BN_set_flags((P)->Z, (flags)); \
} while(0)
-/*
+/*-
* This functions computes (in constant time) a point multiplication over the
* EC group.
*
+ * At a high level, it is Montgomery ladder with conditional swaps.
+ *
* It performs either a fixed scalar point multiplication
* (scalar * generator)
* when point is NULL, or a generic scalar point multiplication
*
* Returns 1 on success, 0 otherwise.
*/
-static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
- const EC_POINT *point, BN_CTX *ctx)
+static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *scalar, const EC_POINT *point,
+ BN_CTX *ctx)
{
int i, order_bits, group_top, kbit, pbit, Z_is_one;
EC_POINT *s = NULL;
BN_set_flags(k, BN_FLG_CONSTTIME);
if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) {
- /*
+ /*-
* this is an unusual input, and we don't guarantee
* constant-timeness
*/
- if(!BN_nnmod(k, k, group->order, ctx))
+ if (!BN_nnmod(k, k, group->order, ctx))
goto err;
}
(b)->Z_is_one ^= (t); \
} while(0)
+ /*-
+ * The ladder step, with branches, is
+ *
+ * k[i] == 0: S = add(R, S), R = dbl(R)
+ * k[i] == 1: R = add(S, R), S = dbl(S)
+ *
+ * Swapping R, S conditionally on k[i] leaves you with state
+ *
+ * k[i] == 0: T, U = R, S
+ * k[i] == 1: T, U = S, R
+ *
+ * Then perform the ECC ops.
+ *
+ * U = add(T, U)
+ * T = dbl(T)
+ *
+ * Which leaves you with state
+ *
+ * k[i] == 0: U = add(R, S), T = dbl(R)
+ * k[i] == 1: U = add(S, R), T = dbl(S)
+ *
+ * Swapping T, U conditionally on k[i] leaves you with state
+ *
+ * k[i] == 0: R, S = T, U
+ * k[i] == 1: R, S = U, T
+ *
+ * Which leaves you with state
+ *
+ * k[i] == 0: S = add(R, S), R = dbl(R)
+ * k[i] == 1: R = add(S, R), S = dbl(S)
+ *
+ * So we get the same logic, but instead of a branch it's a
+ * conditional swap, followed by ECC ops, then another conditional swap.
+ *
+ * Optimization: The end of iteration i and start of i-1 looks like
+ *
+ * ...
+ * CSWAP(k[i], R, S)
+ * ECC
+ * CSWAP(k[i], R, S)
+ * (next iteration)
+ * CSWAP(k[i-1], R, S)
+ * ECC
+ * CSWAP(k[i-1], R, S)
+ * ...
+ *
+ * So instead of two contiguous swaps, you can merge the condition
+ * bits and do a single swap.
+ *
+ * k[i] k[i-1] Outcome
+ * 0 0 No Swap
+ * 0 1 Swap
+ * 1 0 Swap
+ * 1 1 No Swap
+ *
+ * This is XOR. pbit tracks the previous bit of k.
+ */
+
for (i = order_bits - 1; i >= 0; i--) {
kbit = BN_is_bit_set(k, i) ^ pbit;
EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
ret = 1;
-err:
+ err:
EC_POINT_free(s);
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
+
#undef EC_POINT_BN_set_flags
/*
* precomputation is not available */
int ret = 0;
- /* Handle the common cases where the scalar is secret, enforcing a
- * constant time scalar multiplication algorithm.
+ if (group->meth != r->meth) {
+ ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
+ return 0;
+ }
+
+ if ((scalar == NULL) && (num == 0)) {
+ return EC_POINT_set_to_infinity(group, r);
+ }
+
+ /*-
+ * Handle the common cases where the scalar is secret, enforcing a constant
+ * time scalar multiplication algorithm.
*/
if ((scalar != NULL) && (num == 0)) {
- /* In this case we want to compute scalar * GeneratorPoint:
- * this codepath is reached most prominently by (ephemeral) key
- * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
- * ECDH keygen/first half), where the scalar is always secret.
- * This is why we ignore if BN_FLG_CONSTTIME is actually set and we
- * always call the constant time version.
+ /*-
+ * In this case we want to compute scalar * GeneratorPoint: this
+ * codepath is reached most prominently by (ephemeral) key generation
+ * of EC cryptosystems (i.e. ECDSA keygen and sign setup, ECDH
+ * keygen/first half), where the scalar is always secret. This is why
+ * we ignore if BN_FLG_CONSTTIME is actually set and we always call the
+ * constant time version.
*/
return ec_mul_consttime(group, r, scalar, NULL, ctx);
}
if ((scalar == NULL) && (num == 1)) {
- /* In this case we want to compute scalar * GenericPoint:
- * this codepath is reached most prominently by the second half of
- * ECDH, where the secret scalar is multiplied by the peer's public
- * point.
- * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
- * actually set and we always call the constant time version.
+ /*-
+ * In this case we want to compute scalar * GenericPoint: this codepath
+ * is reached most prominently by the second half of ECDH, where the
+ * secret scalar is multiplied by the peer's public point. To protect
+ * the secret scalar, we ignore if BN_FLG_CONSTTIME is actually set and
+ * we always call the constant time version.
*/
return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
}
-
- if (group->meth != r->meth) {
- ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
- return 0;
- }
-
- if ((scalar == NULL) && (num == 0)) {
- return EC_POINT_set_to_infinity(group, r);
- }
-
for (i = 0; i < num; i++) {
if (group->meth != points[i]->meth) {
ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
projects / openssl.git / blobdiff