ec_impl *impl, uint32_t curve_mask)
 	fflush(stdout);
 }
 
+static void
+test_EC_keygen(const char *name, const br_ec_impl *impl, uint32_t curves)
+{
+	int curve;
+	br_hmac_drbg_context rng;
+
+	printf("Test %s keygen: ", name);
+	fflush(stdout);
+
+	br_hmac_drbg_init(&rng, &br_sha256_vtable, "seed for EC keygen", 18);
+	br_hmac_drbg_update(&rng, name, strlen(name));
+
+	for (curve = -1; curve <= 35; curve ++) {
+		br_ec_private_key sk;
+		br_ec_public_key pk;
+		unsigned char kbuf_priv[BR_EC_KBUF_PRIV_MAX_SIZE];
+		unsigned char kbuf_pub[BR_EC_KBUF_PUB_MAX_SIZE];
+
+		if (curve < 0 || curve >= 32 || ((curves >> curve) & 1) == 0) {
+			if (br_ec_keygen(&rng.vtable, impl,
+				&sk, kbuf_priv, curve) != 0)
+			{
+				fprintf(stderr, "br_ec_keygen() did not"
+					" reject unsupported curve %d\n",
+					curve);
+				exit(EXIT_FAILURE);
+			}
+			sk.curve = curve;
+			if (br_ec_compute_pub(impl, NULL, NULL, &sk) != 0) {
+				fprintf(stderr, "br_ec_keygen() did not"
+					" reject unsupported curve %d\n",
+					curve);
+				exit(EXIT_FAILURE);
+			}
+		} else {
+			size_t len, u;
+			unsigned char tmp_priv[sizeof kbuf_priv];
+			unsigned char tmp_pub[sizeof kbuf_pub];
+			unsigned z;
+
+			len = br_ec_keygen(&rng.vtable, impl,
+				NULL, NULL, curve);
+			if (len == 0) {
+				fprintf(stderr, "br_ec_keygen() rejects"
+					" supported curve %d\n", curve);
+				exit(EXIT_FAILURE);
+			}
+			if (len > sizeof kbuf_priv) {
+				fprintf(stderr, "oversized kbuf_priv\n");
+				exit(EXIT_FAILURE);
+			}
+			memset(kbuf_priv, 0, sizeof kbuf_priv);
+			if (br_ec_keygen(&rng.vtable, impl,
+				NULL, kbuf_priv, curve) != len)
+			{
+				fprintf(stderr, "kbuf_priv length mismatch\n");
+				exit(EXIT_FAILURE);
+			}
+			z = 0;
+			for (u = 0; u < len; u ++) {
+				z |= kbuf_priv[u];
+			}
+			if (z == 0) {
+				fprintf(stderr, "kbuf_priv not initialized\n");
+				exit(EXIT_FAILURE);
+			}
+			for (u = len; u < sizeof kbuf_priv; u ++) {
+				if (kbuf_priv[u] != 0) {
+					fprintf(stderr, "kbuf_priv overflow\n");
+					exit(EXIT_FAILURE);
+				}
+			}
+			if (br_ec_keygen(&rng.vtable, impl,
+				NULL, tmp_priv, curve) != len)
+			{
+				fprintf(stderr, "tmp_priv length mismatch\n");
+				exit(EXIT_FAILURE);
+			}
+			if (memcmp(kbuf_priv, tmp_priv, len) == 0) {
+				fprintf(stderr, "keygen stutter\n");
+				exit(EXIT_FAILURE);
+			}
+			memset(&sk, 0, sizeof sk);
+			if (br_ec_keygen(&rng.vtable, impl,
+				&sk, kbuf_priv, curve) != len)
+			{
+				fprintf(stderr,
+					"kbuf_priv length mismatch (2)\n");
+				exit(EXIT_FAILURE);
+			}
+			if (sk.curve != curve || sk.x != kbuf_priv
+				|| sk.xlen != len)
+			{
+				fprintf(stderr, "sk not initialized\n");
+				exit(EXIT_FAILURE);
+			}
+
+			len = br_ec_compute_pub(impl, NULL, NULL, &sk);
+			if (len > sizeof kbuf_pub) {
+				fprintf(stderr, "oversized kbuf_pub\n");
+				exit(EXIT_FAILURE);
+			}
+			memset(kbuf_pub, 0, sizeof kbuf_pub);
+			if (br_ec_compute_pub(impl, NULL,
+				kbuf_pub, &sk) != len)
+			{
+				fprintf(stderr, "kbuf_pub length mismatch\n");
+				exit(EXIT_FAILURE);
+			}
+			for (u = len; u < sizeof kbuf_pub; u ++) {
+				if (kbuf_pub[u] != 0) {
+					fprintf(stderr, "kbuf_pub overflow\n");
+					exit(EXIT_FAILURE);
+				}
+			}
+			memset(&pk, 0, sizeof pk);
+			if (br_ec_compute_pub(impl, &pk,
+				tmp_pub, &sk) != len)
+			{
+				fprintf(stderr, "tmp_pub length mismatch\n");
+				exit(EXIT_FAILURE);
+			}
+			if (memcmp(kbuf_pub, tmp_pub, len) != 0) {
+				fprintf(stderr, "pubkey mismatch\n");
+				exit(EXIT_FAILURE);
+			}
+			if (pk.curve != curve || pk.q != tmp_pub
+				|| pk.qlen != len)
+			{
+				fprintf(stderr, "pk not initialized\n");
+				exit(EXIT_FAILURE);
+			}
+
+			if (impl->mulgen(kbuf_pub,
+				sk.x, sk.xlen, curve) != len
+				|| memcmp(pk.q, kbuf_pub, len) != 0)
+			{
+				fprintf(stderr, "wrong pubkey\n");
+				exit(EXIT_FAILURE);
+			}
+		}
+		printf(".");
+		fflush(stdout);
+	}
+
+	printf(" done.\n");
+	fflush(stdout);
+}
+
 static void
 test_EC_prime_i15(void)
 {
@@ -7244,6 +7464,10 @@ test_EC_prime_i15(void)
 		(uint32_t)1 << BR_EC_secp256r1
 		| (uint32_t)1 << BR_EC_secp384r1
 		| (uint32_t)1 << BR_EC_secp521r1);
+	test_EC_keygen("EC_prime_i15", &br_ec_prime_i15,
+		(uint32_t)1 << BR_EC_secp256r1
+		| (uint32_t)1 << BR_EC_secp384r1
+		| (uint32_t)1 << BR_EC_secp521r1);
 }
 
