* Computes the multiplicative inverse of a in GF(p), storing the result in r.
* If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
* Since we don't have a Mont structure here, SCA hardening is with blinding.
+ * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.)
*/
int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
BN_CTX *ctx)
temp = BN_CTX_get(ctx);
if (temp == NULL) {
ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE);
- goto err;
+ goto end;
}
- /* make sure lambda is not zero */
+ /*-
+ * Make sure lambda is not zero.
+ * If the RNG fails, we cannot blind but nevertheless want
+ * code to continue smoothly and not clobber the error stack.
+ */
do {
- if (!BN_priv_rand_range_ex(lambda, group->field, ctx)) {
- ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB);
- goto err;
+ ERR_set_mark();
+ ret = BN_priv_rand_range_ex(lambda, group->field, ctx);
+ ERR_pop_to_mark();
+ if (ret == 0) {
+ ret = 1;
+ goto end;
}
} while (BN_is_zero(lambda));
/* if field_encode defined convert between representations */
- if (group->meth->field_encode != NULL
- && !group->meth->field_encode(group, lambda, lambda, ctx))
- goto err;
- if (!group->meth->field_mul(group, p->Z, p->Z, lambda, ctx))
- goto err;
- if (!group->meth->field_sqr(group, temp, lambda, ctx))
- goto err;
- if (!group->meth->field_mul(group, p->X, p->X, temp, ctx))
- goto err;
- if (!group->meth->field_mul(group, temp, temp, lambda, ctx))
- goto err;
- if (!group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
- goto err;
- p->Z_is_one = 0;
+ if ((group->meth->field_encode != NULL
+ && !group->meth->field_encode(group, lambda, lambda, ctx))
+ || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx)
+ || !group->meth->field_sqr(group, temp, lambda, ctx)
+ || !group->meth->field_mul(group, p->X, p->X, temp, ctx)
+ || !group->meth->field_mul(group, temp, temp, lambda, ctx)
+ || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
+ goto end;
+ p->Z_is_one = 0;
ret = 1;
- err:
+ end:
BN_CTX_end(ctx);
return ret;
}
/*-
- * Set s := p, r := 2p.
+ * Input:
+ * - p: affine coordinates
+ *
+ * Output:
+ * - s := p, r := 2p: blinded projective (homogeneous) coordinates
*
* For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
- * multiplication resistant against side channel attacks" appendix, as described
- * at
+ * multiplication resistant against side channel attacks" appendix, described at
* https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
+ * simplified for Z1=1.
*
- * The input point p will be in randomized Jacobian projective coords:
- * x = X/Z**2, y=Y/Z**3
- *
- * The output points p, s, and r are converted to standard (homogeneous)
- * projective coords:
- * x = X/Z, y=Y/Z
+ * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z)
+ * for any non-zero \lambda that holds for projective (homogeneous) coords.
*/
int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
EC_POINT *r, EC_POINT *s,
EC_POINT *p, BN_CTX *ctx)
{
- BIGNUM *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
+ BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL;
- t1 = r->Z;
- t2 = r->Y;
+ t1 = s->Z;
+ t2 = r->Z;
t3 = s->X;
t4 = r->X;
t5 = s->Y;
- t6 = s->Z;
-
- /* convert p: (X,Y,Z) -> (XZ,Y,Z**3) */
- if (!group->meth->field_mul(group, p->X, p->X, p->Z, ctx)
- || !group->meth->field_sqr(group, t1, p->Z, ctx)
- || !group->meth->field_mul(group, p->Z, p->Z, t1, ctx)
- /* r := 2p */
- || !group->meth->field_sqr(group, t2, p->X, ctx)
- || !group->meth->field_sqr(group, t3, p->Z, ctx)
- || !group->meth->field_mul(group, t4, t3, group->a, ctx)
- || !BN_mod_sub_quick(t5, t2, t4, group->field)
- || !BN_mod_add_quick(t2, t2, t4, group->field)
