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-rw-r--r--lib/libcrypto/ec/ec2_mult.c374
1 files changed, 213 insertions, 161 deletions
diff --git a/lib/libcrypto/ec/ec2_mult.c b/lib/libcrypto/ec/ec2_mult.c
index 1c575dc47ad..040d7bb2782 100644
--- a/lib/libcrypto/ec/ec2_mult.c
+++ b/lib/libcrypto/ec/ec2_mult.c
@@ -21,7 +21,7 @@
* are met:
*
* 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
+ * notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
@@ -74,178 +74,215 @@
#ifndef OPENSSL_NO_EC2M
-/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
+/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
* coordinates.
- * Uses algorithm Mdouble in appendix of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+ * Uses algorithm Mdouble in appendix of
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
* modified to not require precomputation of c=b^{2^{m-1}}.
*/
-static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
- {
+static int
+gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
+{
BIGNUM *t1;
int ret = 0;
-
+
/* Since Mdouble is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
- if (t1 == NULL) goto err;
+ if (t1 == NULL)
+ goto err;
- if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
- if (!group->meth->field_sqr(group, t1, z, ctx)) goto err;
- if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err;
- if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
- if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err;
- if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err;
- if (!BN_GF2m_add(x, x, t1)) goto err;
+ if (!group->meth->field_sqr(group, x, x, ctx))
+ goto err;
+ if (!group->meth->field_sqr(group, t1, z, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, z, x, t1, ctx))
+ goto err;
+ if (!group->meth->field_sqr(group, x, x, ctx))
+ goto err;
+ if (!group->meth->field_sqr(group, t1, t1, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
+ goto err;
+ if (!BN_GF2m_add(x, x, t1))
+ goto err;
ret = 1;
- err:
+err:
BN_CTX_end(ctx);
return ret;
- }
+}
-/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
+/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
* projective coordinates.
- * Uses algorithm Madd in appendix of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+ * Uses algorithm Madd in appendix of
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
*/
-static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
- const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
- {
+static int
+gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
+ const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
+{
BIGNUM *t1, *t2;
int ret = 0;
-
+
/* Since Madd is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
t2 = BN_CTX_get(ctx);
- if (t2 == NULL) goto err;
+ if (t2 == NULL)
+ goto err;
- if (!BN_copy(t1, x)) goto err;
- if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err;
- if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err;
- if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err;
- if (!BN_GF2m_add(z1, z1, x1)) goto err;
- if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err;
- if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err;
- if (!BN_GF2m_add(x1, x1, t2)) goto err;
+ if (!BN_copy(t1, x))
+ goto err;
+ if (!group->meth->field_mul(group, x1, x1, z2, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, z1, z1, x2, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, t2, x1, z1, ctx))
+ goto err;
+ if (!BN_GF2m_add(z1, z1, x1))
+ goto err;
+ if (!group->meth->field_sqr(group, z1, z1, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, x1, z1, t1, ctx))
+ goto err;
+ if (!BN_GF2m_add(x1, x1, t2))
+ goto err;
ret = 1;
- err:
+err:
BN_CTX_end(ctx);
return ret;
- }
+}
-/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
- * using Montgomery point multiplication algorithm Mxy() in appendix of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
+ * using Montgomery point multiplication algorithm Mxy() in appendix of
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
* Returns:
* 0 on error
* 1 if return value should be the point at infinity
* 2 otherwise
*/
-static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
- BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
- {
+static int
+gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
+ BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
+{
BIGNUM *t3, *t4, *t5;
int ret = 0;
-
- if (BN_is_zero(z1))
- {
+
+ if (BN_is_zero(z1)) {
BN_zero(x2);
BN_zero(z2);
return 1;
- }
-
- if (BN_is_zero(z2))
- {
- if (!BN_copy(x2, x)) return 0;
- if (!BN_GF2m_add(z2, x, y)) return 0;
+ }
+ if (BN_is_zero(z2)) {
+ if (!BN_copy(x2, x))
+ return 0;
+ if (!BN_GF2m_add(z2, x, y))
+ return 0;
return 2;
- }
-
+ }
/* Since Mxy is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
t3 = BN_CTX_get(ctx);
t4 = BN_CTX_get(ctx);
t5 = BN_CTX_get(ctx);
- if (t5 == NULL) goto err;
+ if (t5 == NULL)
+ goto err;
- if (!BN_one(t5)) goto err;
+ if (!BN_one(t5))
+ goto err;
- if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err;
+ if (!group->meth->field_mul(group, t3, z1, z2, ctx))
+ goto err;
- if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err;
- if (!BN_GF2m_add(z1, z1, x1)) goto err;
- if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err;
- if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err;
- if (!BN_GF2m_add(z2, z2, x2)) goto err;
+ if (!group->meth->field_mul(group, z1, z1, x, ctx))
