New implementation of Curve25519 (using multiplications of words of 15 bits or so...

diff --git a/Makefile b/Makefile
index ac5f241..98fefd5 100644 (file)
--- a/Makefile
+++ b/Makefile
@@ -47,7 +47,7 @@ TESTX509 = testx509
 TESTMATH = testmath
 
 OBJCODEC = $(BUILD)/ccopy.o $(BUILD)/dec16be.o $(BUILD)/dec16le.o $(BUILD)/dec32be.o $(BUILD)/dec32le.o $(BUILD)/dec64be.o $(BUILD)/dec64le.o $(BUILD)/enc16be.o $(BUILD)/enc16le.o $(BUILD)/enc32be.o $(BUILD)/enc32le.o $(BUILD)/enc64be.o $(BUILD)/enc64le.o $(BUILD)/pemdec.o
-OBJEC = $(BUILD)/ec_c25519_i15.o $(BUILD)/ec_curve25519.o $(BUILD)/ec_p256_m15.o $(BUILD)/ec_prime_i15.o $(BUILD)/ec_prime_i31.o $(BUILD)/ec_secp256r1.o $(BUILD)/ec_secp384r1.o $(BUILD)/ec_secp521r1.o $(BUILD)/ecdsa_atr.o $(BUILD)/ecdsa_i15_bits.o $(BUILD)/ecdsa_i15_sign_asn1.o $(BUILD)/ecdsa_i15_sign_raw.o $(BUILD)/ecdsa_i15_vrfy_asn1.o $(BUILD)/ecdsa_i15_vrfy_raw.o $(BUILD)/ecdsa_i31_bits.o $(BUILD)/ecdsa_i31_sign_asn1.o $(BUILD)/ecdsa_i31_sign_raw.o $(BUILD)/ecdsa_i31_vrfy_asn1.o $(BUILD)/ecdsa_i31_vrfy_raw.o $(BUILD)/ecdsa_rta.o
+OBJEC = $(BUILD)/ec_c25519_i15.o $(BUILD)/ec_c25519_m15.o $(BUILD)/ec_curve25519.o $(BUILD)/ec_p256_m15.o $(BUILD)/ec_prime_i15.o $(BUILD)/ec_prime_i31.o $(BUILD)/ec_secp256r1.o $(BUILD)/ec_secp384r1.o $(BUILD)/ec_secp521r1.o $(BUILD)/ecdsa_atr.o $(BUILD)/ecdsa_i15_bits.o $(BUILD)/ecdsa_i15_sign_asn1.o $(BUILD)/ecdsa_i15_sign_raw.o $(BUILD)/ecdsa_i15_vrfy_asn1.o $(BUILD)/ecdsa_i15_vrfy_raw.o $(BUILD)/ecdsa_i31_bits.o $(BUILD)/ecdsa_i31_sign_asn1.o $(BUILD)/ecdsa_i31_sign_raw.o $(BUILD)/ecdsa_i31_vrfy_asn1.o $(BUILD)/ecdsa_i31_vrfy_raw.o $(BUILD)/ecdsa_rta.o
 # $(BUILD)/ec_prime_i31_secp256r1.o $(BUILD)/ec_prime_i31_secp384r1.o $(BUILD)/ec_prime_i31_secp521r1.o
 OBJHASH = $(BUILD)/dig_oid.o $(BUILD)/dig_size.o $(BUILD)/ghash_ctmul.o $(BUILD)/ghash_ctmul32.o $(BUILD)/ghash_ctmul64.o $(BUILD)/md5.o $(BUILD)/md5sha1.o $(BUILD)/multihash.o $(BUILD)/sha1.o $(BUILD)/sha2big.o $(BUILD)/sha2small.o
 OBJINT15 = $(BUILD)/i15_core.o $(BUILD)/i15_ext1.o $(BUILD)/i15_ext2.o
@@ -165,6 +165,9 @@ $(BUILD)/ec_g_secp521r1.o: src/ec/ec_g_secp521r1.c $(HEADERS)
 $(BUILD)/ec_c25519_i15.o: src/ec/ec_c25519_i15.c $(HEADERS)
        $(CC) $(CFLAGS) -c -o $(BUILD)/ec_c25519_i15.o src/ec/ec_c25519_i15.c
 
+$(BUILD)/ec_c25519_m15.o: src/ec/ec_c25519_m15.c $(HEADERS)
+       $(CC) $(CFLAGS) -c -o $(BUILD)/ec_c25519_m15.o src/ec/ec_c25519_m15.c
+
 $(BUILD)/ec_curve25519.o: src/ec/ec_curve25519.c $(HEADERS)
        $(CC) $(CFLAGS) -c -o $(BUILD)/ec_curve25519.o src/ec/ec_curve25519.c
 

diff --git a/inc/bearssl_ec.h b/inc/bearssl_ec.h
index 2c84bad..1ecb4cd 100644 (file)
--- a/inc/bearssl_ec.h
+++ b/inc/bearssl_ec.h
@@ -410,12 +410,12 @@ extern const br_ec_impl br_ec_prime_i31;
 extern const br_ec_impl br_ec_prime_i15;
 
 /**
- * \brief EC implementation "i15" for P-256.
+ * \brief EC implementation "m15" for P-256.
  *
  * This implementation uses specialised code for curve secp256r1 (also
- * known as NIST P-256), with Karatsuba decomposition, and fast modular
- * reduction thanks to the field modulus special format. Only 32-bit
- * multiplications are used (with 32-bit results, not 64-bit).
+ * known as NIST P-256), with optional Karatsuba decomposition, and fast
+ * modular reduction thanks to the field modulus special format. Only
+ * 32-bit multiplications are used (with 32-bit results, not 64-bit).
  */
 extern const br_ec_impl br_ec_p256_m15;
 
@@ -428,6 +428,14 @@ extern const br_ec_impl br_ec_p256_m15;
  */
 extern const br_ec_impl br_ec_c25519_i15;
 
+/**
+ * \brief EC implementation "m15" (specialised code) for Curve25519.
+ *
+ * This implementation uses custom code relying on multiplication of
+ * integers up to 15 bits. The `muladd()` method is not implemented.
+ */
+extern const br_ec_impl br_ec_c25519_m15;
+
 /**
  * \brief Convert a signature from "raw" to "asn1".
  *

diff --git a/src/ec/ec_c25519_i15.c b/src/ec/ec_c25519_i15.c
index 79560ae..6e4c4f8 100644 (file)
--- a/src/ec/ec_c25519_i15.c
+++ b/src/ec/ec_c25519_i15.c
@@ -46,6 +46,27 @@ static const uint16_t C255_R2[] = {
        0x0000
 };
 
+/* obsolete
+#include <stdio.h>
+#include <stdlib.h>
+static void
+print_int_mont(const char *name, const uint16_t *x)
+{
+       uint16_t y[18];
+       unsigned char tmp[32];
+       size_t u;
+
+       printf("%s = ", name);
+       memcpy(y, x, sizeof y);
+       br_i15_from_monty(y, C255_P, P0I);
+       br_i15_encode(tmp, sizeof tmp, y);
+       for (u = 0; u < sizeof tmp; u ++) {
+               printf("%02X", tmp[u]);
+       }
+       printf("\n");
+}
+*/
+
 static const uint16_t C255_A24[] = {
        0x0110,
        0x45D3, 0x0046, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
@@ -194,6 +215,10 @@ api_mul(unsigned char *G, size_t Glen,
        k[31] &= 0x7F;
        k[31] |= 0x40;
 
+       /* obsolete
+       print_int_mont("x1", x1);
+       */
+
        swap = 0;
        for (i = 254; i >= 0; i --) {
                uint32_t kt;
@@ -204,6 +229,13 @@ api_mul(unsigned char *G, size_t Glen,
                cswap(z2, z3, swap);
                swap = kt;
 
