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Using Horner's algorithm to evaluate the ec polynomial

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(suggested by Adam Young <ayoung@cigital.com>)

Submitted by: Nils Larsch
This commit is contained in:
Geoff Thorpe 2004-07-16 03:24:19 +00:00
parent 5906e8d5fe
commit 7f5b4dd1e8
2 changed files with 41 additions and 61 deletions
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49
crypto/ec/ec2_smpl.c
View File

@ -805,13 +805,18 @@ int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
*/ */
int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
{ {
BN_CTX *new_ctx = NULL;
BIGNUM *rh, *lh, *tmp1;
int ret = -1; int ret = -1;
BN_CTX *new_ctx = NULL;
BIGNUM *lh, *y2;
int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
if (EC_POINT_is_at_infinity(group, point)) if (EC_POINT_is_at_infinity(group, point))
return 1; return 1;
field_mul = group->meth->field_mul;
field_sqr = group->meth->field_sqr;
/* only support affine coordinates */ /* only support affine coordinates */
if (!point->Z_is_one) goto err; if (!point->Z_is_one) goto err;
@ -823,37 +828,23 @@ int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_
} }
BN_CTX_start(ctx); BN_CTX_start(ctx);
rh = BN_CTX_get(ctx); y2 = BN_CTX_get(ctx);
lh = BN_CTX_get(ctx); lh = BN_CTX_get(ctx);
tmp1 = BN_CTX_get(ctx); if (lh == NULL) goto err;
if (tmp1 == NULL) goto err;
/* We have a curve defined by a Weierstrass equation /* We have a curve defined by a Weierstrass equation
* y^2 + x*y = x^3 + a*x^2 + b. * y^2 + x*y = x^3 + a*x^2 + b.
* To test this, we add up the right-hand side in 'rh' * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
* and the left-hand side in 'lh'. * <=> ((x + a) * x + y ) * x + b + y^2 = 0
*/ */
if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
/* rh := X^3 */ if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
if (!group->meth->field_sqr(group, tmp1, &point->X, ctx)) goto err; if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
if (!group->meth->field_mul(group, rh, tmp1, &point->X, ctx)) goto err; if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
/* rh := rh + a*X^2 */ if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
if (!group->meth->field_mul(group, tmp1, tmp1, &group->a, ctx)) goto err; if (!BN_GF2m_add(lh, lh, y2)) goto err;
if (!BN_GF2m_add(rh, rh, tmp1)) goto err; ret = BN_is_zero(lh);
/* rh := rh + b */
if (!BN_GF2m_add(rh, rh, &group->b)) goto err;
/* lh := Y^2 */
if (!group->meth->field_sqr(group, lh, &point->Y, ctx)) goto err;
/* lh := lh + x*y */
if (!group->meth->field_mul(group, tmp1, &point->X, &point->Y, ctx)) goto err;
if (!BN_GF2m_add(lh, lh, tmp1)) goto err;
ret = (0 == BN_GF2m_cmp(lh, rh));
err: err:
if (ctx) BN_CTX_end(ctx); if (ctx) BN_CTX_end(ctx);
if (new_ctx) BN_CTX_free(new_ctx); if (new_ctx) BN_CTX_free(new_ctx);

53
crypto/ec/ecp_smpl.c
View File

@ -1301,7 +1301,7 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
const BIGNUM *p; const BIGNUM *p;
BN_CTX *new_ctx = NULL; BN_CTX *new_ctx = NULL;
BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6; BIGNUM *rh, *tmp, *Z4, *Z6;
int ret = -1; int ret = -1;
if (EC_POINT_is_at_infinity(group, point)) if (EC_POINT_is_at_infinity(group, point))
@ -1320,8 +1320,7 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
BN_CTX_start(ctx); BN_CTX_start(ctx);
rh = BN_CTX_get(ctx); rh = BN_CTX_get(ctx);
tmp1 = BN_CTX_get(ctx); tmp = BN_CTX_get(ctx);
tmp2 = BN_CTX_get(ctx);
Z4 = BN_CTX_get(ctx); Z4 = BN_CTX_get(ctx);
Z6 = BN_CTX_get(ctx); Z6 = BN_CTX_get(ctx);
if (Z6 == NULL) goto err; if (Z6 == NULL) goto err;
@ -1335,59 +1334,49 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
* To test this, we add up the right-hand side in 'rh'. * To test this, we add up the right-hand side in 'rh'.
*/ */
/* rh := X^3 */ /* rh := X^2 */
if (!field_sqr(group, rh, &point->X, ctx)) goto err; if (!field_sqr(group, rh, &point->X, ctx)) goto err;
if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
if (!point->Z_is_one) if (!point->Z_is_one)
{ {
if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err; if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
if (!field_sqr(group, Z4, tmp1, ctx)) goto err; if (!field_sqr(group, Z4, tmp, ctx)) goto err;
if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err; if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
/* rh := rh + a*X*Z^4 */ /* rh := (rh + a*Z^4)*X */
if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
if (group->a_is_minus3) if (group->a_is_minus3)
{ {
if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err; if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err; if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err; if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
} }
else else
{ {
if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err; if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err; if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
} }
/* rh := rh + b*Z^6 */ /* rh := rh + b*Z^6 */
if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err; if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err; if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
} }
else else
{ {
/* point->Z_is_one */ /* point->Z_is_one */
/* rh := rh + a*X */ /* rh := (rh + a)*X */
if (group->a_is_minus3) if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
{ if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
}
else
{
if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
}
/* rh := rh + b */ /* rh := rh + b */
if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err; if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
} }
/* 'lh' := Y^2 */ /* 'lh' := Y^2 */
if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err; if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
ret = (0 == BN_cmp(tmp1, rh)); ret = (0 == BN_ucmp(tmp, rh));
err: err:
BN_CTX_end(ctx); BN_CTX_end(ctx);