Improved modular exponentiation (automatic window optimisation if there is enough...

[BearSSL] / src / int / i15_modpow2.c

diff --git a/src/int/i15_modpow2.c b/src/int/i15_modpow2.c
new file mode 100644 (file)
index 0000000..dce9941
--- /dev/null
+++ b/src/int/i15_modpow2.c
@@ -0,0 +1,159 @@
+/*
+ * 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"
+
+/* see inner.h */
+uint32_t
+br_i15_modpow_opt(uint16_t *x,
+       const unsigned char *e, size_t elen,
+       const uint16_t *m, uint16_t m0i, uint16_t *tmp, size_t twlen)
+{
+       size_t mlen, mwlen;
+       uint16_t *t1, *t2, *base;
+       size_t u, v;
+       uint32_t acc;
+       int acc_len, win_len;
+
+       /*
+        * Get modulus size.
+        */
+       mwlen = (m[0] + 31) >> 4;
+       mlen = mwlen * sizeof m[0];
+       t1 = tmp;
+       t2 = tmp + mwlen;
+
+       /*
+        * Compute possible window size, with a maximum of 5 bits.
+        * When the window has size 1 bit, we use a specific code
+        * that requires only two temporaries. Otherwise, for a
+        * window of k bits, we need 2^k+1 temporaries.
+        */
+       if (twlen < (mwlen << 1)) {
+               return 0;
+       }
+       for (win_len = 5; win_len > 1; win_len --) {
+               if ((((uint32_t)1 << win_len) + 1) * mwlen <= twlen) {
+                       break;
+               }
+       }
+
+       /*
+        * Everything is done in Montgomery representation.
+        */
+       br_i15_to_monty(x, m);
+
+       /*
+        * Compute window contents. If the window has size one bit only,
+        * then t2 is set to x; otherwise, t2[0] is left untouched, and
+        * t2[k] is set to x^k (for k >= 1).
+        */
+       if (win_len == 1) {
+               memcpy(t2, x, mlen);
+       } else {
+               memcpy(t2 + mwlen, x, mlen);
+               base = t2 + mwlen;
+               for (u = 2; u < ((unsigned)1 << win_len); u ++) {
+                       br_i15_montymul(base + mwlen, base, x, m, m0i);
+                       base += mwlen;
+               }
+       }
+
+       /*
+        * We need to set x to 1, in Montgomery representation. This can
+        * be done efficiently by setting the high word to 1, then doing
+        * one word-sized shift.
+        */
+       br_i15_zero(x, m[0]);
+       x[mwlen - 1] = 1;
+       br_i15_muladd_small(x, 0, m);
+
+       /*
+        * We process bits from most to least significant. At each
+        * loop iteration, we have acc_len bits in acc.
+        */
+       acc = 0;
+       acc_len = 0;
+       while (acc_len > 0 || elen > 0) {
+               int i, k;
+               uint32_t bits;
+
+               /*
+                * Get the next bits.
+                */
+               k = win_len;
+               if (acc_len < win_len) {
+                       if (elen > 0) {
+                               acc = (acc << 8) | *e ++;
+                               elen --;
+                               acc_len += 8;
+                       } else {
+                               k = acc_len;
+                       }
+               }
+               bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
+               acc_len -= k;
+
+               /*
+                * We could get exactly k bits. Compute k squarings.
+                */
+               for (i = 0; i < k; i ++) {
+                       br_i15_montymul(t1, x, x, m, m0i);
+                       memcpy(x, t1, mlen);
+               }
+
+               /*
+                * Window lookup: we want to set t2 to the window
+                * lookup value, assuming the bits are non-zero. If
+                * the window length is 1 bit only, then t2 is
+                * already set; otherwise, we do a constant-time lookup.
+                */
+               if (win_len > 1) {
+                       br_i15_zero(t2, m[0]);
+                       base = t2 + mwlen;
+                       for (u = 1; u < ((uint32_t)1 << k); u ++) {
+                               uint32_t m;
+
+                               m = -EQ(u, bits);
+                               for (v = 1; v < mwlen; v ++) {
+                                       t2[v] |= m & base[v];
+                               }
+                               base += mwlen;
+                       }
+               }
+
+               /*
+                * Multiply with the looked-up value. We keep the
+                * product only if the exponent bits are not all-zero.
+                */
+               br_i15_montymul(t1, x, t2, m, m0i);
+               CCOPY(NEQ(bits, 0), x, t1, mlen);
+       }
+
+       /*
+        * Convert back from Montgomery representation, and exit.
+        */
+       br_i15_from_monty(x, m, m0i);
+       return 1;
+}