/* $OpenBSD: ec2_oct.c,v 1.16 2021/05/03 14:42:45 tb Exp $ */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * * The Elliptic Curve Public-Key Crypto Library (ECC Code) included * herein is developed by SUN MICROSYSTEMS, INC., and is contributed * to the OpenSSL project. * * The ECC Code is licensed pursuant to the OpenSSL open source * license provided below. * * The software is originally written by Sheueling Chang Shantz and * Douglas Stebila of Sun Microsystems Laboratories. * */ /* ==================================================================== * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * 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 * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include #include #include "ec_lcl.h" #ifndef OPENSSL_NO_EC2M /* Calculates and sets the affine coordinates of an EC_POINT from the given * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. * Note that the simple implementation only uses affine coordinates. * * The method is from the following publication: * * Harper, Menezes, Vanstone: * "Public-Key Cryptosystems with Very Small Key Lengths", * EUROCRYPT '92, Springer-Verlag LNCS 658, * published February 1993 * * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe * the same method, but claim no priority date earlier than July 29, 1994 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). */ int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x_, int y_bit, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; BIGNUM *tmp, *x, *y, *z; int ret = 0, z0; /* clear error queue */ ERR_clear_error(); if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } y_bit = (y_bit != 0) ? 1 : 0; BN_CTX_start(ctx); if ((tmp = BN_CTX_get(ctx)) == NULL) goto err; if ((x = BN_CTX_get(ctx)) == NULL) goto err; if ((y = BN_CTX_get(ctx)) == NULL) goto err; if ((z = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; if (BN_is_zero(x)) { if (y_bit != 0) { ECerror(EC_R_INVALID_COMPRESSED_POINT); goto err; } if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; } else { if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; if (!BN_GF2m_add(tmp, x, tmp)) goto err; if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) { unsigned long err = ERR_peek_last_error(); if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) { ERR_clear_error(); ECerror(EC_R_INVALID_COMPRESSED_POINT); } else ECerror(ERR_R_BN_LIB); goto err; } z0 = (BN_is_odd(z)) ? 1 : 0; if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; if (z0 != y_bit) { if (!BN_GF2m_add(y, y, x)) goto err; } } if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx)) goto err; ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } /* Converts an EC_POINT to an octet string. * If buf is NULL, the encoded length will be returned. * If the length len of buf is smaller than required an error will be returned. */ size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, unsigned char *buf, size_t len, BN_CTX * ctx) { size_t ret; BN_CTX *new_ctx = NULL; int used_ctx = 0; BIGNUM *x, *y, *yxi; size_t field_len, i, skip; if ((form != POINT_CONVERSION_COMPRESSED) && (form != POINT_CONVERSION_UNCOMPRESSED) && (form != POINT_CONVERSION_HYBRID)) { ECerror(EC_R_INVALID_FORM); goto err; } if (EC_POINT_is_at_infinity(group, point) > 0) { /* encodes to a single 0 octet */ if (buf != NULL) { if (len < 1) { ECerror(EC_R_BUFFER_TOO_SMALL); return 0; } buf[0] = 0; } return 1; } /* ret := required output buffer length */ field_len = (EC_GROUP_get_degree(group) + 7) / 8; ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; /* if 'buf' is NULL, just return required length */ if (buf != NULL) { if (len < ret) { ECerror(EC_R_BUFFER_TOO_SMALL); goto err; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); used_ctx = 1; if ((x = BN_CTX_get(ctx)) == NULL) goto err; if ((y = BN_CTX_get(ctx)) == NULL) goto err; if ((yxi = BN_CTX_get(ctx)) == NULL) goto err; if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) goto err; buf[0] = form; if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) { if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; if (BN_is_odd(yxi)) buf[0]++; } i = 1; skip = field_len - BN_num_bytes(x); if (skip > field_len) { ECerror(ERR_R_INTERNAL_ERROR); goto err; } while (skip > 0) { buf[i++] = 0; skip--; } skip = BN_bn2bin(x, buf + i); i += skip; if (i != 1 + field_len) { ECerror(ERR_R_INTERNAL_ERROR); goto err; } if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) { skip = field_len - BN_num_bytes(y); if (skip > field_len) { ECerror(ERR_R_INTERNAL_ERROR); goto err; } while (skip > 0) { buf[i++] = 0; skip--; } skip = BN_bn2bin(y, buf + i); i += skip; } if (i != ret) { ECerror(ERR_R_INTERNAL_ERROR); goto err; } } if (used_ctx) BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; err: if (used_ctx) BN_CTX_end(ctx); BN_CTX_free(new_ctx); return 0; } /* * Converts an octet string representation to an EC_POINT. * Note that the simple implementation only uses affine coordinates. */ int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, const unsigned char *buf, size_t len, BN_CTX *ctx) { point_conversion_form_t form; int y_bit; BN_CTX *new_ctx = NULL; BIGNUM *x, *y, *yxi; size_t field_len, enc_len; int ret = 0; if (len == 0) { ECerror(EC_R_BUFFER_TOO_SMALL); return 0; } /* * The first octet is the point conversion octet PC, see X9.62, page 4 * and section 4.4.2. It must be: * 0x00 for the point at infinity * 0x02 or 0x03 for compressed form * 0x04 for uncompressed form * 0x06 or 0x07 for hybrid form. * For compressed or hybrid forms, we store the last bit of buf[0] as * y_bit and clear it from buf[0] so as to obtain a POINT_CONVERSION_*. * We error if buf[0] contains any but the above values. */ y_bit = buf[0] & 1; form = buf[0] & ~1U; if (form != 0 && form != POINT_CONVERSION_COMPRESSED && form != POINT_CONVERSION_UNCOMPRESSED && form != POINT_CONVERSION_HYBRID) { ECerror(EC_R_INVALID_ENCODING); return 0; } if (form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) { if (y_bit != 0) { ECerror(EC_R_INVALID_ENCODING); return 0; } } /* The point at infinity is represented by a single zero octet. */ if (form == 0) { if (len != 1) { ECerror(EC_R_INVALID_ENCODING); return 0; } return EC_POINT_set_to_infinity(group, point); } field_len = (EC_GROUP_get_degree(group) + 7) / 8; enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; if (len != enc_len) { ECerror(EC_R_INVALID_ENCODING); return 0; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); if ((x = BN_CTX_get(ctx)) == NULL) goto err; if ((y = BN_CTX_get(ctx)) == NULL) goto err; if ((yxi = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_bin2bn(buf + 1, field_len, x)) goto err; if (BN_ucmp(x, &group->field) >= 0) { ECerror(EC_R_INVALID_ENCODING); goto err; } if (form == POINT_CONVERSION_COMPRESSED) { /* * EC_POINT_set_compressed_coordinates checks that the * point is on the curve as required by X9.62. */ if (!EC_POINT_set_compressed_coordinates(group, point, x, y_bit, ctx)) goto err; } else { if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; if (BN_ucmp(y, &group->field) >= 0) { ECerror(EC_R_INVALID_ENCODING); goto err; } if (form == POINT_CONVERSION_HYBRID) { /* * Check that the form in the encoding was set * correctly according to X9.62 4.4.2.a, 4(c), * see also first paragraph of X9.62 4.4.1.b. */ if (BN_is_zero(x)) { if (y_bit != 0) { ECerror(EC_R_INVALID_ENCODING); goto err; } } else { if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; if (y_bit != BN_is_odd(yxi)) { ECerror(EC_R_INVALID_ENCODING); goto err; } } } /* * EC_POINT_set_affine_coordinates checks that the * point is on the curve as required by X9.62. */ if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx)) goto err; } ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } #endif