 static void
@@ -7253,6 +7477,10 @@ test_EC_prime_i31(void)
 		(uint32_t)1 << BR_EC_secp256r1
 		| (uint32_t)1 << BR_EC_secp384r1
 		| (uint32_t)1 << BR_EC_secp521r1);
+	test_EC_keygen("EC_prime_i31", &br_ec_prime_i31,
+		(uint32_t)1 << BR_EC_secp256r1
+		| (uint32_t)1 << BR_EC_secp384r1
+		| (uint32_t)1 << BR_EC_secp521r1);
 }
 
 static void
@@ -7260,6 +7488,8 @@ test_EC_p256_m15(void)
 {
 	test_EC_KAT("EC_p256_m15", &br_ec_p256_m15,
 		(uint32_t)1 << BR_EC_secp256r1);
+	test_EC_keygen("EC_p256_m15", &br_ec_p256_m15,
+		(uint32_t)1 << BR_EC_secp256r1);
 }
 
 static void
@@ -7267,6 +7497,8 @@ test_EC_p256_m31(void)
 {
 	test_EC_KAT("EC_p256_m31", &br_ec_p256_m31,
 		(uint32_t)1 << BR_EC_secp256r1);
+	test_EC_keygen("EC_p256_m31", &br_ec_p256_m31,
+		(uint32_t)1 << BR_EC_secp256r1);
 }
 
 const struct {
@@ -7353,24 +7585,32 @@ static void
 test_EC_c25519_i15(void)
 {
 	test_EC_c25519("EC_c25519_i15", &br_ec_c25519_i15);
+	test_EC_keygen("EC_c25519_i15", &br_ec_c25519_i15,
+		(uint32_t)1 << BR_EC_curve25519);
 }
 
 static void
 test_EC_c25519_i31(void)
 {
 	test_EC_c25519("EC_c25519_i31", &br_ec_c25519_i31);
+	test_EC_keygen("EC_c25519_i31", &br_ec_c25519_i31,
+		(uint32_t)1 << BR_EC_curve25519);
 }
 
 static void
 test_EC_c25519_m15(void)
 {
 	test_EC_c25519("EC_c25519_m15", &br_ec_c25519_m15);
+	test_EC_keygen("EC_c25519_m15", &br_ec_c25519_m15,
+		(uint32_t)1 << BR_EC_curve25519);
 }
 
 static void
 test_EC_c25519_m31(void)
 {
 	test_EC_c25519("EC_c25519_m31", &br_ec_c25519_m31);
+	test_EC_keygen("EC_c25519_m31", &br_ec_c25519_m31,
+		(uint32_t)1 << BR_EC_curve25519);
 }
 
 static const unsigned char EC_P256_PUB_POINT[] = {
diff --git a/tools/brssl.h b/tools/brssl.h
index 22fd712..a23ba00 100644
--- a/tools/brssl.h
+++ b/tools/brssl.h
@@ -298,11 +298,22 @@ int uses_ecdhe(unsigned suite);
  */
 void list_names(void);
 
