Added optimised implementation of P-256 that uses 32->64 multiplications (MUL31).

src/ec/ec_c25519_i15.c

@@ -179,8 +179,14 @@ static uint32_t
 api_mul(unsigned char *G, size_t Glen,
 	const unsigned char *kb, size_t kblen, int curve)
 {
+#define ILEN   (18 * sizeof(uint16_t))
+
+	/*
+	 * The a[] and b[] arrays have an extra word to allow for
+	 * decoding without using br_i15_decode_reduce().
+	 */
 	uint16_t x1[18], x2[18], x3[18], z2[18], z3[18];
-	uint16_t a[18], aa[18], b[18], bb[18];
+	uint16_t a[19], aa[18], b[19], bb[18];
 	uint16_t c[18], d[18], e[18], da[18], cb[18];
 	unsigned char k[32];
 	uint32_t swap;
@@ -205,17 +211,33 @@ api_mul(unsigned char *G, size_t Glen,
 	 */
 	byteswap(G);
 
+	/*
+	 * Decode the point ('u' coordinate). This should be reduced
+	 * modulo p, but we prefer to avoid the dependency on
+	 * br_i15_decode_reduce(). Instead, we use br_i15_decode_mod()
+	 * with a synthetic modulus of value 2^255 (this must work
+	 * since G was truncated to 255 bits), then use a conditional
+	 * subtraction. We use br_i15_decode_mod() and not
+	 * br_i15_decode(), because the ec_prime_i15 implementation uses
+	 * the former but not the latter.
+	 *    br_i15_decode_reduce(a, G, 32, C255_P);
+	 */
+	br_i15_zero(b, 0x111);
+	b[18] = 1;
+	br_i15_decode_mod(a, G, 32, b);
+	a[0] = 0x110;
+	br_i15_sub(a, C255_P, NOT(br_i15_sub(a, C255_P, 0)));
+
 	/*
 	 * Initialise variables x1, x2, z2, x3 and z3. We set all of them
 	 * into Montgomery representation.
 	 */
-	br_i15_decode_reduce(a, G, 32, C255_P);
 	br_i15_montymul(x1, a, C255_R2, C255_P, P0I);
-	memcpy(x3, x1, sizeof x1);
+	memcpy(x3, x1, ILEN);
 	br_i15_zero(z2, C255_P[0]);
-	memcpy(x2, z2, sizeof z2);
+	memcpy(x2, z2, ILEN);
 	x2[1] = 19;
-	memcpy(z3, x2, sizeof x2);
+	memcpy(z3, x2, ILEN);
 
 	memcpy(k, kb, kblen);
 	memset(k + kblen, 0, (sizeof k) - kblen);
@@ -291,12 +313,12 @@ api_mul(unsigned char *G, size_t Glen,
 	 * square-and-multiply algorithm; we mutualise most non-squarings
 	 * since the exponent contains almost only ones.
 	 */
-	memcpy(a, z2, sizeof z2);
+	memcpy(a, z2, ILEN);
 	for (i = 0; i < 15; i ++) {
 		c255_mul(a, a, a);
 		c255_mul(a, a, z2);
 	}
-	memcpy(b, a, sizeof a);
+	memcpy(b, a, ILEN);
 	for (i = 0; i < 14; i ++) {
 		int j;
 
@@ -311,11 +333,23 @@ api_mul(unsigned char *G, size_t Glen,
 			c255_mul(b, z2, b);
 		}
 	}
-	c255_mul(x2, x2, b);
-	br_i15_from_monty(x2, C255_P, P0I);
+	c255_mul(b, x2, b);
+
+	/*
+	 * To avoid a dependency on br_i15_from_monty(), we use a
+	 * Montgomery multiplication with 1.
+	 *    memcpy(x2, b, ILEN);
+	 *    br_i15_from_monty(x2, C255_P, P0I);
+	 */
+	br_i15_zero(a, C255_P[0]);
+	a[1] = 1;
+	br_i15_montymul(x2, a, b, C255_P, P0I);
+
 	br_i15_encode(G, 32, x2);
 	byteswap(G);
 	return 1;
+
+#undef ILEN
 }
 
 static size_t