ecdh_simple_compute_key,
0, /* field_inverse_mod_ord */
ec_GFp_simple_blind_coordinates,
- 0, /* ladder_pre */
- 0, /* ladder_step */
- 0 /* ladder_post */
+ ec_GFp_simple_ladder_pre,
+ ec_GFp_simple_ladder_step,
+ ec_GFp_simple_ladder_post
};
return &ret;
ret = 1;
err:
- BN_CTX_end(ctx);
- return ret;
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*-
+ * Set s := p, r := 2p.
+ *
+ * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
+ * multiplication resistant against side channel attacks" appendix, as described
+ * at
+ * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
+ *
+ * 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
+ */
+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;
+
+ t1 = r->Z;
+ t2 = r->Y;
+ 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)
+ /* 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)
+ /* r->Z coord output */
+ || !BN_mod_lshift_quick(r->Z, t1, 2, group->field)
+ || !EC_POINT_copy(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. (8) 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-3
+ */
+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;
+
+ BN_CTX_start(ctx);
+ t0 = BN_CTX_get(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ t3 = 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)
+ || !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
+ || !group->meth->field_mul(group, t4, group->a, t1, ctx)
+ || !BN_mod_sub_quick(t4, t0, t4, group->field)
+ || !BN_mod_add_quick(t5, t3, t2, group->field)
+ || !group->meth->field_sqr(group, t4, t4, ctx)
+ || !group->meth->field_mul(group, t5, t1, t5, ctx)
+ || !BN_mod_lshift_quick(t0, group->b, 2, group->field)
+ || !group->meth->field_mul(group, t5, t0, t5, ctx)
+ || !BN_mod_sub_quick(t5, t4, t5, group->field)
+ /* s->X coord output */
+ || !group->meth->field_mul(group, s->X, t5, p->Z, ctx)
+ || !BN_mod_sub_quick(t3, t2, t3, group->field)
+ || !group->meth->field_sqr(group, t3, t3, ctx)
+ /* s->Z coord output */
+ || !group->meth->field_mul(group, s->Z, t3, p->X, ctx)
+ || !group->meth->field_sqr(group, t2, r->X, ctx)
+ || !group->meth->field_sqr(group, t4, r->Z, ctx)
+ || !group->meth->field_mul(group, t1, t4, group->a, ctx)
+ || !BN_mod_add_quick(t6, r->X, r->Z, group->field)
+ || !group->meth->field_sqr(group, t6, t6, ctx)
+ || !BN_mod_sub_quick(t6, t6, t2, group->field)
+ || !BN_mod_sub_quick(t6, t6, t4, group->field)
+ || !BN_mod_sub_quick(t7, t2, t1, group->field)
+ || !group->meth->field_sqr(group, t7, t7, ctx)
+ || !group->meth->field_mul(group, t5, t4, t6, ctx)
+ || !group->meth->field_mul(group, t5, t0, t5, ctx)
+ /* r->X coord output */
+ || !BN_mod_sub_quick(r->X, t7, t5, group->field)
+ || !BN_mod_add_quick(t2, t2, t1, group->field)
+ || !group->meth->field_sqr(group, t5, t4, ctx)
+ || !group->meth->field_mul(group, t5, t5, t0, ctx)
+ || !group->meth->field_mul(group, t6, t6, t2, ctx)
+ || !BN_mod_lshift1_quick(t6, t6, group->field)
+ /* r->Z coord output */
+ || !BN_mod_add_quick(r->Z, t5, t6, group->field))
+ goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*-
+ * 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.
+ *
+ * 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;
+ *
+ * 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
+ * one of the BN_is_zero(...) branches.
+ */
+int ec_GFp_simple_ladder_post(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 = NULL;
+
+ if (BN_is_zero(r->Z))
+ 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)
+ || !EC_POINT_invert(group, r, ctx))
+ return 0;
+ return 1;
+ }
+
+ BN_CTX_start(ctx);
+ t0 = BN_CTX_get(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ t3 = BN_CTX_get(ctx);
+ t4 = BN_CTX_get(ctx);
+ t5 = BN_CTX_get(ctx);
+ 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)
+ || !group->meth->field_sqr(group, t3, r->Z, ctx)
+ || !group->meth->field_mul(group, r->Y, t4, t3, ctx))
+ goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
}
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