crypto/ec/curve448/point_448.h

   1 /*
   2  * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
   3  * Copyright 2015-2016 Cryptography Research, Inc.
   4  *
   5  * Licensed under the Apache License 2.0 (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  * Originally written by Mike Hamburg
  11  */
  12
  13 #ifndef OSSL_CRYPTO_EC_CURVE448_POINT_448_H
  14 # define OSSL_CRYPTO_EC_CURVE448_POINT_448_H
  15
  16 # include "curve448utils.h"
  17 # include "field.h"
  18
  19 /* Comb config: number of combs, n, t, s. */
  20 #define COMBS_N 5
  21 #define COMBS_T 5
  22 #define COMBS_S 18
  23
  24 /* Projective Niels coordinates */
  25 typedef struct {
  26     gf a, b, c;
  27 } niels_s, niels_t[1];
  28 typedef struct {
  29     niels_t n;
  30     gf z;
  31 } pniels_t[1];
  32
  33 /* Precomputed base */
  34 struct curve448_precomputed_s {
  35     niels_t table[COMBS_N << (COMBS_T - 1)];
  36 };
  37
  38 # define C448_SCALAR_LIMBS ((446-1)/C448_WORD_BITS+1)
  39
  40 /* The number of bits in a scalar */
  41 # define C448_SCALAR_BITS 446
  42
  43 /* Number of bytes in a serialized scalar. */
  44 # define C448_SCALAR_BYTES 56
  45
  46 /* X448 encoding ratio. */
  47 # define X448_ENCODE_RATIO 2
  48
  49 /* Number of bytes in an x448 public key */
  50 # define X448_PUBLIC_BYTES 56
  51
  52 /* Number of bytes in an x448 private key */
  53 # define X448_PRIVATE_BYTES 56
  54
  55 /* Twisted Edwards extended homogeneous coordinates */
  56 typedef struct curve448_point_s {
  57     gf x, y, z, t;
  58 } curve448_point_t[1];
  59
  60 /* Precomputed table based on a point.  Can be trivial implementation. */
  61 struct curve448_precomputed_s;
  62
  63 /* Precomputed table based on a point.  Can be trivial implementation. */
  64 typedef struct curve448_precomputed_s curve448_precomputed_s;
  65
  66 /* Scalar is stored packed, because we don't need the speed. */
  67 typedef struct curve448_scalar_s {
  68     c448_word_t limb[C448_SCALAR_LIMBS];
  69 } curve448_scalar_t[1];
  70
  71 /* A scalar equal to 1. */
  72 extern const curve448_scalar_t ossl_curve448_scalar_one;
  73
  74 /* A scalar equal to 0. */
  75 extern const curve448_scalar_t ossl_curve448_scalar_zero;
  76
  77 /* The identity point on the curve. */
  78 extern const curve448_point_t ossl_curve448_point_identity;
  79
  80 /* Precomputed table for the base point on the curve. */
  81 extern const struct curve448_precomputed_s *ossl_curve448_precomputed_base;
  82 extern const niels_t *ossl_curve448_wnaf_base;
  83
  84 /*
  85  * Read a scalar from wire format or from bytes.
  86  *
  87  * ser (in): Serialized form of a scalar.
  88  * out (out): Deserialized form.
  89  *
  90  * Returns:
  91  * C448_SUCCESS: The scalar was correctly encoded.
  92  * C448_FAILURE: The scalar was greater than the modulus, and has been reduced
  93  * modulo that modulus.
  94  */
  95 c448_error_t
  96 ossl_curve448_scalar_decode(curve448_scalar_t out,
  97                             const unsigned char ser[C448_SCALAR_BYTES]);
  98
  99 /*
 100  * Read a scalar from wire format or from bytes.  Reduces mod scalar prime.
 101  *
 102  * ser (in): Serialized form of a scalar.
 103  * ser_len (in): Length of serialized form.
 104  * out (out): Deserialized form.
 105  */
 106 void
 107 ossl_curve448_scalar_decode_long(curve448_scalar_t out,
 108                                  const unsigned char *ser, size_t ser_len);
 109
 110 /*
 111  * Serialize a scalar to wire format.
 112  *
 113  * ser (out): Serialized form of a scalar.
 114  * s (in): Deserialized scalar.
 115  */
 116 void
 117 ossl_curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
 118                             const curve448_scalar_t s);
 119
 120 /*
 121  * Add two scalars. |a|, |b| and |out| may alias each other.
 122  *
 123  * a (in): One scalar.
 124  * b (in): Another scalar.
 125  * out (out): a+b.
 126  */
 127 void
 128 ossl_curve448_scalar_add(curve448_scalar_t out,
 129                          const curve448_scalar_t a, const curve448_scalar_t b);
 130
 131 /*
 132  * Subtract two scalars.  |a|, |b| and |out| may alias each other.
 133  * a (in): One scalar.
 134  * b (in): Another scalar.
 135  * out (out): a-b.
 136  */
 137 void
 138 ossl_curve448_scalar_sub(curve448_scalar_t out,
 139                          const curve448_scalar_t a, const curve448_scalar_t b);
 140
 141 /*
 142  * Multiply two scalars. |a|, |b| and |out| may alias each other.
 143  *
 144  * a (in): One scalar.
 145  * b (in): Another scalar.
 146  * out (out): a*b.
 147  */
 148 void
 149 ossl_curve448_scalar_mul(curve448_scalar_t out,
 150                          const curve448_scalar_t a, const curve448_scalar_t b);
 151
 152 /*
 153 * Halve a scalar.  |a| and |out| may alias each other.
 154 *
 155 * a (in): A scalar.
 156 * out (out): a/2.