+ goto err;
+ if (!BN_GF2m_add(z1, z1, x1))
+ goto err;
+ if (!group->meth->field_mul(group, z2, z2, x, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, x1, z2, x1, ctx))
+ goto err;
+ if (!BN_GF2m_add(z2, z2, x2))
+ goto err;
- if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err;
- if (!group->meth->field_sqr(group, t4, x, ctx)) goto err;
- if (!BN_GF2m_add(t4, t4, y)) goto err;
- if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err;
- if (!BN_GF2m_add(t4, t4, z2)) goto err;
+ if (!group->meth->field_mul(group, z2, z2, z1, ctx))
+ goto err;
+ if (!group->meth->field_sqr(group, t4, x, ctx))
+ goto err;
+ if (!BN_GF2m_add(t4, t4, y))
+ goto err;
+ if (!group->meth->field_mul(group, t4, t4, t3, ctx))
+ goto err;
+ if (!BN_GF2m_add(t4, t4, z2))
+ goto err;
- if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err;
- if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err;
- if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err;
- if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err;
- if (!BN_GF2m_add(z2, x2, x)) goto err;
+ if (!group->meth->field_mul(group, t3, t3, x, ctx))
+ goto err;
+ if (!group->meth->field_div(group, t3, t5, t3, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, t4, t3, t4, ctx))
+ goto err;
+ if (!group->meth->field_mul(group, x2, x1, t3, ctx))
+ goto err;
+ if (!BN_GF2m_add(z2, x2, x))
+ goto err;
- if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err;
- if (!BN_GF2m_add(z2, z2, y)) goto err;
+ if (!group->meth->field_mul(group, z2, z2, t4, ctx))
+ goto err;
+ if (!BN_GF2m_add(z2, z2, y))
+ goto err;
ret = 2;
- err:
+err:
BN_CTX_end(ctx);
return ret;
- }
+}
/* Computes scalar*point and stores the result in r.
* point can not equal r.
* Uses a modified algorithm 2P of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
*
* To protect against side-channel attack the function uses constant time swap,
* avoiding conditional branches.
*/
-static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
- const EC_POINT *point, BN_CTX *ctx)
- {
+static int
+ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
+ const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx)
+{
BIGNUM *x1, *x2, *z1, *z2;
int ret = 0, i;
- BN_ULONG mask,word;
+ BN_ULONG mask, word;
- if (r == point)
- {
+ if (r == point) {
ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
return 0;
- }
-
+ }
/* if result should be point at infinity */
- if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
- EC_POINT_is_at_infinity(group, point))
- {
+ if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
+ EC_POINT_is_at_infinity(group, point)) {
return EC_POINT_set_to_infinity(group, r);
- }
-
+ }
/* only support affine coordinates */
- if (!point->Z_is_one) return 0;
+ if (!point->Z_is_one)
+ return 0;
/* Since point_multiply is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
x1 = BN_CTX_get(ctx);
z1 = BN_CTX_get(ctx);
- if (z1 == NULL) goto err;
+ if (z1 == NULL)
+ goto err;
x2 = &r->X;
z2 = &r->Y;
@@ -255,53 +292,57 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
bn_wexpand(x2, group->field.top);
bn_wexpand(z2, group->field.top);
- if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */
- if (!BN_one(z1)) goto err; /* z1 = 1 */
- if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */
- if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err;
- if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */
+ if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
+ goto err; /* x1 = x */
+ if (!BN_one(z1))
+ goto err; /* z1 = 1 */
+ if (!group->meth->field_sqr(group, z2, x1, ctx))
+ goto err; /* z2 = x1^2 = x^2 */
+ if (!group->meth->field_sqr(group, x2, z2, ctx))
+ goto err;
+ if (!BN_GF2m_add(x2, x2, &group->b))
+ goto err; /* x2 = x^4 + b */
/* find top most bit and go one past it */
i = scalar->top - 1;
mask = BN_TBIT;
word = scalar->d[i];
- while (!(word & mask)) mask >>= 1;
+ while (!(word & mask))
+ mask >>= 1;
mask >>= 1;
/* if top most bit was at word break, go to next word */
- if (!mask)
- {
+ if (!mask) {
i--;
mask = BN_TBIT;
- }
-
- for (; i >= 0; i--)
- {
+ }
+ for (; i >= 0; i--) {
word = scalar->d[i];
- while (mask)
- {
+ while (mask) {
BN_consttime_swap(word & mask, x1, x2, group->field.top);
BN_consttime_swap(word & mask, z1, z2, group->field.top);
- if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err;
- if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err;
+ if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
+ goto err;
+ if (!gf2m_Mdouble(group, x1, z1, ctx))
+ goto err;
BN_consttime_swap(word & mask, x1, x2, group->field.top);
BN_consttime_swap(word & mask, z1, z2, group->field.top);
mask >>= 1;
- }
- mask = BN_TBIT;
}
+ mask = BN_TBIT;
+ }
/* convert out of "projective" coordinates */
i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
- if (i == 0) goto err;
- else if (i == 1)
- {
- if (!EC_POINT_set_to_infinity(group, r)) goto err;
- }
- else
- {
- if (!BN_one(&r->Z)) goto err;
+ if (i == 0)
+ goto err;
+ else if (i == 1) {
+ if (!EC_POINT_set_to_infinity(group, r))
+ goto err;
+ } else {
+ if (!BN_one(&r->Z))
+ goto err;
r->Z_is_one = 1;
- }
+ }
/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
BN_set_negative(&r->X, 0);
@@ -309,87 +350,98 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
ret = 1;
- err:
+err:
BN_CTX_end(ctx);
return ret;
- }
+}
/* Computes the sum
* scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
* gracefully ignoring NULL scalar values.