+               /* obsolete
+               print_int_mont("x2", x2);
+               print_int_mont("z2", z2);
+               print_int_mont("x3", x3);
+               print_int_mont("z3", z3);
+               */
+
                c255_add(a, x2, z2);
                c255_mul(aa, a, a);
                c255_sub(b, x2, z2);
@@ -213,6 +245,19 @@ api_mul(unsigned char *G, size_t Glen,
                c255_sub(d, x3, z3);
                c255_mul(da, d, a);
                c255_mul(cb, c, b);
+
+               /* obsolete
+               print_int_mont("a ", a);
+               print_int_mont("aa", aa);
+               print_int_mont("b ", b);
+               print_int_mont("bb", bb);
+               print_int_mont("e ", e);
+               print_int_mont("c ", c);
+               print_int_mont("d ", d);
+               print_int_mont("da", da);
+               print_int_mont("cb", cb);
+               */
+
                c255_add(x3, da, cb);
                c255_mul(x3, x3, x3);
                c255_sub(z3, da, cb);
@@ -222,6 +267,13 @@ api_mul(unsigned char *G, size_t Glen,
                c255_mul(z2, C255_A24, e);
                c255_add(z2, z2, aa);
                c255_mul(z2, e, z2);
+
+               /* obsolete
+               print_int_mont("x2", x2);
+               print_int_mont("z2", z2);
+               print_int_mont("x3", x3);
+               print_int_mont("z3", z3);
+               */
        }
        cswap(x2, x3, swap);
        cswap(z2, z3, swap);

