350 lines
9.9 KiB
C
350 lines
9.9 KiB
C
// Originally written by Bodo Moeller for the OpenSSL project.
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// Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
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// Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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//
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// The elliptic curve binary polynomial software is originally written by
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// Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
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// Laboratories.
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//
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// SPDX-License-Identifier: Apache-2.0
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#include <openssl/ec.h>
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#include <openssl/bn.h>
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#include <openssl/err.h>
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#include "internal.h"
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static int is_point_conversion_form_hybrid(int form_bit) {
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return POINT_CONVERSION_HYBRID == (form_bit & ~1u);
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}
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static int is_hybrid_bytes_consistent(const uint8_t *in, size_t field_len) {
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// Check that the encoded solution in the first byte aligns with the computed
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// point's, i.e., that they have the same parity.
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return ((in[0] & 1) == (in[1 + field_len * 2 - 1] & 1));
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}
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size_t ec_point_byte_len(const EC_GROUP *group, point_conversion_form_t form) {
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if (form != POINT_CONVERSION_COMPRESSED &&
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form != POINT_CONVERSION_UNCOMPRESSED &&
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form != POINT_CONVERSION_HYBRID) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FORM);
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return 0;
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}
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const size_t field_len = BN_num_bytes(&group->field.N);
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size_t output_len = 1 /* type byte */ + field_len;
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if (form == POINT_CONVERSION_UNCOMPRESSED ||
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form == POINT_CONVERSION_HYBRID) {
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// Uncompressed and Hybrid points have a second coordinate.
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output_len += field_len;
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}
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return output_len;
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}
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size_t ec_point_to_bytes(const EC_GROUP *group, const EC_AFFINE *point,
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point_conversion_form_t form, uint8_t *buf,
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size_t len) {
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size_t output_len = ec_point_byte_len(group, form);
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if (len < output_len) {
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OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
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return 0;
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}
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size_t field_len;
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ec_felem_to_bytes(group, buf + 1, &field_len, &point->X);
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assert(field_len == BN_num_bytes(&group->field.N));
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if (form == POINT_CONVERSION_UNCOMPRESSED) {
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ec_felem_to_bytes(group, buf + 1 + field_len, &field_len, &point->Y);
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assert(field_len == BN_num_bytes(&group->field.N));
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buf[0] = form;
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} else {
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uint8_t y_buf[EC_MAX_BYTES];
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ec_felem_to_bytes(group, y_buf, &field_len, &point->Y);
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buf[0] = form + (y_buf[field_len - 1] & 1);
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if (form == POINT_CONVERSION_HYBRID) {
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// |POINT_CONVERSION_HYBRID| specifies y's solution of the quadratic
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// equation, but also encodes the y coordinate along with it.
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OPENSSL_memcpy(buf + 1 + field_len, y_buf, field_len);
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}
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}
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return output_len;
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}
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int ec_point_from_uncompressed(const EC_GROUP *group, EC_AFFINE *out,
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const uint8_t *in, size_t len) {
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const size_t field_len = BN_num_bytes(&group->field.N);
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if (len != 1 + 2 * field_len || in[0] != POINT_CONVERSION_UNCOMPRESSED) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
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return 0;
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}
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EC_FELEM x, y;
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if (!ec_felem_from_bytes(group, &x, in + 1, field_len) ||
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!ec_felem_from_bytes(group, &y, in + 1 + field_len, field_len) ||
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!ec_point_set_affine_coordinates(group, out, &x, &y)) {
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return 0;
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}
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return 1;
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}
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static int ec_point_from_hybrid(const EC_GROUP *group, EC_AFFINE *out,
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const uint8_t *in, size_t len) {
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const size_t field_len = BN_num_bytes(&group->field.N);
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// |POINT_CONVERSION_HYBRID| has the solution of y encoded in the first byte
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// as well.
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if (len != 1 + 2 * field_len || !is_point_conversion_form_hybrid(in[0]) ||
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!is_hybrid_bytes_consistent(in, field_len)) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
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return 0;
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}
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EC_FELEM x, y;
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if (!ec_felem_from_bytes(group, &x, in + 1, field_len) ||
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!ec_felem_from_bytes(group, &y, in + 1 + field_len, field_len) ||
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!ec_point_set_affine_coordinates(group, out, &x, &y)) {
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return 0;
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}
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return 1;
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}
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static int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
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const uint8_t *buf, size_t len,
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BN_CTX *ctx) {
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if (len == 0) {
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OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
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return 0;
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}
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point_conversion_form_t form = buf[0];
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// OpenSSL supports decoding infinity.
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if (form == 0) {
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if (len != 1) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
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return 0;
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}
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ec_GFp_simple_point_set_to_infinity(group, &point->raw);
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return 1;
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}
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const int y_bit = form & 1;
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form = form & ~1u;
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if (form == POINT_CONVERSION_UNCOMPRESSED) {
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EC_AFFINE affine;
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if (!ec_point_from_uncompressed(group, &affine, buf, len)) {
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// In the event of an error, defend against the caller not checking the
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// return value by setting a known safe value.
