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1/*
2 * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved.
4 *
5 * Licensed under the OpenSSL license (the "License").  You may not use
6 * this file except in compliance with the License.  You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 */
10
11#include <openssl/ec.h>
12
13#include <openssl/bn.h>
14#include <openssl/err.h>
15
16#include "internal.h"
17
18
19size_t ec_point_byte_len(const EC_GROUP *group, point_conversion_form_t form) {
20  if (form != POINT_CONVERSION_COMPRESSED &&
21      form != POINT_CONVERSION_UNCOMPRESSED) {
22    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FORM);
23    return 0;
24  }
25
26  const size_t field_len = BN_num_bytes(&group->field.N);
27  size_t output_len = 1 /* type byte */ + field_len;
28  if (form == POINT_CONVERSION_UNCOMPRESSED) {
29    // Uncompressed points have a second coordinate.
30    output_len += field_len;
31  }
32  return output_len;
33}
34
35size_t ec_point_to_bytes(const EC_GROUP *group, const EC_AFFINE *point,
36                         point_conversion_form_t form, uint8_t *buf,
37                         size_t max_out) {
38  size_t output_len = ec_point_byte_len(group, form);
39  if (max_out < output_len) {
40    OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
41    return 0;
42  }
43
44  size_t field_len;
45  ec_felem_to_bytes(group, buf + 1, &field_len, &point->X);
46  assert(field_len == BN_num_bytes(&group->field.N));
47
48  if (form == POINT_CONVERSION_UNCOMPRESSED) {
49    ec_felem_to_bytes(group, buf + 1 + field_len, &field_len, &point->Y);
50    assert(field_len == BN_num_bytes(&group->field.N));
51    buf[0] = form;
52  } else {
53    uint8_t y_buf[EC_MAX_BYTES];
54    ec_felem_to_bytes(group, y_buf, &field_len, &point->Y);
55    buf[0] = form + (y_buf[field_len - 1] & 1);
56  }
57
58  return output_len;
59}
60
61int ec_point_from_uncompressed(const EC_GROUP *group, EC_AFFINE *out,
62                               const uint8_t *in, size_t len) {
63  const size_t field_len = BN_num_bytes(&group->field.N);
64  if (len != 1 + 2 * field_len || in[0] != POINT_CONVERSION_UNCOMPRESSED) {
65    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
66    return 0;
67  }
68
69  EC_FELEM x, y;
70  if (!ec_felem_from_bytes(group, &x, in + 1, field_len) ||
71      !ec_felem_from_bytes(group, &y, in + 1 + field_len, field_len) ||
72      !ec_point_set_affine_coordinates(group, out, &x, &y)) {
73    return 0;
74  }
75
76  return 1;
77}
78
79static int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
80                                   const uint8_t *buf, size_t len,
81                                   BN_CTX *ctx) {
82  if (len == 0) {
83    OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
84    return 0;
85  }
86
87  uint8_t form = buf[0];
88  if (form == static_cast<uint8_t>(POINT_CONVERSION_UNCOMPRESSED)) {
89    EC_AFFINE affine;
90    if (!ec_point_from_uncompressed(group, &affine, buf, len)) {
91      // In the event of an error, defend against the caller not checking the
92      // return value by setting a known safe value.
93      ec_set_to_safe_point(group, &point->raw);
94      return 0;
95    }
96    ec_affine_to_jacobian(group, &point->raw, &affine);
97    return 1;
98  }
99
100  const int y_bit = form & 1;
101  const size_t field_len = BN_num_bytes(&group->field.N);
102  form = form & ~1u;
103  if (form != static_cast<uint8_t>(POINT_CONVERSION_COMPRESSED) ||
104      len != 1 /* type byte */ + field_len) {
105    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
106    return 0;
107  }
108
109  // TODO(davidben): Integrate compressed coordinates with the lower-level EC
110  // abstractions. This requires a way to compute square roots, which is tricky
111  // for primes which are not 3 (mod 4), namely P-224 and custom curves. P-224's
112  // prime is particularly inconvenient for compressed coordinates. See
113  // https://cr.yp.to/papers/sqroot.pdf
114  BN_CTX *new_ctx = NULL;
115  if (ctx == NULL) {
116    ctx = new_ctx = BN_CTX_new();
117    if (ctx == NULL) {
118      return 0;
119    }
120  }
121
122  int ret = 0;
123  BN_CTX_start(ctx);
124  BIGNUM *x = BN_CTX_get(ctx);
125  if (x == NULL || !BN_bin2bn(buf + 1, field_len, x)) {
126    goto err;
127  }
128  if (BN_ucmp(x, &group->field.N) >= 0) {
129    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
130    goto err;
131  }
132
133  if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) {
134    goto err;
135  }
136
137  ret = 1;
138
139err:
140  BN_CTX_end(ctx);
141  BN_CTX_free(new_ctx);
142  return ret;
143}
144
145int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point,
146                       const uint8_t *buf, size_t len, BN_CTX *ctx) {
147  if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
148    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
149    return 0;
150  }
151  return ec_GFp_simple_oct2point(group, point, buf, len, ctx);
152}
153
154size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point,
155                          point_conversion_form_t form, uint8_t *buf,
156                          size_t max_out, BN_CTX *ctx) {
157  if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
158    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
159    return 0;
160  }
161  if (buf == NULL) {
162    // When |buf| is NULL, just return the number of bytes that would be
163    // written, without doing an expensive Jacobian-to-affine conversion.