- || !group->meth->field_sqr(group, t5, t5, ctx)
- || !group->meth->field_mul(group, t6, t3, group->b, ctx)
- || !group->meth->field_mul(group, t1, p->X, p->Z, ctx)
- || !group->meth->field_mul(group, t4, t1, t6, ctx)
- || !BN_mod_lshift_quick(t4, t4, 3, group->field)
+
+ if (!p->Z_is_one /* r := 2p */
+ || !group->meth->field_sqr(group, t3, p->X, ctx)
+ || !BN_mod_sub_quick(t4, t3, group->a, group->field)
+ || !group->meth->field_sqr(group, t4, t4, ctx)
+ || !group->meth->field_mul(group, t5, p->X, group->b, ctx)
+ || !BN_mod_lshift_quick(t5, t5, 3, group->field)
/* r->X coord output */
- || !BN_mod_sub_quick(r->X, t5, t4, group->field)
- || !group->meth->field_mul(group, t1, t1, t2, ctx)
- || !group->meth->field_mul(group, t2, t3, t6, ctx)
- || !BN_mod_add_quick(t1, t1, t2, group->field)
+ || !BN_mod_sub_quick(r->X, t4, t5, group->field)
+ || !BN_mod_add_quick(t1, t3, group->a, group->field)
+ || !group->meth->field_mul(group, t2, p->X, t1, ctx)
+ || !BN_mod_add_quick(t2, group->b, t2, group->field)
/* r->Z coord output */
- || !BN_mod_lshift_quick(r->Z, t1, 2, group->field)
- || !EC_POINT_copy(s, p))
+ || !BN_mod_lshift_quick(r->Z, t2, 2, group->field))
+ return 0;
+
+ /* make sure lambda (r->Y here for storage) is not zero */
+ do {
+ if (!BN_priv_rand_range_ex(r->Y, group->field, ctx))
+ return 0;
+ } while (BN_is_zero(r->Y));
+
+ /* make sure lambda (s->Z here for storage) is not zero */
+ do {
+ if (!BN_priv_rand_range_ex(s->Z, group->field, ctx))
+ return 0;
+ } while (BN_is_zero(s->Z));
+
+ /* if field_encode defined convert between representations */
+ if (group->meth->field_encode != NULL
+ && (!group->meth->field_encode(group, r->Y, r->Y, ctx)
+ || !group->meth->field_encode(group, s->Z, s->Z, ctx)))
+ return 0;
+
+ /* blind r and s independently */
+ if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
+ || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)
+ || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */
return 0;
r->Z_is_one = 0;
s->Z_is_one = 0;
- p->Z_is_one = 0;
return 1;
}
/*-
- * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
+ * Input:
+ * - s, r: projective (homogeneous) coordinates
+ * - p: affine coordinates
+ *
+ * Output:
+ * - s := r + s, r := 2r: projective (homogeneous) coordinates
+ *
+ * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
* "A fast parallel elliptic curve multiplication resistant against side channel
* attacks", as described at
- * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4
+ * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4
*/
int ec_GFp_simple_ladder_step(const EC_GROUP *group,
EC_POINT *r, EC_POINT *s,
EC_POINT *p, BN_CTX *ctx)
{
int ret = 0;
- BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6, *t7 = NULL;
+ BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
BN_CTX_start(ctx);
t0 = BN_CTX_get(ctx);
t4 = BN_CTX_get(ctx);
t5 = BN_CTX_get(ctx);
t6 = BN_CTX_get(ctx);
- t7 = BN_CTX_get(ctx);
- if (t7 == NULL
- || !group->meth->field_mul(group, t0, r->X, s->X, ctx)
- || !group->meth->field_mul(group, t1, r->Z, s->Z, ctx)
- || !group->meth->field_mul(group, t2, r->X, s->Z, ctx)
+ if (t6 == NULL
+ || !group->meth->field_mul(group, t6, r->X, s->X, ctx)
+ || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
+ || !group->meth->field_mul(group, t4, r->X, s->Z, ctx)
|| !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
- || !group->meth->field_mul(group, t4, group->a, t1, ctx)
- || !BN_mod_add_quick(t0, t0, t4, group->field)
- || !BN_mod_add_quick(t4, t3, t2, group->field)
- || !group->meth->field_mul(group, t0, t4, t0, ctx)
- || !group->meth->field_sqr(group, t1, t1, ctx)