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ec_set_to_safe_point(group, &point->raw);
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return 0;
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}
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ec_affine_to_jacobian(group, &point->raw, &affine);
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return 1;
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}
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if (form == POINT_CONVERSION_HYBRID) {
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EC_AFFINE affine;
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if (!ec_point_from_hybrid(group, &affine, buf, len)) {
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ec_set_to_safe_point(group, &point->raw);
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return 0;
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}
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ec_affine_to_jacobian(group, &point->raw, &affine);
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return 1;
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}
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const size_t field_len = BN_num_bytes(&group->field.N);
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if (form != POINT_CONVERSION_COMPRESSED ||
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len != 1 /* type byte */ + field_len) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
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return 0;
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}
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// TODO(davidben): Integrate compressed coordinates with the lower-level EC
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// abstractions. This requires a way to compute square roots, which is tricky
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// for primes which are not 3 (mod 4), namely P-224 and custom curves. P-224's
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// prime is particularly inconvenient for compressed coordinates. See
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// https://cr.yp.to/papers/sqroot.pdf
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BN_CTX *new_ctx = NULL;
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if (ctx == NULL) {
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL) {
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return 0;
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}
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}
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int ret = 0;
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BN_CTX_start(ctx);
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BIGNUM *x = BN_CTX_get(ctx);
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if (x == NULL || !BN_bin2bn(buf + 1, field_len, x)) {
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goto err;
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}
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if (BN_ucmp(x, &group->field.N) >= 0) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
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goto err;
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}
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if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) {
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goto err;
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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BN_CTX_free(new_ctx);
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return ret;
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}
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int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point,
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const uint8_t *buf, size_t len, BN_CTX *ctx) {
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if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
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OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
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return 0;
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}
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return ec_GFp_simple_oct2point(group, point, buf, len, ctx);
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}
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size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point,
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point_conversion_form_t form, uint8_t *buf,
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size_t len, BN_CTX *ctx) {
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if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
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OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
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return 0;
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}
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// OpenSSL encodes infinity to a single 0 octet.
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if (ec_GFp_simple_is_at_infinity(group, &point->raw)) {
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if(buf != NULL) {
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if (len < 1) {
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OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
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return 0;
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}
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buf[0] = 0;
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}
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return 1;
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}
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if (buf == NULL) {
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// When |buf| is NULL, just return the number of bytes that would be
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// written, without doing an expensive Jacobian-to-affine conversion.
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return ec_point_byte_len(group, form);
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}
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EC_AFFINE affine;
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if (!ec_jacobian_to_affine(group, &affine, &point->raw)) {
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return 0;
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}
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return ec_point_to_bytes(group, &affine, form, buf, len);
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}
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int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
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EC_POINT *point, const BIGNUM *x,
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int y_bit, BN_CTX *ctx) {
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if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
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OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
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return 0;
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}
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const BIGNUM *field = &group->field.N;
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if (BN_is_negative(x) || BN_cmp(x, field) >= 0) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
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return 0;
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}
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BN_CTX *new_ctx = NULL;
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int ret = 0;
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ERR_clear_error();
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if (ctx == NULL) {
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL) {
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return 0;
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}
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}
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y_bit = (y_bit != 0);
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BN_CTX_start(ctx);
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BIGNUM *tmp1 = BN_CTX_get(ctx);
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BIGNUM *tmp2 = BN_CTX_get(ctx);
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BIGNUM *a = BN_CTX_get(ctx);
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BIGNUM *b = BN_CTX_get(ctx);
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BIGNUM *y = BN_CTX_get(ctx);
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if (y == NULL ||
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!EC_GROUP_get_curve_GFp(group, NULL, a, b, ctx)) {
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goto err;
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}
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// Recover y. We have a Weierstrass equation
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// y^2 = x^3 + a*x + b,
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// so y is one of the square roots of x^3 + a*x + b.
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// tmp1 := x^3
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if (!BN_mod_sqr(tmp2, x, field, ctx) ||
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!BN_mod_mul(tmp1, tmp2, x, field, ctx)) {
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goto err;
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}
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// tmp1 := tmp1 + a*x
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if (group->a_is_minus3) {
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if (!bn_mod_lshift1_consttime(tmp2, x, field, ctx) ||
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!bn_mod_add_consttime(tmp2, tmp2, x, field, ctx) ||
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!bn_mod_sub_consttime(tmp1, tmp1, tmp2, field, ctx)) {
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goto err;
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}
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} else {
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if (!BN_mod_mul(tmp2, a, x, field, ctx) ||
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!bn_mod_add_consttime(tmp1, tmp1, tmp2, field, ctx)) {
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goto err;
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}
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}
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// tmp1 := tmp1 + b
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if (!bn_mod_add_consttime(tmp1, tmp1, b, field, ctx)) {
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goto err;
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}
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if (!BN_mod_sqrt(y, tmp1, field, ctx)) {
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uint32_t err = ERR_peek_last_error();
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if (ERR_GET_LIB(err) == ERR_LIB_BN &&
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ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
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ERR_clear_error();
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
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} else {
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OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
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}
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goto err;
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}
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if (y_bit != BN_is_odd(y)) {
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if (BN_is_zero(y)) {
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OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSION_BIT);
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goto err;
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}
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if (!BN_usub(y, field, y)) {
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goto err;
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}
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}
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if (y_bit != BN_is_odd(y)) {
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OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
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goto err;
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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BN_CTX_free(new_ctx);
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return ret;
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}
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