diff --git a/src/ec/ec_c25519_m15.c b/src/ec/ec_c25519_m15.c
new file mode 100644 (file)
index 0000000..5079d5e
--- /dev/null
+++ b/src/ec/ec_c25519_m15.c
@@ -0,0 +1,1451 @@
+/*
+ * Copyright (c) 2017 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"
+
+/* obsolete
+#include <stdio.h>
+#include <stdlib.h>
+static void
+print_int(const char *name, const uint32_t *x)
+{
+       size_t u;
+       unsigned char tmp[36];
+
+       printf("%s = ", name);
+       for (u = 0; u < 20; u ++) {
+               if (x[u] > 0x1FFF) {
+                       printf("INVALID:");
+                       for (u = 0; u < 20; u ++) {
+                               printf(" %04X", x[u]);
+                       }
+                       printf("\n");
+                       return;
+               }
+       }
+       memset(tmp, 0, sizeof tmp);
+       for (u = 0; u < 20; u ++) {
+               uint32_t w;
+               int j, k;
+
+               w = x[u];
+               j = 13 * (int)u;
+               k = j & 7;
+               if (k != 0) {
+                       w <<= k;
+                       j -= k;
+               }
+               k = j >> 3;
+               tmp[35 - k] |= (unsigned char)w;
+               tmp[34 - k] |= (unsigned char)(w >> 8);
+               tmp[33 - k] |= (unsigned char)(w >> 16);
+               tmp[32 - k] |= (unsigned char)(w >> 24);
+       }
+       for (u = 4; u < 36; u ++) {
+               printf("%02X", tmp[u]);
+       }
+       printf("\n");
+}
+*/
+
+/*
+ * If BR_NO_ARITH_SHIFT is undefined, or defined to 0, then we _assume_
+ * that right-shifting a signed negative integer copies the sign bit
+ * (arithmetic right-shift). This is "implementation-defined behaviour",
+ * i.e. it is not undefined, but it may differ between compilers. Each
+ * compiler is supposed to document its behaviour in that respect. GCC
+ * explicitly defines that an arithmetic right shift is used. We expect
+ * all other compilers to do the same, because underlying CPU offer an
+ * arithmetic right shift opcode that could not be used otherwise.
+ */
+#if BR_NO_ARITH_SHIFT
+#define ARSH(x, n)   (((uint32_t)(x) >> (n)) \
+                    | ((-((uint32_t)(x) >> 31)) << (32 - (n))))
+#else
+#define ARSH(x, n)   ((*(int32_t *)&(x)) >> (n))
+#endif
+
+/*
+ * Convert an integer from unsigned little-endian encoding to a sequence of
+ * 13-bit words in little-endian order. The final "partial" word is
+ * returned.
+ */
+static uint32_t
+le8_to_le13(uint32_t *dst, const unsigned char *src, size_t len)
+{
+       uint32_t acc;
+       int acc_len;
+
+       acc = 0;
+       acc_len = 0;
+       while (len -- > 0) {
+               acc |= (uint32_t)(*src ++) << acc_len;
+               acc_len += 8;
+               if (acc_len >= 13) {
+                       *dst ++ = acc & 0x1FFF;
+                       acc >>= 13;
+                       acc_len -= 13;
+               }
+       }
+       return acc;
+}
+
+/*
+ * Convert an integer (13-bit words, little-endian) to unsigned
+ * little-endian encoding. The total encoding length is provided; all
+ * the destination bytes will be filled.
+ */
+static void
+le13_to_le8(unsigned char *dst, size_t len, const uint32_t *src)
+{
+       uint32_t acc;
+       int acc_len;
+
+       acc = 0;
+       acc_len = 0;
+       while (len -- > 0) {
+               if (acc_len < 8) {
+                       acc |= (*src ++) << acc_len;
+                       acc_len += 13;
+               }
+               *dst ++ = (unsigned char)acc;
+               acc >>= 8;
+               acc_len -= 8;
+       }
+}
+
+/*
+ * Normalise an array of words to a strict 13 bits per word. Returned
+ * value is the resulting carry. The source (w) and destination (d)
+ * arrays may be identical, but shall not overlap partially.
+ */
+static inline uint32_t
+norm13(uint32_t *d, const uint32_t *w, size_t len)
+{
+       size_t u;
+       uint32_t cc;
+
+       cc = 0;
+       for (u = 0; u < len; u ++) {
+               int32_t z;
+
+               z = w[u] + cc;
+               d[u] = z & 0x1FFF;
+               cc = ARSH(z, 13);
+       }
+       return cc;
+}
+
+/*
+ * mul20() multiplies two 260-bit integers together. Each word must fit
+ * on 13 bits; source operands use 20 words, destination operand
+ * receives 40 words. All overlaps allowed.
+ *
+ * square20() computes the square of a 260-bit integer. Each word must
+ * fit on 13 bits; source operand uses 20 words, destination operand
+ * receives 40 words. All overlaps allowed.
+ */
+
+#if BR_SLOW_MUL15
+
+static void
+mul20(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+       /*
+        * Two-level Karatsuba: turns a 20x20 multiplication into
+        * nine 5x5 multiplications. We use 13-bit words but do not
+        * propagate carries immediately, so words may expand:
+        *
+        *  - First Karatsuba decomposition turns the 20x20 mul on
+        *    13-bit words into three 10x10 muls, two on 13-bit words
+        *    and one on 14-bit words.
+        *
+        *  - Second Karatsuba decomposition further splits these into:
+        *
+        *     * four 5x5 muls on 13-bit words
+        *     * four 5x5 muls on 14-bit words
+        *     * one 5x5 mul on 15-bit words
+        *
+        * Highest word value is 8191, 16382 or 32764, for 13-bit, 14-bit
+        * or 15-bit words, respectively.
+        */
+       uint32_t u[45], v[45], w[90];
+       uint32_t cc;
+       int i;
+
+#define ZADD(dw, d_off, s1w, s1_off, s2w, s2_off)   do { \
+               (dw)[5 * (d_off) + 0] = (s1w)[5 * (s1_off) + 0] \
+                       + (s2w)[5 * (s2_off) + 0]; \
+               (dw)[5 * (d_off) + 1] = (s1w)[5 * (s1_off) + 1] \
+                       + (s2w)[5 * (s2_off) + 1]; \
+               (dw)[5 * (d_off) + 2] = (s1w)[5 * (s1_off) + 2] \
+                       + (s2w)[5 * (s2_off) + 2]; \
+               (dw)[5 * (d_off) + 3] = (s1w)[5 * (s1_off) + 3] \
+                       + (s2w)[5 * (s2_off) + 3]; \
+               (dw)[5 * (d_off) + 4] = (s1w)[5 * (s1_off) + 4] \
+                       + (s2w)[5 * (s2_off) + 4]; \
+       } while (0)
+
+#define ZADDT(dw, d_off, sw, s_off)   do { \
+               (dw)[5 * (d_off) + 0] += (sw)[5 * (s_off) + 0]; \
+               (dw)[5 * (d_off) + 1] += (sw)[5 * (s_off) + 1]; \
+               (dw)[5 * (d_off) + 2] += (sw)[5 * (s_off) + 2]; \
+               (dw)[5 * (d_off) + 3] += (sw)[5 * (s_off) + 3]; \
+               (dw)[5 * (d_off) + 4] += (sw)[5 * (s_off) + 4]; \
+       } while (0)
+
+#define ZSUB2F(dw, d_off, s1w, s1_off, s2w, s2_off)   do { \
+               (dw)[5 * (d_off) + 0] -= (s1w)[5 * (s1_off) + 0] \
+                       + (s2w)[5 * (s2_off) + 0]; \
+               (dw)[5 * (d_off) + 1] -= (s1w)[5 * (s1_off) + 1] \
+                       + (s2w)[5 * (s2_off) + 1]; \
+               (dw)[5 * (d_off) + 2] -= (s1w)[5 * (s1_off) + 2] \
+                       + (s2w)[5 * (s2_off) + 2]; \
+               (dw)[5 * (d_off) + 3] -= (s1w)[5 * (s1_off) + 3] \
+                       + (s2w)[5 * (s2_off) + 3]; \
+               (dw)[5 * (d_off) + 4] -= (s1w)[5 * (s1_off) + 4] \
+                       + (s2w)[5 * (s2_off) + 4]; \
+       } while (0)
+
+#define CPR1(w, cprcc)   do { \
+               uint32_t cprz = (w) + cprcc; \
+               (w) = cprz & 0x1FFF; \
+               cprcc = cprz >> 13; \
+       } while (0)
+
+#define CPR(dw, d_off)   do { \
+               uint32_t cprcc; \
+               cprcc = 0; \
+               CPR1((dw)[(d_off) + 0], cprcc); \
+               CPR1((dw)[(d_off) + 1], cprcc); \
+               CPR1((dw)[(d_off) + 2], cprcc); \
+               CPR1((dw)[(d_off) + 3], cprcc); \
+               CPR1((dw)[(d_off) + 4], cprcc); \
+               CPR1((dw)[(d_off) + 5], cprcc); \
+               CPR1((dw)[(d_off) + 6], cprcc); \
+               CPR1((dw)[(d_off) + 7], cprcc); \
+               CPR1((dw)[(d_off) + 8], cprcc); \
+               (dw)[(d_off) + 9] = cprcc; \
+       } while (0)
+
+       memcpy(u, a, 20 * sizeof *a);
+       ZADD(u, 4, a, 0, a, 1);
+       ZADD(u, 5, a, 2, a, 3);
+       ZADD(u, 6, a, 0, a, 2);
+       ZADD(u, 7, a, 1, a, 3);
+       ZADD(u, 8, u, 6, u, 7);
+
+       memcpy(v, b, 20 * sizeof *b);
+       ZADD(v, 4, b, 0, b, 1);
+       ZADD(v, 5, b, 2, b, 3);
+       ZADD(v, 6, b, 0, b, 2);
+       ZADD(v, 7, b, 1, b, 3);
+       ZADD(v, 8, v, 6, v, 7);
+
+       /*
+        * Do the eight first 8x8 muls. Source words are at most 16382
+        * each, so we can add product results together "as is" in 32-bit
+        * words.
+        */
+       for (i = 0; i < 40; i += 5) {
+               w[(i << 1) + 0] = MUL15(u[i + 0], v[i + 0]);
+               w[(i << 1) + 1] = MUL15(u[i + 0], v[i + 1])
+                       + MUL15(u[i + 1], v[i + 0]);
+               w[(i << 1) + 2] = MUL15(u[i + 0], v[i + 2])
+                       + MUL15(u[i + 1], v[i + 1])
+                       + MUL15(u[i + 2], v[i + 0]);
+               w[(i << 1) + 3] = MUL15(u[i + 0], v[i + 3])
+                       + MUL15(u[i + 1], v[i + 2])
+                       + MUL15(u[i + 2], v[i + 1])
+                       + MUL15(u[i + 3], v[i + 0]);
+               w[(i << 1) + 4] = MUL15(u[i + 0], v[i + 4])
+                       + MUL15(u[i + 1], v[i + 3])
+                       + MUL15(u[i + 2], v[i + 2])
+                       + MUL15(u[i + 3], v[i + 1])
+                       + MUL15(u[i + 4], v[i + 0]);
+               w[(i << 1) + 5] = MUL15(u[i + 1], v[i + 4])
+                       + MUL15(u[i + 2], v[i + 3])
+                       + MUL15(u[i + 3], v[i + 2])
+                       + MUL15(u[i + 4], v[i + 1]);
+               w[(i << 1) + 6] = MUL15(u[i + 2], v[i + 4])
+                       + MUL15(u[i + 3], v[i + 3])
+                       + MUL15(u[i + 4], v[i + 2]);
+               w[(i << 1) + 7] = MUL15(u[i + 3], v[i + 4])
+                       + MUL15(u[i + 4], v[i + 3]);
+               w[(i << 1) + 8] = MUL15(u[i + 4], v[i + 4]);
+               w[(i << 1) + 9] = 0;
+       }
+
+       /*
+        * For the 9th multiplication, source words are up to 32764,
+        * so we must do some carry propagation. If we add up to
+        * 4 products and the carry is no more than 524224, then the
+        * result fits in 32 bits, and the next carry will be no more
+        * than 524224 (because 4*(32764^2)+524224 < 8192*524225).
+        *
+        * We thus just skip one of the products in the middle word,
+        * then do a carry propagation (this reduces words to 13 bits
+        * each, except possibly the last, which may use up to 17 bits
+        * or so), then add the missing product.
+        */
+       w[80 + 0] = MUL15(u[40 + 0], v[40 + 0]);
+       w[80 + 1] = MUL15(u[40 + 0], v[40 + 1])
+               + MUL15(u[40 + 1], v[40 + 0]);
+       w[80 + 2] = MUL15(u[40 + 0], v[40 + 2])
+               + MUL15(u[40 + 1], v[40 + 1])
+               + MUL15(u[40 + 2], v[40 + 0]);
+       w[80 + 3] = MUL15(u[40 + 0], v[40 + 3])
+               + MUL15(u[40 + 1], v[40 + 2])
+               + MUL15(u[40 + 2], v[40 + 1])
+               + MUL15(u[40 + 3], v[40 + 0]);
+       w[80 + 4] = MUL15(u[40 + 0], v[40 + 4])
+               + MUL15(u[40 + 1], v[40 + 3])
+               + MUL15(u[40 + 2], v[40 + 2])
+               + MUL15(u[40 + 3], v[40 + 1]);
+               /* + MUL15(u[40 + 4], v[40 + 0]) */
+       w[80 + 5] = MUL15(u[40 + 1], v[40 + 4])
+               + MUL15(u[40 + 2], v[40 + 3])
+               + MUL15(u[40 + 3], v[40 + 2])
+               + MUL15(u[40 + 4], v[40 + 1]);
+       w[80 + 6] = MUL15(u[40 + 2], v[40 + 4])
+               + MUL15(u[40 + 3], v[40 + 3])
+               + MUL15(u[40 + 4], v[40 + 2]);
+       w[80 + 7] = MUL15(u[40 + 3], v[40 + 4])
+               + MUL15(u[40 + 4], v[40 + 3]);
+       w[80 + 8] = MUL15(u[40 + 4], v[40 + 4]);
+
+       CPR(w, 80);
+
+       w[80 + 4] += MUL15(u[40 + 4], v[40 + 0]);
+
+       /*
+        * The products on 14-bit words in slots 6 and 7 yield values
+        * up to 5*(16382^2) each, and we need to subtract two such
+        * values from the higher word. We need the subtraction to fit