- || !BN_mod_lshift_quick(t7, group->b, 2, group->field)
- || !group->meth->field_mul(group, t1, t7, t1, ctx)
- || !BN_mod_lshift1_quick(t0, t0, group->field)
- || !BN_mod_add_quick(t0, t1, t0, group->field)
- || !BN_mod_sub_quick(t1, t2, t3, group->field)
- || !group->meth->field_sqr(group, t1, t1, ctx)
- || !group->meth->field_mul(group, t3, t1, p->X, ctx)
- || !group->meth->field_mul(group, t0, p->Z, t0, ctx)
- /* s->X coord output */
- || !BN_mod_sub_quick(s->X, t0, t3, group->field)
- /* s->Z coord output */
- || !group->meth->field_mul(group, s->Z, p->Z, t1, ctx)
- || !group->meth->field_sqr(group, t3, r->X, ctx)
- || !group->meth->field_sqr(group, t2, r->Z, ctx)
- || !group->meth->field_mul(group, t4, t2, group->a, ctx)
- || !BN_mod_add_quick(t5, r->X, r->Z, group->field)
- || !group->meth->field_sqr(group, t5, t5, ctx)
- || !BN_mod_sub_quick(t5, t5, t3, group->field)
- || !BN_mod_sub_quick(t5, t5, t2, group->field)
- || !BN_mod_sub_quick(t6, t3, t4, group->field)
- || !group->meth->field_sqr(group, t6, t6, ctx)
- || !group->meth->field_mul(group, t0, t2, t5, ctx)
- || !group->meth->field_mul(group, t0, t7, t0, ctx)
- /* r->X coord output */
- || !BN_mod_sub_quick(r->X, t6, t0, group->field)
+ || !group->meth->field_mul(group, t5, group->a, t0, ctx)
+ || !BN_mod_add_quick(t5, t6, t5, group->field)
|| !BN_mod_add_quick(t6, t3, t4, group->field)
- || !group->meth->field_sqr(group, t3, t2, ctx)
- || !group->meth->field_mul(group, t7, t3, t7, ctx)
- || !group->meth->field_mul(group, t5, t5, t6, ctx)
+ || !group->meth->field_mul(group, t5, t6, t5, ctx)
+ || !group->meth->field_sqr(group, t0, t0, ctx)
+ || !BN_mod_lshift_quick(t2, group->b, 2, group->field)
+ || !group->meth->field_mul(group, t0, t2, t0, ctx)
|| !BN_mod_lshift1_quick(t5, t5, group->field)
+ || !BN_mod_sub_quick(t3, t4, t3, group->field)
+ /* s->Z coord output */
+ || !group->meth->field_sqr(group, s->Z, t3, ctx)
+ || !group->meth->field_mul(group, t4, s->Z, p->X, ctx)
+ || !BN_mod_add_quick(t0, t0, t5, group->field)
+ /* s->X coord output */
+ || !BN_mod_sub_quick(s->X, t0, t4, group->field)
+ || !group->meth->field_sqr(group, t4, r->X, ctx)
+ || !group->meth->field_sqr(group, t5, r->Z, ctx)
+ || !group->meth->field_mul(group, t6, t5, group->a, ctx)
+ || !BN_mod_add_quick(t1, r->X, r->Z, group->field)
+ || !group->meth->field_sqr(group, t1, t1, ctx)
+ || !BN_mod_sub_quick(t1, t1, t4, group->field)
+ || !BN_mod_sub_quick(t1, t1, t5, group->field)
+ || !BN_mod_sub_quick(t3, t4, t6, group->field)
+ || !group->meth->field_sqr(group, t3, t3, ctx)
+ || !group->meth->field_mul(group, t0, t5, t1, ctx)
+ || !group->meth->field_mul(group, t0, t2, t0, ctx)
+ /* r->X coord output */
+ || !BN_mod_sub_quick(r->X, t3, t0, group->field)
+ || !BN_mod_add_quick(t3, t4, t6, group->field)
+ || !group->meth->field_sqr(group, t4, t5, ctx)
+ || !group->meth->field_mul(group, t4, t4, t2, ctx)
+ || !group->meth->field_mul(group, t1, t1, t3, ctx)
+ || !BN_mod_lshift1_quick(t1, t1, group->field)
/* r->Z coord output */
- || !BN_mod_add_quick(r->Z, t7, t5, group->field))
+ || !BN_mod_add_quick(r->Z, t4, t1, group->field))
goto err;
ret = 1;
}
/*-
+ * Input:
+ * - s, r: projective (homogeneous) coordinates
+ * - p: affine coordinates
+ *
+ * Output:
+ * - r := (x,y): affine coordinates
+ *
* Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
- * Elliptic Curves and Side-Channel Attacks", modified to work in projective
- * coordinates and return r in Jacobian projective coordinates.
+ * Elliptic Curves and Side-Channel Attacks", modified to work in mixed
+ * projective coords, i.e. p is affine and (r,s) in projective (homogeneous)
+ * coords, and return r in affine coordinates.