164    if (ec_GFp_simple_is_at_infinity(group, &point->raw)) {
165      OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
166      return 0;
167    }
168    return ec_point_byte_len(group, form);
169  }
170  EC_AFFINE affine;
171  if (!ec_jacobian_to_affine(group, &affine, &point->raw)) {
172    return 0;
173  }
174  return ec_point_to_bytes(group, &affine, form, buf, max_out);
175}
176
177size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point,
178                          point_conversion_form_t form, uint8_t **out_buf,
179                          BN_CTX *ctx) {
180  *out_buf = NULL;
181  size_t len = EC_POINT_point2oct(group, point, form, NULL, 0, ctx);
182  if (len == 0) {
183    return 0;
184  }
185  uint8_t *buf = reinterpret_cast<uint8_t *>(OPENSSL_malloc(len));
186  if (buf == NULL) {
187    return 0;
188  }
189  len = EC_POINT_point2oct(group, point, form, buf, len, ctx);
190  if (len == 0) {
191    OPENSSL_free(buf);
192    return 0;
193  }
194  *out_buf = buf;
195  return len;
196}
197
198int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
199                                            EC_POINT *point, const BIGNUM *x,
200                                            int y_bit, BN_CTX *ctx) {
201  if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
202    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
203    return 0;
204  }
205
206  const BIGNUM *field = &group->field.N;
207  if (BN_is_negative(x) || BN_cmp(x, field) >= 0) {
208    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
209    return 0;
210  }
211
212  BN_CTX *new_ctx = NULL;
213  int ret = 0;
214
215  ERR_clear_error();
216
217  if (ctx == NULL) {
218    ctx = new_ctx = BN_CTX_new();
219    if (ctx == NULL) {
220      return 0;
221    }
222  }
223
224  y_bit = (y_bit != 0);
225
226  BN_CTX_start(ctx);
227  BIGNUM *tmp1 = BN_CTX_get(ctx);
228  BIGNUM *tmp2 = BN_CTX_get(ctx);
229  BIGNUM *a = BN_CTX_get(ctx);
230  BIGNUM *b = BN_CTX_get(ctx);
231  BIGNUM *y = BN_CTX_get(ctx);
232  if (y == NULL || !EC_GROUP_get_curve_GFp(group, NULL, a, b, ctx)) {
233    goto err;
234  }
235
236  // Recover y.  We have a Weierstrass equation
237  //     y^2 = x^3 + a*x + b,
238  // so  y  is one of the square roots of  x^3 + a*x + b.
239
240  // tmp1 := x^3
241  if (!BN_mod_sqr(tmp2, x, field, ctx) ||
242      !BN_mod_mul(tmp1, tmp2, x, field, ctx)) {
243    goto err;
244  }
245
246  // tmp1 := tmp1 + a*x
247  if (group->a_is_minus3) {
248    if (!bn_mod_lshift1_consttime(tmp2, x, field, ctx) ||
249        !bn_mod_add_consttime(tmp2, tmp2, x, field, ctx) ||
250        !bn_mod_sub_consttime(tmp1, tmp1, tmp2, field, ctx)) {
251      goto err;
252    }
253  } else {
254    if (!BN_mod_mul(tmp2, a, x, field, ctx) ||
255        !bn_mod_add_consttime(tmp1, tmp1, tmp2, field, ctx)) {
256      goto err;
257    }
258  }
259
260  // tmp1 := tmp1 + b
261  if (!bn_mod_add_consttime(tmp1, tmp1, b, field, ctx)) {
262    goto err;
263  }
264
265  if (!BN_mod_sqrt(y, tmp1, field, ctx)) {
266    uint32_t err = ERR_peek_last_error();
267    if (ERR_GET_LIB(err) == ERR_LIB_BN &&
268        ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
269      ERR_clear_error();
270      OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
271    } else {
272      OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
273    }
274    goto err;
275  }
276
277  if (y_bit != BN_is_odd(y)) {
278    if (BN_is_zero(y)) {
279      OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSION_BIT);
280      goto err;
281    }
282    if (!BN_usub(y, field, y)) {
283      goto err;
284    }
285  }
286  if (y_bit != BN_is_odd(y)) {
287    OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
288    goto err;
289  }
290
291  if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
292    goto err;
293  }
294
295  ret = 1;
296
297err:
298  BN_CTX_end(ctx);
299  BN_CTX_free(new_ctx);
300  return ret;
301}
302