+        * in a _signed_ 32-bit integer, i.e. 31 bits + a sign bit.
+        * However, 10*(16382^2) does not fit. So we must perform a
+        * bit of reduction here.
+        */
+       CPR(w, 60);
+       CPR(w, 70);
+
+       /*
+        * Recompose results.
+        */
+
+       /* 0..1*0..1 into 0..3 */
+       ZSUB2F(w, 8, w, 0, w, 2);
+       ZSUB2F(w, 9, w, 1, w, 3);
+       ZADDT(w, 1, w, 8);
+       ZADDT(w, 2, w, 9);
+
+       /* 2..3*2..3 into 4..7 */
+       ZSUB2F(w, 10, w, 4, w, 6);
+       ZSUB2F(w, 11, w, 5, w, 7);
+       ZADDT(w, 5, w, 10);
+       ZADDT(w, 6, w, 11);
+
+       /* (0..1+2..3)*(0..1+2..3) into 12..15 */
+       ZSUB2F(w, 16, w, 12, w, 14);
+       ZSUB2F(w, 17, w, 13, w, 15);
+       ZADDT(w, 13, w, 16);
+       ZADDT(w, 14, w, 17);
+
+       /* first-level recomposition */
+       ZSUB2F(w, 12, w, 0, w, 4);
+       ZSUB2F(w, 13, w, 1, w, 5);
+       ZSUB2F(w, 14, w, 2, w, 6);
+       ZSUB2F(w, 15, w, 3, w, 7);
+       ZADDT(w, 2, w, 12);
+       ZADDT(w, 3, w, 13);
+       ZADDT(w, 4, w, 14);
+       ZADDT(w, 5, w, 15);
+
+       /*
+        * Perform carry propagation to bring all words down to 13 bits.
+        */
+       cc = norm13(d, w, 40);
+       d[39] += (cc << 13);
+
+#undef ZADD
+#undef ZADDT
+#undef ZSUB2F
+#undef CPR1
+#undef CPR
+}
+
+static inline void
+square20(uint32_t *d, const uint32_t *a)
+{
+       mul20(d, a, a);
+}
+
+#else
+
+static void
+mul20(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+       uint32_t t[39];
+
+       t[ 0] = MUL15(a[ 0], b[ 0]);
+       t[ 1] = MUL15(a[ 0], b[ 1])
+               + MUL15(a[ 1], b[ 0]);
+       t[ 2] = MUL15(a[ 0], b[ 2])
+               + MUL15(a[ 1], b[ 1])
+               + MUL15(a[ 2], b[ 0]);
+       t[ 3] = MUL15(a[ 0], b[ 3])
+               + MUL15(a[ 1], b[ 2])
+               + MUL15(a[ 2], b[ 1])
+               + MUL15(a[ 3], b[ 0]);
+       t[ 4] = MUL15(a[ 0], b[ 4])
+               + MUL15(a[ 1], b[ 3])
+               + MUL15(a[ 2], b[ 2])
+               + MUL15(a[ 3], b[ 1])
+               + MUL15(a[ 4], b[ 0]);
+       t[ 5] = MUL15(a[ 0], b[ 5])
+               + MUL15(a[ 1], b[ 4])
+               + MUL15(a[ 2], b[ 3])
+               + MUL15(a[ 3], b[ 2])
+               + MUL15(a[ 4], b[ 1])
+               + MUL15(a[ 5], b[ 0]);
+       t[ 6] = MUL15(a[ 0], b[ 6])
+               + MUL15(a[ 1], b[ 5])
+               + MUL15(a[ 2], b[ 4])
+               + MUL15(a[ 3], b[ 3])
+               + MUL15(a[ 4], b[ 2])
+               + MUL15(a[ 5], b[ 1])
+               + MUL15(a[ 6], b[ 0]);
+       t[ 7] = MUL15(a[ 0], b[ 7])
+               + MUL15(a[ 1], b[ 6])
+               + MUL15(a[ 2], b[ 5])
+               + MUL15(a[ 3], b[ 4])
+               + MUL15(a[ 4], b[ 3])
+               + MUL15(a[ 5], b[ 2])
+               + MUL15(a[ 6], b[ 1])
+               + MUL15(a[ 7], b[ 0]);
+       t[ 8] = MUL15(a[ 0], b[ 8])
+               + MUL15(a[ 1], b[ 7])
+               + MUL15(a[ 2], b[ 6])
+               + MUL15(a[ 3], b[ 5])
+               + MUL15(a[ 4], b[ 4])
+               + MUL15(a[ 5], b[ 3])
+               + MUL15(a[ 6], b[ 2])
+               + MUL15(a[ 7], b[ 1])
+               + MUL15(a[ 8], b[ 0]);
+       t[ 9] = MUL15(a[ 0], b[ 9])
+               + MUL15(a[ 1], b[ 8])
+               + MUL15(a[ 2], b[ 7])
+               + MUL15(a[ 3], b[ 6])
+               + MUL15(a[ 4], b[ 5])
+               + MUL15(a[ 5], b[ 4])
+               + MUL15(a[ 6], b[ 3])
+               + MUL15(a[ 7], b[ 2])
+               + MUL15(a[ 8], b[ 1])
+               + MUL15(a[ 9], b[ 0]);
+       t[10] = MUL15(a[ 0], b[10])
+               + MUL15(a[ 1], b[ 9])
+               + MUL15(a[ 2], b[ 8])
+               + MUL15(a[ 3], b[ 7])
+               + MUL15(a[ 4], b[ 6])
+               + MUL15(a[ 5], b[ 5])
+               + MUL15(a[ 6], b[ 4])
+               + MUL15(a[ 7], b[ 3])
+               + MUL15(a[ 8], b[ 2])
+               + MUL15(a[ 9], b[ 1])
+               + MUL15(a[10], b[ 0]);
+       t[11] = MUL15(a[ 0], b[11])
+               + MUL15(a[ 1], b[10])
+               + MUL15(a[ 2], b[ 9])
+               + MUL15(a[ 3], b[ 8])
+               + MUL15(a[ 4], b[ 7])
+               + MUL15(a[ 5], b[ 6])
+               + MUL15(a[ 6], b[ 5])
+               + MUL15(a[ 7], b[ 4])
+               + MUL15(a[ 8], b[ 3])
+               + MUL15(a[ 9], b[ 2])
+               + MUL15(a[10], b[ 1])
+               + MUL15(a[11], b[ 0]);
+       t[12] = MUL15(a[ 0], b[12])
+               + MUL15(a[ 1], b[11])
+               + MUL15(a[ 2], b[10])
+               + MUL15(a[ 3], b[ 9])
+               + MUL15(a[ 4], b[ 8])
+               + MUL15(a[ 5], b[ 7])
+               + MUL15(a[ 6], b[ 6])
+               + MUL15(a[ 7], b[ 5])
+               + MUL15(a[ 8], b[ 4])
+               + MUL15(a[ 9], b[ 3])
+               + MUL15(a[10], b[ 2])
+               + MUL15(a[11], b[ 1])
+               + MUL15(a[12], b[ 0]);
+       t[13] = MUL15(a[ 0], b[13])
+               + MUL15(a[ 1], b[12])
+               + MUL15(a[ 2], b[11])
+               + MUL15(a[ 3], b[10])
+               + MUL15(a[ 4], b[ 9])
+               + MUL15(a[ 5], b[ 8])
+               + MUL15(a[ 6], b[ 7])
+               + MUL15(a[ 7], b[ 6])
+               + MUL15(a[ 8], b[ 5])
+               + MUL15(a[ 9], b[ 4])
+               + MUL15(a[10], b[ 3])
+               + MUL15(a[11], b[ 2])
+               + MUL15(a[12], b[ 1])
+               + MUL15(a[13], b[ 0]);
+       t[14] = MUL15(a[ 0], b[14])
+               + MUL15(a[ 1], b[13])
+               + MUL15(a[ 2], b[12])
+               + MUL15(a[ 3], b[11])
+               + MUL15(a[ 4], b[10])
+               + MUL15(a[ 5], b[ 9])
+               + MUL15(a[ 6], b[ 8])
+               + MUL15(a[ 7], b[ 7])
+               + MUL15(a[ 8], b[ 6])
+               + MUL15(a[ 9], b[ 5])
+               + MUL15(a[10], b[ 4])
+               + MUL15(a[11], b[ 3])
+               + MUL15(a[12], b[ 2])
+               + MUL15(a[13], b[ 1])
+               + MUL15(a[14], b[ 0]);
+       t[15] = MUL15(a[ 0], b[15])
+               + MUL15(a[ 1], b[14])
+               + MUL15(a[ 2], b[13])
+               + MUL15(a[ 3], b[12])
+               + MUL15(a[ 4], b[11])
+               + MUL15(a[ 5], b[10])
+               + MUL15(a[ 6], b[ 9])
+               + MUL15(a[ 7], b[ 8])
+               + MUL15(a[ 8], b[ 7])
+               + MUL15(a[ 9], b[ 6])
+               + MUL15(a[10], b[ 5])
+               + MUL15(a[11], b[ 4])
+               + MUL15(a[12], b[ 3])
+               + MUL15(a[13], b[ 2])
+               + MUL15(a[14], b[ 1])
+               + MUL15(a[15], b[ 0]);
+       t[16] = MUL15(a[ 0], b[16])
+               + MUL15(a[ 1], b[15])
+               + MUL15(a[ 2], b[14])
+               + MUL15(a[ 3], b[13])
+               + MUL15(a[ 4], b[12])
+               + MUL15(a[ 5], b[11])
+               + MUL15(a[ 6], b[10])
+               + MUL15(a[ 7], b[ 9])
+               + MUL15(a[ 8], b[ 8])
+               + MUL15(a[ 9], b[ 7])
+               + MUL15(a[10], b[ 6])
+               + MUL15(a[11], b[ 5])
+               + MUL15(a[12], b[ 4])
+               + MUL15(a[13], b[ 3])
+               + MUL15(a[14], b[ 2])
+               + MUL15(a[15], b[ 1])
+               + MUL15(a[16], b[ 0]);
+       t[17] = MUL15(a[ 0], b[17])
+               + MUL15(a[ 1], b[16])
+               + MUL15(a[ 2], b[15])
+               + MUL15(a[ 3], b[14])
+               + MUL15(a[ 4], b[13])
+               + MUL15(a[ 5], b[12])
+               + MUL15(a[ 6], b[11])
+               + MUL15(a[ 7], b[10])
+               + MUL15(a[ 8], b[ 9])
+               + MUL15(a[ 9], b[ 8])
+               + MUL15(a[10], b[ 7])
+               + MUL15(a[11], b[ 6])
+               + MUL15(a[12], b[ 5])
+               + MUL15(a[13], b[ 4])
+               + MUL15(a[14], b[ 3])
+               + MUL15(a[15], b[ 2])
+               + MUL15(a[16], b[ 1])
+               + MUL15(a[17], b[ 0]);
+       t[18] = MUL15(a[ 0], b[18])
+               + MUL15(a[ 1], b[17])
+               + MUL15(a[ 2], b[16])
+               + MUL15(a[ 3], b[15])
+               + MUL15(a[ 4], b[14])
+               + MUL15(a[ 5], b[13])
+               + MUL15(a[ 6], b[12])
+               + MUL15(a[ 7], b[11])
+               + MUL15(a[ 8], b[10])
+               + MUL15(a[ 9], b[ 9])
+               + MUL15(a[10], b[ 8])
+               + MUL15(a[11], b[ 7])
+               + MUL15(a[12], b[ 6])
+               + MUL15(a[13], b[ 5])
+               + MUL15(a[14], b[ 4])
+               + MUL15(a[15], b[ 3])
+               + MUL15(a[16], b[ 2])
+               + MUL15(a[17], b[ 1])
+               + MUL15(a[18], b[ 0]);
+       t[19] = MUL15(a[ 0], b[19])
+               + MUL15(a[ 1], b[18])
+               + MUL15(a[ 2], b[17])
+               + MUL15(a[ 3], b[16])
+               + MUL15(a[ 4], b[15])
+               + MUL15(a[ 5], b[14])
+               + MUL15(a[ 6], b[13])
+               + MUL15(a[ 7], b[12])
+               + MUL15(a[ 8], b[11])
+               + MUL15(a[ 9], b[10])
+               + MUL15(a[10], b[ 9])
+               + MUL15(a[11], b[ 8])
+               + MUL15(a[12], b[ 7])
+               + MUL15(a[13], b[ 6])
+               + MUL15(a[14], b[ 5])
+               + MUL15(a[15], b[ 4])
+               + MUL15(a[16], b[ 3])
+               + MUL15(a[17], b[ 2])
+               + MUL15(a[18], b[ 1])
+               + MUL15(a[19], b[ 0]);
+       t[20] = MUL15(a[ 1], b[19])
+               + MUL15(a[ 2], b[18])
+               + MUL15(a[ 3], b[17])
+               + MUL15(a[ 4], b[16])
+               + MUL15(a[ 5], b[15])
+               + MUL15(a[ 6], b[14])
+               + MUL15(a[ 7], b[13])
+               + MUL15(a[ 8], b[12])
+               + MUL15(a[ 9], b[11])
+               + MUL15(a[10], b[10])
+               + MUL15(a[11], b[ 9])
+               + MUL15(a[12], b[ 8])
+               + MUL15(a[13], b[ 7])
+               + MUL15(a[14], b[ 6])
+               + MUL15(a[15], b[ 5])
+               + MUL15(a[16], b[ 4])
+               + MUL15(a[17], b[ 3])
+               + MUL15(a[18], b[ 2])
+               + MUL15(a[19], b[ 1]);
+       t[21] = MUL15(a[ 2], b[19])
+               + MUL15(a[ 3], b[18])
+               + MUL15(a[ 4], b[17])
+               + MUL15(a[ 5], b[16])
+               + MUL15(a[ 6], b[15])
+               + MUL15(a[ 7], b[14])
+               + MUL15(a[ 8], b[13])
+               + MUL15(a[ 9], b[12])
+               + MUL15(a[10], b[11])
+               + MUL15(a[11], b[10])
+               + MUL15(a[12], b[ 9])
+               + MUL15(a[13], b[ 8])
+               + MUL15(a[14], b[ 7])
+               + MUL15(a[15], b[ 6])
+               + MUL15(a[16], b[ 5])
+               + MUL15(a[17], b[ 4])
+               + MUL15(a[18], b[ 3])
+               + MUL15(a[19], b[ 2]);
+       t[22] = MUL15(a[ 3], b[19])
+               + MUL15(a[ 4], b[18])
+               + MUL15(a[ 5], b[17])
+               + MUL15(a[ 6], b[16])
+               + MUL15(a[ 7], b[15])
+               + MUL15(a[ 8], b[14])
+               + MUL15(a[ 9], b[13])
+               + MUL15(a[10], b[12])
+               + MUL15(a[11], b[11])
+               + MUL15(a[12], b[10])
+               + MUL15(a[13], b[ 9])
+               + MUL15(a[14], b[ 8])
+               + MUL15(a[15], b[ 7])
+               + MUL15(a[16], b[ 6])
+               + MUL15(a[17], b[ 5])
+               + MUL15(a[18], b[ 4])
+               + MUL15(a[19], b[ 3]);
+       t[23] = MUL15(a[ 4], b[19])
+               + MUL15(a[ 5], b[18])
+               + MUL15(a[ 6], b[17])
+               + MUL15(a[ 7], b[16])
+               + MUL15(a[ 8], b[15])
+               + MUL15(a[ 9], b[14])
+               + MUL15(a[10], b[13])
+               + MUL15(a[11], b[12])
+               + MUL15(a[12], b[11])
+               + MUL15(a[13], b[10])
+               + MUL15(a[14], b[ 9])
+               + MUL15(a[15], b[ 8])
+               + MUL15(a[16], b[ 7])
+               + MUL15(a[17], b[ 6])
+               + MUL15(a[18], b[ 5])
+               + MUL15(a[19], b[ 4]);
+       t[24] = MUL15(a[ 5], b[19])