*
- * X4 = two*Y1*X2*Z3*Z2*Z1;
- * Y4 = two*b*Z3*SQR(Z2*Z1) + Z3*(a*Z2*Z1+X1*X2)*(X1*Z2+X2*Z1) - X3*SQR(X1*Z2-X2*Z1);
- * Z4 = two*Y1*Z3*SQR(Z2)*Z1;
+ * X4 = two*Y1*X2*Z3*Z2;
+ * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2);
+ * Z4 = two*Y1*Z3*SQR(Z2);
*
* Z4 != 0 because:
- * - Z1==0 implies p is at infinity, which would have caused an early exit in
- * the caller;
* - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch);
* - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch);
* - Y1==0 implies p has order 2, so either r or s are infinity and handled by
return EC_POINT_set_to_infinity(group, r);
if (BN_is_zero(s->Z)) {
- /* (X,Y,Z) -> (XZ,YZ**2,Z) */
- if (!group->meth->field_mul(group, r->X, p->X, p->Z, ctx)
- || !group->meth->field_sqr(group, r->Z, p->Z, ctx)
- || !group->meth->field_mul(group, r->Y, p->Y, r->Z, ctx)
- || !BN_copy(r->Z, p->Z)
+ if (!EC_POINT_copy(r, p)
|| !EC_POINT_invert(group, r, ctx))
return 0;
return 1;
t6 = BN_CTX_get(ctx);
if (t6 == NULL
- || !BN_mod_lshift1_quick(t0, p->Y, group->field)
- || !group->meth->field_mul(group, t1, r->X, p->Z, ctx)
- || !group->meth->field_mul(group, t2, r->Z, s->Z, ctx)
- || !group->meth->field_mul(group, t2, t1, t2, ctx)
- || !group->meth->field_mul(group, t3, t2, t0, ctx)
- || !group->meth->field_mul(group, t2, r->Z, p->Z, ctx)
- || !group->meth->field_sqr(group, t4, t2, ctx)
- || !BN_mod_lshift1_quick(t5, group->b, group->field)
- || !group->meth->field_mul(group, t4, t4, t5, ctx)
- || !group->meth->field_mul(group, t6, t2, group->a, ctx)
- || !group->meth->field_mul(group, t5, r->X, p->X, ctx)
- || !BN_mod_add_quick(t5, t6, t5, group->field)
- || !group->meth->field_mul(group, t6, r->Z, p->X, ctx)
- || !BN_mod_add_quick(t2, t6, t1, group->field)
- || !group->meth->field_mul(group, t5, t5, t2, ctx)
- || !BN_mod_sub_quick(t6, t6, t1, group->field)
- || !group->meth->field_sqr(group, t6, t6, ctx)
- || !group->meth->field_mul(group, t6, t6, s->X, ctx)
- || !BN_mod_add_quick(t4, t5, t4, group->field)
- || !group->meth->field_mul(group, t4, t4, s->Z, ctx)
- || !BN_mod_sub_quick(t4, t4, t6, group->field)
- || !group->meth->field_sqr(group, t5, r->Z, ctx)
- || !group->meth->field_mul(group, r->Z, p->Z, s->Z, ctx)
- || !group->meth->field_mul(group, r->Z, t5, r->Z, ctx)
- || !group->meth->field_mul(group, r->Z, r->Z, t0, ctx)
- /* t3 := X, t4 := Y */
- /* (X,Y,Z) -> (XZ,YZ**2,Z) */
- || !group->meth->field_mul(group, r->X, t3, r->Z, ctx)
+ || !BN_mod_lshift1_quick(t4, p->Y, group->field)
+ || !group->meth->field_mul(group, t6, r->X, t4, ctx)
+ || !group->meth->field_mul(group, t6, s->Z, t6, ctx)
+ || !group->meth->field_mul(group, t5, r->Z, t6, ctx)
+ || !BN_mod_lshift1_quick(t1, group->b, group->field)
+ || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
|| !group->meth->field_sqr(group, t3, r->Z, ctx)
- || !group->meth->field_mul(group, r->Y, t4, t3, ctx))
+ || !group->meth->field_mul(group, t2, t3, t1, ctx)
+ || !group->meth->field_mul(group, t6, r->Z, group->a, ctx)
+ || !group->meth->field_mul(group, t1, p->X, r->X, ctx)
+ || !BN_mod_add_quick(t1, t1, t6, group->field)
+ || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
+ || !group->meth->field_mul(group, t0, p->X, r->Z, ctx)
+ || !BN_mod_add_quick(t6, r->X, t0, group->field)
+ || !group->meth->field_mul(group, t6, t6, t1, ctx)
+ || !BN_mod_add_quick(t6, t6, t2, group->field)
+ || !BN_mod_sub_quick(t0, t0, r->X, group->field)
+ || !group->meth->field_sqr(group, t0, t0, ctx)
+ || !group->meth->field_mul(group, t0, t0, s->X, ctx)
+ || !BN_mod_sub_quick(t0, t6, t0, group->field)
+ || !group->meth->field_mul(group, t1, s->Z, t4, ctx)
+ || !group->meth->field_mul(group, t1, t3, t1, ctx)
+ || (group->meth->field_decode != NULL
+ && !group->meth->field_decode(group, t1, t1, ctx))
+ || !group->meth->field_inv(group, t1, t1, ctx)
+ || (group->meth->field_encode != NULL
+ && !group->meth->field_encode(group, t1, t1, ctx))
+ || !group->meth->field_mul(group, r->X, t5, t1, ctx)
+ || !group->meth->field_mul(group, r->Y, t0, t1, ctx))
goto err;
+ if (group->meth->field_set_to_one != NULL) {
+ if (!group->meth->field_set_to_one(group, r->Z, ctx))
+ goto err;
+ } else {
+ if (!BN_one(r->Z))
+ goto err;
+ }
+
+ r->Z_is_one = 1;
ret = 1;
err:
projects / openssl.git / blobdiff