+/*
+ * Print out all known elliptic curve names.
+ */
+void list_curves(void);
+
 /*
  * Get the symbolic name for an elliptic curve (by ID).
  */
 const char *ec_curve_name(int curve);
 
+/*
+ * Get a curve by symbolic name. If the name is not recognized, -1 is
+ * returned.
+ */
+int get_curve_by_name(const char *str);
+
 /*
  * Get the symbolic name for a hash function name (by ID).
  */
diff --git a/tools/names.c b/tools/names.c
index 3ea7f1b..f9487fd 100644
--- a/tools/names.c
+++ b/tools/names.c
@@ -322,68 +322,99 @@ const cipher_suite cipher_suites[] = {
 static const struct {
 	int id;
 	const char *name;
+	const char *sid[4];
 } curves[] = {
 	{ BR_EC_sect163k1,
-	  "sect163k1" },
+	  "sect163k1",
+	  { "sect163k1", "K-163", NULL, NULL } },
 	{ BR_EC_sect163r1,
-	  "sect163r1" },
+	  "sect163r1",
+	  { "sect163r1", NULL, NULL, NULL } },
 	{ BR_EC_sect163r2,
-	  "sect163r2" },
+	  "sect163r2",
+	  { "sect163r2", "B-163", NULL, NULL } },
 	{ BR_EC_sect193r1,
-	  "sect193r1" },
+	  "sect193r1",
+	  { "sect193r1", NULL, NULL, NULL } },
 	{ BR_EC_sect193r2,
-	  "sect193r2" },
+	  "sect193r2",
+	  { "sect193r2", NULL, NULL, NULL } },
 	{ BR_EC_sect233k1,
-	  "sect233k1" },
+	  "sect233k1",
+	  { "sect233k1", "K-233", NULL, NULL } },
 	{ BR_EC_sect233r1,
-	  "sect233r1" },
+	  "sect233r1",
+	  { "sect233r1", "B-233", NULL, NULL } },
 	{ BR_EC_sect239k1,
-	  "sect239k1" },
+	  "sect239k1",
+	  { "sect239k1", NULL, NULL, NULL } },
 	{ BR_EC_sect283k1,
-	  "sect283k1" },
+	  "sect283k1",
+	  { "sect283k1", "K-283", NULL, NULL } },
 	{ BR_EC_sect283r1,
-	  "sect283r1" },
+	  "sect283r1",
+	  { "sect283r1", "B-283", NULL, NULL } },
 	{ BR_EC_sect409k1,
-	  "sect409k1" },
+	  "sect409k1",
+	  { "sect409k1", "K-409", NULL, NULL } },
 	{ BR_EC_sect409r1,
-	  "sect409r1" },
+	  "sect409r1",
+	  { "sect409r1", "B-409", NULL, NULL } },
 	{ BR_EC_sect571k1,
-	  "sect571k1" },
+	  "sect571k1",
+	  { "sect571k1", "K-571", NULL, NULL } },
 	{ BR_EC_sect571r1,
-	  "sect571r1" },
+	  "sect571r1",
+	  { "sect571r1", "B-571", NULL, NULL } },
 	{ BR_EC_secp160k1,
-	  "secp160k1" },
+	  "secp160k1",
+	  { "secp160k1", NULL, NULL, NULL } },
 	{ BR_EC_secp160r1,
-	  "secp160r1" },
+	  "secp160r1",
+	  { "secp160r1", NULL, NULL, NULL } },
 	{ BR_EC_secp160r2,
-	  "secp160r2" },
+	  "secp160r2",
+	  { "secp160r2", NULL, NULL, NULL } },
 	{ BR_EC_secp192k1,
-	  "secp192k1" },
+	  "secp192k1",
+	  { "secp192k1", NULL, NULL, NULL } },
 	{ BR_EC_secp192r1,
-	  "secp192r1" },
+	  "secp192r1",
+	  { "secp192r1", "P-192", NULL, NULL } },
 	{ BR_EC_secp224k1,
-	  "secp224k1" },
+	  "secp224k1",
+	  { "secp224k1", NULL, NULL, NULL } },
 	{ BR_EC_secp224r1,
-	  "secp224r1" },
+	  "secp224r1",
+	  { "secp224r1", "P-224", NULL, NULL } },
 	{ BR_EC_secp256k1,
-	  "secp256k1" },
+	  "secp256k1",
+	  { "secp256k1", NULL, NULL, NULL } },
 	{ BR_EC_secp256r1,
-	  "secp256r1 (P-256)" },
+	  "secp256r1 (P-256)",
+	  { "secp256r1", "P-256", "prime256v1", NULL } },
 	{ BR_EC_secp384r1,
-	  "secp384r1 (P-384)" },
+	  "secp384r1 (P-384)",
+	  { "secp384r1", "P-384", NULL, NULL } },
 	{ BR_EC_secp521r1,
-	  "secp521r1 (P-521)" },
+	  "secp521r1 (P-521)",
+	  { "secp521r1", "P-521", NULL, NULL } },
 	{ BR_EC_brainpoolP256r1,
-	  "brainpoolP256r1" },
+	  "brainpoolP256r1",
+	  { "brainpoolP256r1", NULL, NULL, NULL } },
 	{ BR_EC_brainpoolP384r1,
-	  "brainpoolP384r1" },
+	  "brainpoolP384r1",
+	  { "brainpoolP384r1", NULL, NULL, NULL } },
 	{ BR_EC_brainpoolP512r1,
-	  "brainpoolP512r1" },
+	  "brainpoolP512r1",
+	  { "brainpoolP512r1", NULL, NULL, NULL } },
 	{ BR_EC_curve25519,
-	  "Curve25519" },
+	  "Curve25519",
+	  { "curve25519", "c25519", NULL, NULL } },
 	{ BR_EC_curve448,
-	  "Curve448" },
-	{ 0, 0 }
+	  "Curve448",
+	  { "curve448", "c448", NULL, NULL } },
+	{ 0, 0, { 0, 0, 0, 0 } }
 };
 