+               + MUL15(a[ 6], b[18])
+               + MUL15(a[ 7], b[17])
+               + MUL15(a[ 8], b[16])
+               + MUL15(a[ 9], b[15])
+               + MUL15(a[10], b[14])
+               + MUL15(a[11], b[13])
+               + MUL15(a[12], b[12])
+               + MUL15(a[13], b[11])
+               + MUL15(a[14], b[10])
+               + MUL15(a[15], b[ 9])
+               + MUL15(a[16], b[ 8])
+               + MUL15(a[17], b[ 7])
+               + MUL15(a[18], b[ 6])
+               + MUL15(a[19], b[ 5]);
+       t[25] = MUL15(a[ 6], b[19])
+               + MUL15(a[ 7], b[18])
+               + MUL15(a[ 8], b[17])
+               + MUL15(a[ 9], b[16])
+               + MUL15(a[10], b[15])
+               + MUL15(a[11], b[14])
+               + MUL15(a[12], b[13])
+               + MUL15(a[13], b[12])
+               + MUL15(a[14], b[11])
+               + MUL15(a[15], b[10])
+               + MUL15(a[16], b[ 9])
+               + MUL15(a[17], b[ 8])
+               + MUL15(a[18], b[ 7])
+               + MUL15(a[19], b[ 6]);
+       t[26] = MUL15(a[ 7], b[19])
+               + MUL15(a[ 8], b[18])
+               + MUL15(a[ 9], b[17])
+               + MUL15(a[10], b[16])
+               + MUL15(a[11], b[15])
+               + MUL15(a[12], b[14])
+               + MUL15(a[13], b[13])
+               + MUL15(a[14], b[12])
+               + MUL15(a[15], b[11])
+               + MUL15(a[16], b[10])
+               + MUL15(a[17], b[ 9])
+               + MUL15(a[18], b[ 8])
+               + MUL15(a[19], b[ 7]);
+       t[27] = MUL15(a[ 8], b[19])
+               + MUL15(a[ 9], b[18])
+               + MUL15(a[10], b[17])
+               + MUL15(a[11], b[16])
+               + MUL15(a[12], b[15])
+               + MUL15(a[13], b[14])
+               + MUL15(a[14], b[13])
+               + MUL15(a[15], b[12])
+               + MUL15(a[16], b[11])
+               + MUL15(a[17], b[10])
+               + MUL15(a[18], b[ 9])
+               + MUL15(a[19], b[ 8]);
+       t[28] = MUL15(a[ 9], b[19])
+               + MUL15(a[10], b[18])
+               + MUL15(a[11], b[17])
+               + MUL15(a[12], b[16])
+               + MUL15(a[13], b[15])
+               + MUL15(a[14], b[14])
+               + MUL15(a[15], b[13])
+               + MUL15(a[16], b[12])
+               + MUL15(a[17], b[11])
+               + MUL15(a[18], b[10])
+               + MUL15(a[19], b[ 9]);
+       t[29] = MUL15(a[10], b[19])
+               + MUL15(a[11], b[18])
+               + MUL15(a[12], b[17])
+               + MUL15(a[13], b[16])
+               + MUL15(a[14], b[15])
+               + MUL15(a[15], b[14])
+               + MUL15(a[16], b[13])
+               + MUL15(a[17], b[12])
+               + MUL15(a[18], b[11])
+               + MUL15(a[19], b[10]);
+       t[30] = MUL15(a[11], b[19])
+               + MUL15(a[12], b[18])
+               + MUL15(a[13], b[17])
+               + MUL15(a[14], b[16])
+               + MUL15(a[15], b[15])
+               + MUL15(a[16], b[14])
+               + MUL15(a[17], b[13])
+               + MUL15(a[18], b[12])
+               + MUL15(a[19], b[11]);
+       t[31] = MUL15(a[12], b[19])
+               + MUL15(a[13], b[18])
+               + MUL15(a[14], b[17])
+               + MUL15(a[15], b[16])
+               + MUL15(a[16], b[15])
+               + MUL15(a[17], b[14])
+               + MUL15(a[18], b[13])
+               + MUL15(a[19], b[12]);
+       t[32] = MUL15(a[13], b[19])
+               + MUL15(a[14], b[18])
+               + MUL15(a[15], b[17])
+               + MUL15(a[16], b[16])
+               + MUL15(a[17], b[15])
+               + MUL15(a[18], b[14])
+               + MUL15(a[19], b[13]);
+       t[33] = MUL15(a[14], b[19])
+               + MUL15(a[15], b[18])
+               + MUL15(a[16], b[17])
+               + MUL15(a[17], b[16])
+               + MUL15(a[18], b[15])
+               + MUL15(a[19], b[14]);
+       t[34] = MUL15(a[15], b[19])
+               + MUL15(a[16], b[18])
+               + MUL15(a[17], b[17])
+               + MUL15(a[18], b[16])
+               + MUL15(a[19], b[15]);
+       t[35] = MUL15(a[16], b[19])
+               + MUL15(a[17], b[18])
+               + MUL15(a[18], b[17])
+               + MUL15(a[19], b[16]);
+       t[36] = MUL15(a[17], b[19])
+               + MUL15(a[18], b[18])
+               + MUL15(a[19], b[17]);
+       t[37] = MUL15(a[18], b[19])
+               + MUL15(a[19], b[18]);
+       t[38] = MUL15(a[19], b[19]);
+       d[39] = norm13(d, t, 39);
+}
+
+static void
+square20(uint32_t *d, const uint32_t *a)
+{
+       uint32_t t[39];
+
+       t[ 0] = MUL15(a[ 0], a[ 0]);
+       t[ 1] = ((MUL15(a[ 0], a[ 1])) << 1);
+       t[ 2] = MUL15(a[ 1], a[ 1])
+               + ((MUL15(a[ 0], a[ 2])) << 1);
+       t[ 3] = ((MUL15(a[ 0], a[ 3])
+               + MUL15(a[ 1], a[ 2])) << 1);
+       t[ 4] = MUL15(a[ 2], a[ 2])
+               + ((MUL15(a[ 0], a[ 4])
+               + MUL15(a[ 1], a[ 3])) << 1);
+       t[ 5] = ((MUL15(a[ 0], a[ 5])
+               + MUL15(a[ 1], a[ 4])
+               + MUL15(a[ 2], a[ 3])) << 1);
+       t[ 6] = MUL15(a[ 3], a[ 3])
+               + ((MUL15(a[ 0], a[ 6])
+               + MUL15(a[ 1], a[ 5])
+               + MUL15(a[ 2], a[ 4])) << 1);
+       t[ 7] = ((MUL15(a[ 0], a[ 7])
+               + MUL15(a[ 1], a[ 6])
+               + MUL15(a[ 2], a[ 5])
+               + MUL15(a[ 3], a[ 4])) << 1);
+       t[ 8] = MUL15(a[ 4], a[ 4])
+               + ((MUL15(a[ 0], a[ 8])
+               + MUL15(a[ 1], a[ 7])
+               + MUL15(a[ 2], a[ 6])
+               + MUL15(a[ 3], a[ 5])) << 1);
+       t[ 9] = ((MUL15(a[ 0], a[ 9])
+               + MUL15(a[ 1], a[ 8])
+               + MUL15(a[ 2], a[ 7])
+               + MUL15(a[ 3], a[ 6])
+               + MUL15(a[ 4], a[ 5])) << 1);
+       t[10] = MUL15(a[ 5], a[ 5])
+               + ((MUL15(a[ 0], a[10])
+               + MUL15(a[ 1], a[ 9])
+               + MUL15(a[ 2], a[ 8])
+               + MUL15(a[ 3], a[ 7])
+               + MUL15(a[ 4], a[ 6])) << 1);
+       t[11] = ((MUL15(a[ 0], a[11])
+               + MUL15(a[ 1], a[10])
+               + MUL15(a[ 2], a[ 9])
+               + MUL15(a[ 3], a[ 8])
+               + MUL15(a[ 4], a[ 7])
+               + MUL15(a[ 5], a[ 6])) << 1);
+       t[12] = MUL15(a[ 6], a[ 6])
+               + ((MUL15(a[ 0], a[12])
+               + MUL15(a[ 1], a[11])
+               + MUL15(a[ 2], a[10])
+               + MUL15(a[ 3], a[ 9])
+               + MUL15(a[ 4], a[ 8])
+               + MUL15(a[ 5], a[ 7])) << 1);
+       t[13] = ((MUL15(a[ 0], a[13])
+               + MUL15(a[ 1], a[12])
+               + MUL15(a[ 2], a[11])
+               + MUL15(a[ 3], a[10])
+               + MUL15(a[ 4], a[ 9])
+               + MUL15(a[ 5], a[ 8])
+               + MUL15(a[ 6], a[ 7])) << 1);
+       t[14] = MUL15(a[ 7], a[ 7])
+               + ((MUL15(a[ 0], a[14])
+               + MUL15(a[ 1], a[13])
+               + MUL15(a[ 2], a[12])
+               + MUL15(a[ 3], a[11])
+               + MUL15(a[ 4], a[10])
+               + MUL15(a[ 5], a[ 9])
+               + MUL15(a[ 6], a[ 8])) << 1);
+       t[15] = ((MUL15(a[ 0], a[15])
+               + MUL15(a[ 1], a[14])
+               + MUL15(a[ 2], a[13])
+               + MUL15(a[ 3], a[12])
+               + MUL15(a[ 4], a[11])
+               + MUL15(a[ 5], a[10])
+               + MUL15(a[ 6], a[ 9])
+               + MUL15(a[ 7], a[ 8])) << 1);
+       t[16] = MUL15(a[ 8], a[ 8])
+               + ((MUL15(a[ 0], a[16])
+               + MUL15(a[ 1], a[15])
+               + MUL15(a[ 2], a[14])
+               + MUL15(a[ 3], a[13])
+               + MUL15(a[ 4], a[12])
+               + MUL15(a[ 5], a[11])
+               + MUL15(a[ 6], a[10])
+               + MUL15(a[ 7], a[ 9])) << 1);
+       t[17] = ((MUL15(a[ 0], a[17])
+               + MUL15(a[ 1], a[16])
+               + MUL15(a[ 2], a[15])
+               + MUL15(a[ 3], a[14])
+               + MUL15(a[ 4], a[13])
+               + MUL15(a[ 5], a[12])
+               + MUL15(a[ 6], a[11])
+               + MUL15(a[ 7], a[10])
+               + MUL15(a[ 8], a[ 9])) << 1);
+       t[18] = MUL15(a[ 9], a[ 9])
+               + ((MUL15(a[ 0], a[18])
+               + MUL15(a[ 1], a[17])
+               + MUL15(a[ 2], a[16])
+               + MUL15(a[ 3], a[15])
+               + MUL15(a[ 4], a[14])
+               + MUL15(a[ 5], a[13])
+               + MUL15(a[ 6], a[12])
+               + MUL15(a[ 7], a[11])
+               + MUL15(a[ 8], a[10])) << 1);
+       t[19] = ((MUL15(a[ 0], a[19])
+               + MUL15(a[ 1], a[18])
+               + MUL15(a[ 2], a[17])
+               + MUL15(a[ 3], a[16])
+               + MUL15(a[ 4], a[15])
+               + MUL15(a[ 5], a[14])
+               + MUL15(a[ 6], a[13])
+               + MUL15(a[ 7], a[12])
+               + MUL15(a[ 8], a[11])
+               + MUL15(a[ 9], a[10])) << 1);
+       t[20] = MUL15(a[10], a[10])
+               + ((MUL15(a[ 1], a[19])
+               + MUL15(a[ 2], a[18])
+               + MUL15(a[ 3], a[17])
+               + MUL15(a[ 4], a[16])
+               + MUL15(a[ 5], a[15])
+               + MUL15(a[ 6], a[14])
+               + MUL15(a[ 7], a[13])
+               + MUL15(a[ 8], a[12])
+               + MUL15(a[ 9], a[11])) << 1);
+       t[21] = ((MUL15(a[ 2], a[19])
+               + MUL15(a[ 3], a[18])
+               + MUL15(a[ 4], a[17])
+               + MUL15(a[ 5], a[16])
+               + MUL15(a[ 6], a[15])
+               + MUL15(a[ 7], a[14])
+               + MUL15(a[ 8], a[13])
+               + MUL15(a[ 9], a[12])
+               + MUL15(a[10], a[11])) << 1);
+       t[22] = MUL15(a[11], a[11])
+               + ((MUL15(a[ 3], a[19])
+               + MUL15(a[ 4], a[18])
+               + MUL15(a[ 5], a[17])
+               + MUL15(a[ 6], a[16])
+               + MUL15(a[ 7], a[15])
+               + MUL15(a[ 8], a[14])
+               + MUL15(a[ 9], a[13])
+               + MUL15(a[10], a[12])) << 1);
+       t[23] = ((MUL15(a[ 4], a[19])
+               + MUL15(a[ 5], a[18])
+               + MUL15(a[ 6], a[17])
+               + MUL15(a[ 7], a[16])
+               + MUL15(a[ 8], a[15])
+               + MUL15(a[ 9], a[14])
+               + MUL15(a[10], a[13])
+               + MUL15(a[11], a[12])) << 1);
+       t[24] = MUL15(a[12], a[12])
+               + ((MUL15(a[ 5], a[19])
+               + MUL15(a[ 6], a[18])
+               + MUL15(a[ 7], a[17])
+               + MUL15(a[ 8], a[16])
+               + MUL15(a[ 9], a[15])
+               + MUL15(a[10], a[14])
+               + MUL15(a[11], a[13])) << 1);
+       t[25] = ((MUL15(a[ 6], a[19])
+               + MUL15(a[ 7], a[18])
+               + MUL15(a[ 8], a[17])
+               + MUL15(a[ 9], a[16])
+               + MUL15(a[10], a[15])
+               + MUL15(a[11], a[14])
+               + MUL15(a[12], a[13])) << 1);
+       t[26] = MUL15(a[13], a[13])
+               + ((MUL15(a[ 7], a[19])
+               + MUL15(a[ 8], a[18])
+               + MUL15(a[ 9], a[17])
+               + MUL15(a[10], a[16])
+               + MUL15(a[11], a[15])
+               + MUL15(a[12], a[14])) << 1);
+       t[27] = ((MUL15(a[ 8], a[19])
+               + MUL15(a[ 9], a[18])
+               + MUL15(a[10], a[17])
+               + MUL15(a[11], a[16])
+               + MUL15(a[12], a[15])
+               + MUL15(a[13], a[14])) << 1);
+       t[28] = MUL15(a[14], a[14])
+               + ((MUL15(a[ 9], a[19])
+               + MUL15(a[10], a[18])
+               + MUL15(a[11], a[17])
+               + MUL15(a[12], a[16])
+               + MUL15(a[13], a[15])) << 1);
+       t[29] = ((MUL15(a[10], a[19])
+               + MUL15(a[11], a[18])
+               + MUL15(a[12], a[17])
+               + MUL15(a[13], a[16])
+               + MUL15(a[14], a[15])) << 1);
+       t[30] = MUL15(a[15], a[15])
+               + ((MUL15(a[11], a[19])
+               + MUL15(a[12], a[18])
+               + MUL15(a[13], a[17])
+               + MUL15(a[14], a[16])) << 1);
+       t[31] = ((MUL15(a[12], a[19])
+               + MUL15(a[13], a[18])
+               + MUL15(a[14], a[17])