*/
-int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
- size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
- {
+int
+ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
+{
BN_CTX *new_ctx = NULL;
int ret = 0;
size_t i;
- EC_POINT *p=NULL;
+ EC_POINT *p = NULL;
EC_POINT *acc = NULL;
- if (ctx == NULL)
- {
+ if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
return 0;
- }
-
- /* This implementation is more efficient than the wNAF implementation for 2
- * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points,
- * or if we can perform a fast multiplication based on precomputation.
+ }
+ /*
+ * This implementation is more efficient than the wNAF implementation
+ * for 2 or fewer points. Use the ec_wNAF_mul implementation for 3
+ * or more points, or if we can perform a fast multiplication based
+ * on precomputation.
*/
- if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group)))
- {
+ if ((scalar && (num > 1)) || (num > 2) ||
+ (num == 0 && EC_GROUP_have_precompute_mult(group))) {
ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
goto err;
- }
-
- if ((p = EC_POINT_new(group)) == NULL) goto err;
- if ((acc = EC_POINT_new(group)) == NULL) goto err;
+ }
+ if ((p = EC_POINT_new(group)) == NULL)
+ goto err;
+ if ((acc = EC_POINT_new(group)) == NULL)
+ goto err;
- if (!EC_POINT_set_to_infinity(group, acc)) goto err;
+ if (!EC_POINT_set_to_infinity(group, acc))
+ goto err;
- if (scalar)
- {
- if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err;
+ if (scalar) {
+ if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx))
+ goto err;
if (BN_is_negative(scalar))
- if (!group->meth->invert(group, p, ctx)) goto err;
- if (!group->meth->add(group, acc, acc, p, ctx)) goto err;
- }
-
- for (i = 0; i < num; i++)
- {
- if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err;
+ if (!group->meth->invert(group, p, ctx))
+ goto err;
+ if (!group->meth->add(group, acc, acc, p, ctx))
+ goto err;
+ }
+ for (i = 0; i < num; i++) {
+ if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx))
+ goto err;
if (BN_is_negative(scalars[i]))
- if (!group->meth->invert(group, p, ctx)) goto err;
- if (!group->meth->add(group, acc, acc, p, ctx)) goto err;
- }
+ if (!group->meth->invert(group, p, ctx))
+ goto err;
+ if (!group->meth->add(group, acc, acc, p, ctx))
+ goto err;
+ }
- if (!EC_POINT_copy(r, acc)) goto err;
+ if (!EC_POINT_copy(r, acc))
+ goto err;
ret = 1;
- err:
- if (p) EC_POINT_free(p);
- if (acc) EC_POINT_free(acc);
+err:
+ if (p)
+ EC_POINT_free(p);
+ if (acc)
+ EC_POINT_free(acc);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
return ret;
- }
+}
/* Precomputation for point multiplication: fall back to wNAF methods
* because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
-int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
- {
+int
+ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
+{
return ec_wNAF_precompute_mult(group, ctx);
- }
+}
-int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
- {
+int
+ec_GF2m_have_precompute_mult(const EC_GROUP * group)
+{
return ec_wNAF_have_precompute_mult(group);
- }
+}
#endif
Copyright © 1996 – 2023 Jason A. Donenfeld. All Rights Reverse Engineered.