 static const struct {
@@ -627,6 +658,31 @@ list_names(void)
 	}
 }
 
+/* see brssl.h */
+void
+list_curves(void)
+{
+	size_t u;
+	for (u = 0; curves[u].name; u ++) {
+		size_t v;
+
+		for (v = 0; curves[u].sid[v]; v ++) {
+			if (v == 0) {
+				printf("   ");
+			} else if (v == 1) {
+				printf(" (");
+			} else {
+				printf(", ");
+			}
+			printf("%s", curves[u].sid[v]);
+		}
+		if (v > 1) {
+			printf(")");
+		}
+		printf("\n");
+	}
+}
+
 static int
 is_ign(int c)
 {
@@ -956,6 +1012,22 @@ ec_curve_name(int curve)
 	}
 }
 
+/* see brssl.h */
+int
+get_curve_by_name(const char *str)
+{
+	size_t u, v;
+
+	for (u = 0; curves[u].name; u ++) {
+		for (v = 0; curves[u].sid[v]; v ++) {
+			if (eqstr(curves[u].sid[v], str)) {
+				return curves[u].id;
+			}
+		}
+	}
+	return -1;
+}
+
 /* see brssl.h */
 const char *
 hash_function_name(int id)
diff --git a/tools/skey.c b/tools/skey.c
index 0f672bf..90ecf63 100644
--- a/tools/skey.c
+++ b/tools/skey.c
@@ -31,6 +31,15 @@
 #include "brssl.h"
 #include "bearssl.h"
 
+typedef struct {
+	int print_text;
+	int print_C;
+	const char *rawder;
+	const char *rawpem;
+	const char *pk8der;
+	const char *pk8pem;
+} outspec;
+
 static void
 print_int_text(const char *name, const unsigned char *buf, size_t len)
 {
@@ -63,17 +72,70 @@ print_int_C(const char *name, const unsigned char *buf, size_t len)
 	printf("\n};\n");
 }
 