+               + MUL15(a[15], a[16])) << 1);
+       t[32] = MUL15(a[16], a[16])
+               + ((MUL15(a[13], a[19])
+               + MUL15(a[14], a[18])
+               + MUL15(a[15], a[17])) << 1);
+       t[33] = ((MUL15(a[14], a[19])
+               + MUL15(a[15], a[18])
+               + MUL15(a[16], a[17])) << 1);
+       t[34] = MUL15(a[17], a[17])
+               + ((MUL15(a[15], a[19])
+               + MUL15(a[16], a[18])) << 1);
+       t[35] = ((MUL15(a[16], a[19])
+               + MUL15(a[17], a[18])) << 1);
+       t[36] = MUL15(a[18], a[18])
+               + ((MUL15(a[17], a[19])) << 1);
+       t[37] = ((MUL15(a[18], a[19])) << 1);
+       t[38] = MUL15(a[19], a[19]);
+       d[39] = norm13(d, t, 39);
+}
+
+#endif
+
+/*
+ * Perform a "final reduction" in field F255 (field for Curve25519)
+ * The source value must be less than twice the modulus. If the value
+ * is not lower than the modulus, then the modulus is subtracted and
+ * this function returns 1; otherwise, it leaves it untouched and it
+ * returns 0.
+ */
+static uint32_t
+reduce_final_f255(uint32_t *d)
+{
+       uint32_t t[20];
+       uint32_t cc;
+       int i;
+
+       memcpy(t, d, sizeof t);
+       cc = 19;
+       for (i = 0; i < 20; i ++) {
+               uint32_t w;
+
+               w = t[i] + cc;
+               cc = w >> 13;
+               t[i] = w & 0x1FFF;
+       }
+       cc = t[19] >> 8;
+       t[19] &= 0xFF;
+       CCOPY(cc, d, t, sizeof t);
+       return cc;
+}
+
+/*
+ * Perform a multiplication of two integers modulo 2^255-19.
+ * Operands are arrays of 20 words, each containing 13 bits of data, in
+ * little-endian order. Input value may be up to 2^256-1; on output, value
+ * fits on 256 bits and is lower than twice the modulus.
+ */
+static void
+f255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+       uint32_t t[40], cc, w;
+       int i;
+
+       /*
+        * Compute raw multiplication. All result words fit in 13 bits
+        * each; upper word (t[39]) must fit on 5 bits, since the product
+        * of two 256-bit integers must fit on 512 bits.
+        */
+       mul20(t, a, b);
+
+       /*
+        * Modular reduction: each high word is added where necessary.
+        * Since the modulus is 2^255-19 and word 20 corresponds to
+        * offset 20*13 = 260, word 20+k must be added to word k with
+        * a factor of 19*2^5 = 608. The extra bits in word 19 are also
+        * added that way.
+        */
+       cc = MUL15(t[19] >> 8, 19);
+       t[19] &= 0xFF;
+       for (i = 0; i < 20; i ++) {
+               w = t[i] + cc + MUL15(t[i + 20], 608);
+               t[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+       cc = MUL15(w >> 8, 19);
+       t[19] &= 0xFF;
+       for (i = 0; i < 20; i ++) {
+               w = t[i] + cc;
+               d[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+}
+
+/*
+ * Square an integer modulo 2^255-19.
+ * Operand is an array of 20 words, each containing 13 bits of data, in
+ * little-endian order. Input value may be up to 2^256-1; on output, value
+ * fits on 256 bits and is lower than twice the modulus.
+ */
+static void
+f255_square(uint32_t *d, const uint32_t *a)
+{
+       uint32_t t[40], cc, w;
+       int i;
+
+       /*
+        * Compute raw multiplication. All result words fit in 13 bits
+        * each; upper word (t[39]) must fit on 5 bits, since the product
+        * of two 256-bit integers must fit on 512 bits.
+        */
+       square20(t, a);
+
+       /*
+        * Modular reduction: each high word is added where necessary.
+        * Since the modulus is 2^255-19 and word 20 corresponds to
+        * offset 20*13 = 260, word 20+k must be added to word k with
+        * a factor of 19*2^5 = 608. The extra bits in word 19 are also
+        * added that way.
+        */
+       cc = MUL15(t[19] >> 8, 19);
+       t[19] &= 0xFF;
+       for (i = 0; i < 20; i ++) {
+               w = t[i] + cc + MUL15(t[i + 20], 608);
+               t[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+       cc = MUL15(w >> 8, 19);
+       t[19] &= 0xFF;
+       for (i = 0; i < 20; i ++) {
+               w = t[i] + cc;
+               d[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+}
+
+/*
+ * Add two values in F255. Partial reduction is performed (down to less
+ * than twice the modulus).
+ */
+static void
+f255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+       int i;
+       uint32_t cc, w;
+
+       cc = 0;
+       for (i = 0; i < 20; i ++) {
+               w = a[i] + b[i] + cc;
+               d[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+       cc = MUL15(w >> 8, 19);
+       d[19] &= 0xFF;
+       for (i = 0; i < 20; i ++) {
+               w = d[i] + cc;
+               d[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+}
+
+/*
+ * Subtract one value from another in F255. Partial reduction is
+ * performed (down to less than twice the modulus).
+ */
+static void
+f255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+       /*
+        * We actually compute a - b + 2*p, so that the final value is
+        * necessarily positive.
+        */
+       int i;
+       uint32_t cc, w;
+
+       cc = (uint32_t)-38;
+       for (i = 0; i < 20; i ++) {
+               w = a[i] - b[i] + cc;
+               d[i] = w & 0x1FFF;
+               cc = ARSH(w, 13);
+       }
+       cc = MUL15((w + 0x200) >> 8, 19);
+       d[19] &= 0xFF;
+       for (i = 0; i < 20; i ++) {
+               w = d[i] + cc;
+               d[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+}
+
+/*
+ * Multiply an integer by the 'A24' constant (121665). Partial reduction
+ * is performed (down to less than twice the modulus).
+ */
+static void
+f255_mul_a24(uint32_t *d, const uint32_t *a)
+{
+       int i;
+       uint32_t cc, w;
+
+       cc = 0;
+       for (i = 0; i < 20; i ++) {
+               w = MUL15(a[i], 121665) + cc;
+               d[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+       cc = MUL15(w >> 8, 19);
+       d[19] &= 0xFF;
+       for (i = 0; i < 20; i ++) {
+               w = d[i] + cc;
+               d[i] = w & 0x1FFF;
+               cc = w >> 13;
+       }
+}
+
+static const unsigned char GEN[] = {
+       0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+};
+
+static const unsigned char ORDER[] = {
+       0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+       0x14, 0xDE, 0xF9, 0xDE, 0xA2, 0xF7, 0x9C, 0xD6,
+       0x58, 0x12, 0x63, 0x1A, 0x5C, 0xF5, 0xD3, 0xED
+};
+
+static const unsigned char *
+api_generator(int curve, size_t *len)
+{
+       (void)curve;
+       *len = 32;
+       return GEN;
+}
+
+static const unsigned char *
+api_order(int curve, size_t *len)
+{
+       (void)curve;
+       *len = 32;
+       return ORDER;
+}
+
+static void
+cswap(uint32_t *a, uint32_t *b, uint32_t ctl)
+{
+       int i;
+
+       ctl = -ctl;
+       for (i = 0; i < 20; i ++) {
+               uint32_t aw, bw, tw;
+
+               aw = a[i];
+               bw = b[i];
+               tw = ctl & (aw ^ bw);
+               a[i] = aw ^ tw;
+               b[i] = bw ^ tw;
+       }
+}
+
+static uint32_t
+api_mul(unsigned char *G, size_t Glen,
+       const unsigned char *kb, size_t kblen, int curve)
+{
+       uint32_t x1[20], x2[20], x3[20], z2[20], z3[20];
+       uint32_t a[20], aa[20], b[20], bb[20];
+       uint32_t c[20], d[20], e[20], da[20], cb[20];
+       unsigned char k[32];
+       uint32_t swap;
+       int i;
+
+       (void)curve;
+
+       /*
+        * Points are encoded over exactly 32 bytes. Multipliers must fit
+        * in 32 bytes as well.
+        * RFC 7748 mandates that the high bit of the last point byte must
+        * be ignored/cleared.
+        */
+       if (Glen != 32 || kblen > 32) {
+               return 0;
+       }
+       G[31] &= 0x7F;
+
+       /*
+        * Initialise variables x1, x2, z2, x3 and z3. We set all of them
+        * into Montgomery representation.
+        */
+       x1[19] = le8_to_le13(x1, G, 32);
+       memcpy(x3, x1, sizeof x1);
+       memset(z2, 0, sizeof z2);
+       memset(x2, 0, sizeof x2);
+       x2[0] = 1;
+       memset(z3, 0, sizeof z3);
+       z3[0] = 1;
+
+       memcpy(k, kb, kblen);
+       memset(k + kblen, 0, (sizeof k) - kblen);
+       k[0] &= 0xF8;
+       k[31] &= 0x7F;
+       k[31] |= 0x40;
+
+       /* obsolete
+       print_int("x1", x1);
+       */
+
+       swap = 0;
+       for (i = 254; i >= 0; i --) {
+               uint32_t kt;
+
+               kt = (k[i >> 3] >> (i & 7)) & 1;
+               swap ^= kt;
+               cswap(x2, x3, swap);
+               cswap(z2, z3, swap);
+               swap = kt;
+
+               /* obsolete
+               print_int("x2", x2);
+               print_int("z2", z2);
+               print_int("x3", x3);
+               print_int("z3", z3);
+               */
+
+               f255_add(a, x2, z2);
+               f255_square(aa, a);
+               f255_sub(b, x2, z2);
+               f255_square(bb, b);
+               f255_sub(e, aa, bb);
+               f255_add(c, x3, z3);
+               f255_sub(d, x3, z3);
+               f255_mul(da, d, a);
+               f255_mul(cb, c, b);
+
+               /* obsolete
+               print_int("a ", a);
+               print_int("aa", aa);
+               print_int("b ", b);
+               print_int("bb", bb);
+               print_int("e ", e);
+               print_int("c ", c);
+               print_int("d ", d);
+               print_int("da", da);
+               print_int("cb", cb);
+               */
+
+               f255_add(x3, da, cb);
+               f255_square(x3, x3);
+               f255_sub(z3, da, cb);
+               f255_square(z3, z3);
+               f255_mul(z3, z3, x1);
+               f255_mul(x2, aa, bb);
+               f255_mul_a24(z2, e);
+               f255_add(z2, z2, aa);
+               f255_mul(z2, e, z2);
+
+               /* obsolete
+               print_int("x2", x2);
+               print_int("z2", z2);
+               print_int("x3", x3);
+               print_int("z3", z3);
+               */
+       }
+       cswap(x2, x3, swap);
+       cswap(z2, z3, swap);
+
+       /*
+        * Inverse z2 with a modular exponentiation. This is a simple
+        * square-and-multiply algorithm; we mutualise most non-squarings
+        * since the exponent contains almost only ones.
+        */
+       memcpy(a, z2, sizeof z2);
+       for (i = 0; i < 15; i ++) {
+               f255_square(a, a);
+               f255_mul(a, a, z2);
+       }
+       memcpy(b, a, sizeof a);
+       for (i = 0; i < 14; i ++) {
+               int j;
+
+               for (j = 0; j < 16; j ++) {
+                       f255_square(b, b);
+               }
+               f255_mul(b, b, a);
+       }
+       for (i = 14; i >= 0; i --) {
+               f255_square(b, b);
+               if ((0xFFEB >> i) & 1) {
+                       f255_mul(b, z2, b);
+               }
+       }
+       f255_mul(x2, x2, b);
+       reduce_final_f255(x2);
+       le13_to_le8(G, 32, x2);
+       return 1;
+}
+
+static size_t
+api_mulgen(unsigned char *R,
+       const unsigned char *x, size_t xlen, int curve)
+{
+       const unsigned char *G;
+       size_t Glen;
+
+       G = api_generator(curve, &Glen);
+       memcpy(R, G, Glen);
+       api_mul(R, Glen, x, xlen, curve);
+       return Glen;
+}
+
+static uint32_t
+api_muladd(unsigned char *A, const unsigned char *B, size_t len,
+       const unsigned char *x, size_t xlen,
+       const unsigned char *y, size_t ylen, int curve)
+{
+       /*
+        * We don't implement this method, since it is used for ECDSA
+        * only, and there is no ECDSA over Curve25519 (which instead
+        * uses EdDSA).
+        */
+       (void)A;
+       (void)B;
+       (void)len;
+       (void)x;
+       (void)xlen;
+       (void)y;
+       (void)ylen;
+       (void)curve;
+       return 0;
+}
+
+/* see bearssl_ec.h */
+const br_ec_impl br_ec_c25519_m15 = {
+       (uint32_t)0x20000000,
+       &api_generator,
+       &api_order,
+       &api_mul,
+       &api_mulgen,
+       &api_muladd
+};

