*/
byteswap(G);
+ /*
+ * Decode the point ('u' coordinate). This should be reduced
+ * modulo p, but we prefer to avoid the dependency on
+ * br_i31_decode_reduce(). Instead, we use br_i31_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_i31_decode_mod() and not
+ * br_i31_decode(), because the ec_prime_i31 implementation uses
+ * the former but not the latter.
+ * br_i31_decode_reduce(a, G, 32, C255_P);
+ */
+ br_i31_zero(b, 0x108);
+ b[9] = 0x0080;
+ br_i31_decode_mod(a, G, 32, b);
+ a[0] = 0x107;
+ br_i31_sub(a, C255_P, NOT(br_i31_sub(a, C255_P, 0)));
+
/*
* Initialise variables x1, x2, z2, x3 and z3. We set all of them
* into Montgomery representation.
*/
- br_i31_decode_reduce(a, G, 32, C255_P);
br_i31_montymul(x1, a, C255_R2, C255_P, P0I);
memcpy(x3, x1, sizeof x1);
br_i31_zero(z2, C255_P[0]);
x2[1] = 0x13000000;
memcpy(z3, x2, sizeof x2);
- memcpy(k, kb, kblen);
- memset(k + kblen, 0, (sizeof k) - kblen);
- k[0] &= 0xF8;
- k[31] &= 0x7F;
- k[31] |= 0x40;
+ /*
+ * kb[] is in big-endian notation, but possibly shorter than k[].
+ */
+ memset(k, 0, (sizeof k) - kblen);
+ memcpy(k + (sizeof k) - kblen, kb, kblen);
+ k[31] &= 0xF8;
+ k[0] &= 0x7F;
+ k[0] |= 0x40;
/* obsolete
print_int_mont("x1", x1);
for (i = 254; i >= 0; i --) {
uint32_t kt;
- kt = (k[i >> 3] >> (i & 7)) & 1;
+ kt = (k[31 - (i >> 3)] >> (i & 7)) & 1;
swap ^= kt;
cswap(x2, x3, swap);
cswap(z2, z3, swap);
c255_mul(b, z2, b);
}
}
- c255_mul(x2, x2, b);
- br_i31_from_monty(x2, C255_P, P0I);
+ c255_mul(b, x2, b);
+
+ /*
+ * To avoid a dependency on br_i31_from_monty(), we use
+ * a Montgomery multiplication with 1.
+ * memcpy(x2, b, sizeof b);
+ * br_i31_from_monty(x2, C255_P, P0I);
+ */
+ br_i31_zero(a, C255_P[0]);
+ a[1] = 1;
+ br_i31_montymul(x2, a, b, C255_P, P0I);
+
br_i31_encode(G, 32, x2);
byteswap(G);
return 1;