-static void
-print_rsa(const br_rsa_private_key *sk, int print_text, int print_C)
+static int
+write_to_file(const char *name, const void *data, size_t len)
+{
+	FILE *f;
+
+	f = fopen(name, "wb");
+	if (f == NULL) {
+		fprintf(stderr,
+			"ERROR: cannot open file '%s' for writing\n",
+			name);
+		return 0;
+	}
+	if (fwrite(data, 1, len, f) != len) {
+		fclose(f);
+		fprintf(stderr,
+			"ERROR: cannot write to file '%s'\n",
+			name);
+		return 0;
+	}
+	fclose(f);
+	return 1;
+}
+
+static int
+write_to_pem_file(const char *name,
+	const void *data, size_t len, const char *banner)
+{
+	void *pem;
+	size_t pemlen;
+	int r;
+
+	pemlen = br_pem_encode(NULL, NULL, len, banner, 0);
+	pem = xmalloc(pemlen + 1);
+	br_pem_encode(pem, data, len, banner, 0);
+	r = write_to_file(name, pem, pemlen);
+	xfree(pem);
+	return r;
+}
+
+static int
+print_rsa(const br_rsa_private_key *sk, outspec *os)
 {
-	if (print_text) {
+	int ret;
+	unsigned char *n, *d, *buf;
+	uint32_t e;
+	size_t nlen, dlen, len;
+	br_rsa_compute_modulus cm;
+	br_rsa_compute_pubexp ce;
+	br_rsa_compute_privexp cd;
+	br_rsa_public_key pk;
+	unsigned char ebuf[4];
+
+	n = NULL;
+	d = NULL;
+	buf = NULL;
+	ret = 1;
+	if (os->print_text) {
 		print_int_text("p ", sk->p, sk->plen);
 		print_int_text("q ", sk->q, sk->qlen);
 		print_int_text("dp", sk->dp, sk->dplen);
 		print_int_text("dq", sk->dq, sk->dqlen);
 		print_int_text("iq", sk->iq, sk->iqlen);
 	}
-	if (print_C) {
+	if (os->print_C) {
 		print_int_C("RSA_P", sk->p, sk->plen);
 		print_int_C("RSA_Q", sk->q, sk->qlen);
 		print_int_C("RSA_DP", sk->dp, sk->dplen);
@@ -88,21 +150,174 @@ print_rsa(const br_rsa_private_key *sk, int print_text, int print_C)
 		printf("\t(unsigned char *)RSA_IQ, sizeof RSA_IQ\n");
 		printf("};\n");
 	}
+
+	if (os->rawder == NULL && os->rawpem == NULL
+		&& os->pk8der == NULL && os->pk8pem == NULL)
+	{
+		return ret;
+	}
+
+	cm = br_rsa_compute_modulus_get_default();
+	ce = br_rsa_compute_pubexp_get_default();
+	cd = br_rsa_compute_privexp_get_default();
+	nlen = cm(NULL, sk);
+	if (nlen == 0) {
+		goto print_RSA_error;
+	}
+	n = xmalloc(nlen);
+	if (cm(n, sk) != nlen) {
+		goto print_RSA_error;
+	}
+	e = ce(sk);
+	if (e == 0) {
+		goto print_RSA_error;
+	}
+	dlen = cd(NULL, sk, e);
+	if (dlen == 0) {
+		goto print_RSA_error;
+	}
+	d = xmalloc(dlen);
+	if (cd(d, sk, e) != dlen) {
+		goto print_RSA_error;
+	}
+	ebuf[0] = e >> 24;
+	ebuf[1] = e >> 16;
+	ebuf[2] = e >> 8;
+	ebuf[3] = e;
+	pk.n = n;
+	pk.nlen = nlen;
+	pk.e = ebuf;
+	pk.elen = sizeof ebuf;
+
+	if (os->rawder != NULL || os->rawpem != NULL) {
+		len = br_encode_rsa_raw_der(NULL, sk, &pk, d, dlen);
+		if (len == 0) {
+			goto print_RSA_error;
+		}
+		buf = xmalloc(len);
+		if (br_encode_rsa_raw_der(buf, sk, &pk, d, dlen) != len) {
+			goto print_RSA_error;
+		}
+		if (os->rawder != NULL) {
+			ret &= write_to_file(os->rawder, buf, len);
+		}
+		if (os->rawpem != NULL) {
+			ret &= write_to_pem_file(os->rawpem,
+				buf, len, "RSA PRIVATE KEY");
+		}
+		xfree(buf);
+		buf = NULL;
+	}
+
+	if (os->pk8der != NULL || os->pk8pem != NULL) {
+		len = br_encode_rsa_pkcs8_der(NULL, sk, &pk, d, dlen);
+		if (len == 0) {
+			goto print_RSA_error;
+		}
+		buf = xmalloc(len);
+		if (br_encode_rsa_pkcs8_der(buf, sk, &pk, d, dlen) != len) {
+			goto print_RSA_error;
+		}
+		if (os->pk8der != NULL) {
+			ret &= write_to_file(os->pk8der, buf, len);
+		}
+		if (os->pk8pem != NULL) {
+			ret &= write_to_pem_file(os->pk8pem,
+				buf, len, "PRIVATE KEY");
+		}
+		xfree(buf);
+		buf = NULL;
+	}
+
+print_RSA_exit:
+	xfree(n);
+	xfree(d);
+	xfree(buf);
+	return ret;
+
+print_RSA_error:
+	fprintf(stderr, "ERROR: cannot encode RSA key\n");
+	ret = 0;
+	goto print_RSA_exit;
 }
 