diff --git a/test/test_crypto.c b/test/test_crypto.c
index ddba9ac..46c8fa2 100644 (file)
--- a/test/test_crypto.c
+++ b/test/test_crypto.c
@@ -4935,13 +4935,13 @@ const struct {
 static void
 test_EC_c25519(const char *name, const br_ec_impl *iec)
 {
+       unsigned char bu[32], bk[32], br[32];
        size_t v;
+       int i;
 
        printf("Test %s: ", name);
        fflush(stdout);
        for (v = 0; C25519_KAT[v].scalar; v ++) {
-               unsigned char bu[32], bk[32], br[32];
-
                hextobin(bk, C25519_KAT[v].scalar);
                hextobin(bu, C25519_KAT[v].u_in);
                hextobin(br, C25519_KAT[v].u_out);
@@ -4956,6 +4956,44 @@ test_EC_c25519(const char *name, const br_ec_impl *iec)
                printf(".");
                fflush(stdout);
        }
+       printf(" ");
+       fflush(stdout);
+
+       memset(bu, 0, sizeof bu);
+       bu[0] = 0x09;
+       memcpy(bk, bu, sizeof bu);
+       for (i = 1; i <= 1000; i ++) {
+               if (!iec->mul(bu, sizeof bu, bk, sizeof bk, BR_EC_curve25519)) {
+                       fprintf(stderr, "Curve25519 multiplication failed"
+                               " (iter=%d)\n", i);
+                       exit(EXIT_FAILURE);
+               }
+               for (v = 0; v < sizeof bu; v ++) {
+                       unsigned t;
+
+                       t = bu[v];
+                       bu[v] = bk[v];
+                       bk[v] = t;
+               }
+               if (i == 1 || i == 1000) {
+                       const char *sref;
+
+                       sref = (i == 1)
+                               ? "422C8E7A6227D7BCA1350B3E2BB7279F7897B87BB6854B783C60E80311AE3079"
+                               : "684CF59BA83309552800EF566F2F4D3C1C3887C49360E3875F2EB94D99532C51";
+                       hextobin(br, sref);
+                       if (memcmp(bk, br, sizeof bk) != 0) {
+                               fprintf(stderr,
+                                       "Curve25519 failed KAT (iter=%d)\n", i);
+                               exit(EXIT_FAILURE);
+                       }
+               }
+               if (i % 100 == 0) {
+                       printf(".");
+                       fflush(stdout);
+               }
+       }
+
        printf(" done.\n");
        fflush(stdout);
 }
@@ -4966,6 +5004,12 @@ test_EC_c25519_i15(void)
        test_EC_c25519("EC_c25519_i15", &br_ec_c25519_i15);
 }
 