 157 */
 158 void
 159 ossl_curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);
 160
 161 /*
 162  * Copy a scalar.  The scalars may alias each other, in which case this
 163  * function does nothing.
 164  *
 165  * a (in): A scalar.
 166  * out (out): Will become a copy of a.
 167  */
 168 static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,
 169                                              const curve448_scalar_t a)
 170 {
 171     *out = *a;
 172 }
 173
 174 /*
 175  * Copy a point.  The input and output may alias, in which case this function
 176  * does nothing.
 177  *
 178  * a (out): A copy of the point.
 179  * b (in): Any point.
 180  */
 181 static ossl_inline void curve448_point_copy(curve448_point_t a,
 182                                             const curve448_point_t b)
 183 {
 184     *a = *b;
 185 }
 186
 187 /*
 188  * Test whether two points are equal.  If yes, return C448_TRUE, else return
 189  * C448_FALSE.
 190  *
 191  * a (in): A point.
 192  * b (in): Another point.
 193  *
 194  * Returns:
 195  * C448_TRUE: The points are equal.
 196  * C448_FALSE: The points are not equal.
 197  */
 198 __owur c448_bool_t
 199 ossl_curve448_point_eq(const curve448_point_t a,
 200                        const curve448_point_t b);
 201
 202 /*
 203  * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially
 204  * faster.
 205  *
 206  * two_a (out): The sum a+a.
 207  * a (in): A point.
 208  */
 209 void
 210 ossl_curve448_point_double(curve448_point_t two_a, const curve448_point_t a);
 211
 212 /*
 213  * RFC 7748 Diffie-Hellman scalarmul.  This function uses a different
 214  * (non-Decaf) encoding.
 215  *
 216  * out (out): The scaled point base*scalar
 217  * base (in): The point to be scaled.
 218  * scalar (in): The scalar to multiply by.
 219  *
 220  * Returns:
 221  * C448_SUCCESS: The scalarmul succeeded.
 222  * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a
 223  * small subgroup.
 224  */
 225 __owur c448_error_t
 226 ossl_x448_int(uint8_t out[X448_PUBLIC_BYTES],
 227               const uint8_t base[X448_PUBLIC_BYTES],
 228               const uint8_t scalar[X448_PRIVATE_BYTES]);
 229
 230 /*
 231  * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748.
 232  *
 233  * This function is mainly used internally, but is exported in case
 234  * it will be useful.
 235  *
 236  * The ratio is necessary because the internal representation doesn't
 237  * track the cofactor information, so on output we must clear the cofactor.
 238  * This would multiply by the cofactor, but in fact internally points are always
 239  * even, so it multiplies by half the cofactor instead.
 240  *
 241  * As it happens, this aligns with the base point definitions; that is,
 242  * if you pass the Decaf/Ristretto base point to this function, the result
 243  * will be X448_ENCODE_RATIO times the X448
 244  * base point.
 245  *
 246  * out (out): The scaled and encoded point.
 247  * p (in): The point to be scaled and encoded.
 248  */
 249 void
 250 ossl_curve448_point_mul_by_ratio_and_encode_like_x448(
 251                                         uint8_t out[X448_PUBLIC_BYTES],
 252                                         const curve448_point_t p);
 253
 254 /*
 255  * RFC 7748 Diffie-Hellman base point scalarmul.  This function uses a different
 256  * (non-Decaf) encoding.
 257  *
 258  * out (out): The scaled point base*scalar
 259  * scalar (in): The scalar to multiply by.
 260  */
 261 void
 262 ossl_x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES],
 263                             const uint8_t scalar[X448_PRIVATE_BYTES]);
 264
 265 /*
 266  * Multiply a precomputed base point by a scalar: out = scalar*base.
 267  *
 268  * scaled (out): The scaled point base*scalar
 269  * base (in): The point to be scaled.
 270  * scalar (in): The scalar to multiply by.
 271  */
 272 void
 273 ossl_curve448_precomputed_scalarmul(curve448_point_t scaled,
 274                                     const curve448_precomputed_s * base,
 275                                     const curve448_scalar_t scalar);
 276
 277 /*
 278  * Multiply two base points by two scalars:
 279  * combo = scalar1*curve448_point_base + scalar2*base2.
 280  *
 281  * Otherwise equivalent to curve448_point_double_scalarmul, but may be
 282  * faster at the expense of being variable time.
 283  *
 284  * combo (out): The linear combination scalar1*base + scalar2*base2.
 285  * scalar1 (in): A first scalar to multiply by.
 286  * base2 (in): A second point to be scaled.
 287  * scalar2 (in) A second scalar to multiply by.
 288  *
 289  * Warning: This function takes variable time, and may leak the scalars used.
 290  * It is designed for signature verification.
 291  */
 292 void
 293 ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
 294                                                const curve448_scalar_t scalar1,
 295                                                const curve448_point_t base2,
 296                                                const curve448_scalar_t scalar2);
 297
 298 /*
 299  * Test that a point is valid, for debugging purposes.
 300  *
 301  * to_test (in): The point to test.
 302  *
 303  * Returns:
 304  * C448_TRUE The point is valid.
 305  * C448_FALSE The point is invalid.
 306  */
 307 __owur c448_bool_t
 308 ossl_curve448_point_valid(const curve448_point_t to_test);
 309
 310 /* Overwrite scalar with zeros. */
 311 void ossl_curve448_scalar_destroy(curve448_scalar_t scalar);
 312
 313 /* Overwrite point with zeros. */
 314 void ossl_curve448_point_destroy(curve448_point_t point);
 315
 316 #endif                          /* OSSL_CRYPTO_EC_CURVE448_POINT_448_H */