-static void
-print_ec(const br_ec_private_key *sk, int print_text, int print_C)
+static int
+print_ec(const br_ec_private_key *sk, outspec *os)
 {
-	if (print_text) {
+	br_ec_public_key pk;
+	unsigned kbuf[BR_EC_KBUF_PUB_MAX_SIZE];
+	unsigned char *buf;
+	size_t len;
+	int r;
+
+	if (os->print_text) {
 		print_int_text("x", sk->x, sk->xlen);
 	}
-	if (print_C) {
+	if (os->print_C) {
 		print_int_C("EC_X", sk->x, sk->xlen);
 		printf("\nstatic const br_ec_private_key EC = {\n");
 		printf("\t%d,\n", sk->curve);
 		printf("\t(unsigned char *)EC_X, sizeof EC_X\n");
 		printf("};\n");
 	}
+
+	if (os->rawder == NULL && os->rawpem == NULL
+		&& os->pk8der == NULL && os->pk8pem == NULL)
+	{
+		return 1;
+	}
+	if (br_ec_compute_pub(br_ec_get_default(), &pk, kbuf, sk) == 0) {
+		fprintf(stderr,
+			"ERROR: cannot re-encode (unsupported curve)\n");
+		return 0;
+	}
+
+	r = 1;
+	if (os->rawder != NULL || os->rawpem != NULL) {
+		len = br_encode_ec_raw_der(NULL, sk, &pk);
+		if (len == 0) {
+			fprintf(stderr, "ERROR: cannot re-encode"
+				" (unsupported curve)\n");
+			return 0;
+		}
+		buf = xmalloc(len);
+		if (br_encode_ec_raw_der(buf, sk, &pk) != len) {
+			fprintf(stderr, "ERROR: re-encode failure\n");
+			xfree(buf);
+			return 0;
+		}
+		if (os->rawder != NULL) {
+			r &= write_to_file(os->rawder, buf, len);
+		}
+		if (os->rawpem != NULL) {
+			r &= write_to_pem_file(os->rawpem,
+				buf, len, "EC PRIVATE KEY");
+		}
+		xfree(buf);
+	}
+	if (os->pk8der != NULL || os->pk8pem != NULL) {
+		len = br_encode_ec_pkcs8_der(NULL, sk, &pk);
+		if (len == 0) {
+			fprintf(stderr, "ERROR: cannot re-encode"
+				" (unsupported curve)\n");
+			return 0;
+		}
+		buf = xmalloc(len);
+		if (br_encode_ec_pkcs8_der(buf, sk, &pk) != len) {
+			fprintf(stderr, "ERROR: re-encode failure\n");
+			xfree(buf);
+			return 0;
+		}
+		if (os->pk8der != NULL) {
+			r &= write_to_file(os->pk8der, buf, len);
+		}
+		if (os->pk8pem != NULL) {
+			r &= write_to_pem_file(os->pk8pem,
+				buf, len, "PRIVATE KEY");
+		}
+		xfree(buf);
+	}
+	return r;
 }
 
 static int
@@ -158,7 +373,7 @@ parse_rsa_spec(const char *kgen_spec, unsigned *size, uint32_t *pubexp)
 }
 
 static int
-keygen_rsa(unsigned size, uint32_t pubexp, int print_text, int print_C)
+keygen_rsa(unsigned size, uint32_t pubexp, outspec *os)
 {
 	br_hmac_drbg_context rng;
 	br_prng_seeder seeder;
@@ -183,17 +398,72 @@ keygen_rsa(unsigned size, uint32_t pubexp, int print_text, int print_C)
 	if (!r) {
 		fprintf(stderr, "ERROR: RSA key pair generation failed\n");
 	} else {
-		print_rsa(&sk, print_text, print_C);
+		r = print_rsa(&sk, os);
 	}
 	xfree(kbuf_priv);
 	return r;
 }
 
