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,
};
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
+ 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
};
static const unsigned char *
return ORDER;
}
+static size_t
+api_xoff(int curve, size_t *len)
+{
+ (void)curve;
+ *len = 32;
+ return 0;
+}
+
static void
cswap(uint16_t *a, uint16_t *b, uint32_t ctl)
{
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;
*/
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);
k[31] &= 0x7F;
k[31] |= 0x40;
+ /* obsolete
+ print_int_mont("x1", x1);
+ */
+
swap = 0;
for (i = 254; i >= 0; i --) {
uint32_t kt;
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);
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);
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);
* 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;
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
(uint32_t)0x20000000,
&api_generator,
&api_order,
+ &api_xoff,
&api_mul,
&api_mulgen,
&api_muladd