+static void
+test_EC_c25519_m15(void)
+{
+       test_EC_c25519("EC_c25519_m15", &br_ec_c25519_m15);
+}
+
 static const unsigned char EC_P256_PUB_POINT[] = {
        0x04, 0x60, 0xFE, 0xD4, 0xBA, 0x25, 0x5A, 0x9D,
        0x31, 0xC9, 0x61, 0xEB, 0x74, 0xC6, 0x35, 0x6D,
@@ -5513,6 +5557,7 @@ static const struct {
        STU(EC_p256_m15),
        /* STU(EC_prime_i32), */
        STU(EC_c25519_i15),
+       STU(EC_c25519_m15),
        STU(ECDSA_i15),
        STU(ECDSA_i31),
        { 0, 0 }

diff --git a/test/test_speed.c b/test/test_speed.c
index 48f5fe3..48c2fdb 100644 (file)
--- a/test/test_speed.c
+++ b/test/test_speed.c
@@ -714,6 +714,13 @@ test_speed_ec_c25519_i15(void)
                &br_ec_c25519_i15, &br_curve25519);
 }
 
+static void
+test_speed_ec_c25519_m15(void)
+{
+       test_speed_ec_inner("EC m15 C25519",
+               &br_ec_c25519_m15, &br_curve25519);
+}
+
 static void
 test_speed_ecdsa_inner(const char *name,
        const br_ec_impl *impl, const br_ec_curve_def *cd,
@@ -1256,6 +1263,7 @@ static const struct {
        STU(ec_prime_i15),
        STU(ec_prime_i31),
        STU(ec_c25519_i15),
+       STU(ec_c25519_m15),
        STU(ecdsa_p256_m15),
        STU(ecdsa_i15),
        STU(ecdsa_i31),