 static int
-decode_key(const unsigned char *buf, size_t len, int print_text, int print_C)
+parse_ec_spec(const char *kgen_spec, int *curve)
+{
+	const char *p;
+
+	*curve = 0;
+	p = kgen_spec;
+	if (*p != 'e' && *p != 'E') {
+		return 0;
+	}
+	p ++;
+	if (*p != 'c' && *p != 'C') {
+		return 0;
+	}
+	p ++;
+	if (*p == 0) {
+		*curve = BR_EC_secp256r1;
+		return 1;
+	}
+	if (*p != ':') {
+		return 0;
+	}
+	*curve = get_curve_by_name(p);
+	return *curve > 0;
+}
+
+static int
+keygen_ec(int curve, outspec *os)
+{
+	br_hmac_drbg_context rng;
+	br_prng_seeder seeder;
+	const br_ec_impl *impl;
+	br_ec_private_key sk;
+	unsigned char kbuf_priv[BR_EC_KBUF_PRIV_MAX_SIZE];
+	size_t len;
+
+	seeder = br_prng_seeder_system(NULL);
+	if (seeder == 0) {
+		fprintf(stderr, "ERROR: no system source of randomness\n");
+		return 0;
+	}
+	br_hmac_drbg_init(&rng, &br_sha256_vtable, NULL, 0);
+	if (!seeder(&rng.vtable)) {
+		fprintf(stderr, "ERROR: system source of randomness failed\n");
+		return 0;
+	}
+	impl = br_ec_get_default();
+	len = br_ec_keygen(&rng.vtable, impl, &sk, kbuf_priv, curve);
+	if (len == 0) {
+		fprintf(stderr, "ERROR: curve is not supported\n");
+		return 0;
+	}
+	return print_ec(&sk, os);
+}
+
+static int
+decode_key(const unsigned char *buf, size_t len, outspec *os)
 {
 	br_skey_decoder_context dc;
-	int err;
+	int err, ret;
 
 	br_skey_decoder_init(&dc);
 	br_skey_decoder_push(&dc, buf, len);
@@ -208,8 +478,9 @@ decode_key(const unsigned char *buf, size_t len, int print_text, int print_C)
 		} else {
 			fprintf(stderr, "  (unknown)\n");
 		}
-		return -1;
+		return 0;
 	}
+	ret = 1;
 	switch (br_skey_decoder_key_type(&dc)) {
 		const br_rsa_private_key *rk;
 		const br_ec_private_key *ek;
@@ -217,23 +488,24 @@ decode_key(const unsigned char *buf, size_t len, int print_text, int print_C)
 	case BR_KEYTYPE_RSA:
 		rk = br_skey_decoder_get_rsa(&dc);
 		printf("RSA key (%lu bits)\n", (unsigned long)rk->n_bitlen);
-		print_rsa(rk, print_text, print_C);
+		ret = print_rsa(rk, os);
 		break;
 
 	case BR_KEYTYPE_EC:
 		ek = br_skey_decoder_get_ec(&dc);
 		printf("EC key (curve = %d: %s)\n",
 			ek->curve, ec_curve_name(ek->curve));
-		print_ec(ek, print_text, print_C);
+		ret = print_ec(ek, os);
 		break;
 
 	default:
 		fprintf(stderr, "Unknown key type: %d\n",
 			br_skey_decoder_key_type(&dc));
-		return -1;
+		ret = 0;
+		break;
 	}
 
-	return 0;
+	return ret;
 }
 
 static void
@@ -244,19 +516,31 @@ usage_skey(void)
 	fprintf(stderr,
 "options:\n");
 	fprintf(stderr,
-"   -q            suppress verbose messages\n");
+"   -q             suppress verbose messages\n");
+	fprintf(stderr,
+"   -text          print private key details (human-readable)\n");
 	fprintf(stderr,
-"   -text         print public key details (human-readable)\n");
+"   -C             print private key details (C code)\n");
 	fprintf(stderr,
-"   -C            print public key details (C code)\n");
+"   -rawder file   save private key in 'file' (raw format, DER)\n");
 	fprintf(stderr,
-"   -gen spec     generate a new key using the provided key specification\n");
+"   -rawpem file   save private key in 'file' (raw format, PEM)\n");
+	fprintf(stderr,
+"   -pk8der file   save private key in 'file' (PKCS#8 format, DER)\n");
+	fprintf(stderr,
+"   -pk8pem file   save private key in 'file' (PKCS#8 format, PEM)\n");
+	fprintf(stderr,
+"   -gen spec      generate a new key using the provided key specification\n");
+	fprintf(stderr,
+"   -list          list known elliptic curve names\n");
 	fprintf(stderr,
 "Key specification begins with a key type, followed by optional parameters\n");
 	fprintf(stderr,
 "that depend on the key type, separated by colon characters:\n");
 	fprintf(stderr,
 "   rsa[:size[:pubexep]]   RSA key (defaults: size = 2048, pubexp = 3)\n");
+	fprintf(stderr,
+"   ec[:curvename]         EC key (default curve: secp256r1)\n");
 }
 
 /* see brssl.h */
@@ -266,7 +550,7 @@ do_skey(int argc, char *argv[])
 	int retcode;
 	int verbose;
 	int i, num_files;
-	int print_text, print_C;
+	outspec os;
 	unsigned char *buf;
 	size_t len;
 	pem_object *pos;
@@ -274,8 +558,12 @@ do_skey(int argc, char *argv[])
 
 	retcode = 0;
 	verbose = 1;
-	print_text = 0;
-	print_C = 0;
+	os.print_text = 0;
+	os.print_C = 0;
+	os.rawder = NULL;
+	os.rawpem = NULL;
+	os.pk8der = NULL;
+	os.pk8pem = NULL;
 	num_files = 0;
 	buf = NULL;
 	pos = NULL;
@@ -294,9 +582,69 @@ do_skey(int argc, char *argv[])
 		} else if (eqstr(arg, "-q") || eqstr(arg, "-quiet")) {
 			verbose = 0;
 		} else if (eqstr(arg, "-text")) {
-			print_text = 1;
+			os.print_text = 1;
 		} else if (eqstr(arg, "-C")) {
-			print_C = 1;
+			os.print_C = 1;
+		} else if (eqstr(arg, "-rawder")) {
+			if (++ i >= argc) {
+				fprintf(stderr,
+					"ERROR: no argument for '-rawder'\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			if (os.rawder != NULL) {
+				fprintf(stderr,
+					"ERROR: multiple '-rawder' options\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			os.rawder = argv[i];
+			argv[i] = NULL;
+		} else if (eqstr(arg, "-rawpem")) {
+			if (++ i >= argc) {
+				fprintf(stderr,
+					"ERROR: no argument for '-rawpem'\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			if (os.rawpem != NULL) {
+				fprintf(stderr,
+					"ERROR: multiple '-rawpem' options\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			os.rawpem = argv[i];
+			argv[i] = NULL;
+		} else if (eqstr(arg, "-pk8der")) {
+			if (++ i >= argc) {
+				fprintf(stderr,
+					"ERROR: no argument for '-pk8der'\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			if (os.pk8der != NULL) {
+				fprintf(stderr,
+					"ERROR: multiple '-pk8der' options\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			os.pk8der = argv[i];
+			argv[i] = NULL;
+		} else if (eqstr(arg, "-pk8pem")) {
+			if (++ i >= argc) {
+				fprintf(stderr,
+					"ERROR: no argument for '-pk8pem'\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			if (os.pk8pem != NULL) {
+				fprintf(stderr,
+					"ERROR: multiple '-pk8pem' options\n");
+				usage_skey();
+				goto skey_exit_error;
+			}
+			os.pk8pem = argv[i];
+			argv[i] = NULL;
 		} else if (eqstr(arg, "-gen")) {
 			if (++ i >= argc) {
 				fprintf(stderr,
@@ -312,6 +660,9 @@ do_skey(int argc, char *argv[])
 			}
 			kgen_spec = argv[i];
 			argv[i] = NULL;
+		} else if (eqstr(arg, "-list")) {
+			list_curves();
+			goto skey_exit;
 		} else {
 			fprintf(stderr, "ERROR: unknown option: '%s'\n", arg);
 			usage_skey();
@@ -321,6 +672,7 @@ do_skey(int argc, char *argv[])
 	if (kgen_spec != NULL) {
 		unsigned rsa_size;
 		uint32_t rsa_pubexp;
+		int curve;
 
 		if (num_files != 0) {
 			fprintf(stderr,
@@ -330,7 +682,13 @@ do_skey(int argc, char *argv[])
 		}
 
 		if (parse_rsa_spec(kgen_spec, &rsa_size, &rsa_pubexp)) {
-			keygen_rsa(rsa_size, rsa_pubexp, print_text, print_C);
+			if (!keygen_rsa(rsa_size, rsa_pubexp, &os)) {
+				goto skey_exit_error;
+			}
+		} else if (parse_ec_spec(kgen_spec, &curve)) {
+			if (!keygen_ec(curve, &os)) {
+				goto skey_exit_error;
+			}
 		} else {
 			fprintf(stderr,
 				"ERROR: unknown key specification: '%s'\n",
@@ -360,7 +718,7 @@ do_skey(int argc, char *argv[])
 				fprintf(stderr, "File '%s': ASN.1/DER object\n",
 					fname);
 			}
-			if (decode_key(buf, len, print_text, print_C) < 0) {
+			if (!decode_key(buf, len, &os)) {
 				goto skey_exit_error;
 			}
 		} else {
@@ -382,9 +740,8 @@ do_skey(int argc, char *argv[])
 					|| eqstr(name, "EC PRIVATE KEY")
 					|| eqstr(name, "PRIVATE KEY"))
 				{
-					if (decode_key(pos[u].data,
-						pos[u].data_len,
-						print_text, print_C) < 0)
+					if (!decode_key(pos[u].data,
+						pos[u].data_len, &os))
 					{
 						goto skey_exit_error;
 					}