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 HEADER_POINT_448_H
  14 # define HEADER_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 curve448_scalar_one;
  73
  74 /* A scalar equal to 0. */
  75 extern const curve448_scalar_t curve448_scalar_zero;
  76
  77 /* The identity point on the curve. */
  78 extern const curve448_point_t curve448_point_identity;
  79
  80 /* Precomputed table for the base point on the curve. */
  81 extern const struct curve448_precomputed_s *curve448_precomputed_base;
  82 extern const niels_t *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 curve448_scalar_decode(curve448_scalar_t out,
  96                                     const unsigned char ser[C448_SCALAR_BYTES]);
  97
  98 /*
  99  * Read a scalar from wire format or from bytes.  Reduces mod scalar prime.
 100  *
 101  * ser (in): Serialized form of a scalar.
 102  * ser_len (in): Length of serialized form.
 103  * out (out): Deserialized form.
 104  */
 105 void curve448_scalar_decode_long(curve448_scalar_t out,
 106                                  const unsigned char *ser, size_t ser_len);
 107
 108 /*
 109  * Serialize a scalar to wire format.
 110  *
 111  * ser (out): Serialized form of a scalar.
 112  * s (in): Deserialized scalar.
 113  */
 114 void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
 115                             const curve448_scalar_t s);
 116
 117 /*
 118  * Add two scalars. |a|, |b| and |out| may alias each other.
 119  *
 120  * a (in): One scalar.
 121  * b (in): Another scalar.
 122  * out (out): a+b.
 123  */
 124 void curve448_scalar_add(curve448_scalar_t out,
 125                          const curve448_scalar_t a, const curve448_scalar_t b);
 126
 127 /*
 128  * Subtract two scalars.  |a|, |b| and |out| may alias each other.
 129  * a (in): One scalar.
 130  * b (in): Another scalar.
 131  * out (out): a-b.
 132  */
 133 void curve448_scalar_sub(curve448_scalar_t out,
 134                          const curve448_scalar_t a, const curve448_scalar_t b);
 135
 136 /*
 137  * Multiply two scalars. |a|, |b| and |out| may alias each other.
 138  *
 139  * a (in): One scalar.
 140  * b (in): Another scalar.
 141  * out (out): a*b.
 142  */
 143 void curve448_scalar_mul(curve448_scalar_t out,
 144                          const curve448_scalar_t a, const curve448_scalar_t b);
 145
 146 /*
 147 * Halve a scalar.  |a| and |out| may alias each other.
 148 *
 149 * a (in): A scalar.
 150 * out (out): a/2.
 151 */
 152 void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);
 153
 154 /*
 155  * Copy a scalar.  The scalars may alias each other, in which case this
 156  * function does nothing.
 157  *
 158  * a (in): A scalar.
 159  * out (out): Will become a copy of a.
 160  */
 161 static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,
 162                                              const curve448_scalar_t a)
 163 {
 164     *out = *a;
 165 }
 166
 167 /*
 168  * Copy a point.  The input and output may alias, in which case this function
 169  * does nothing.
 170  *
 171  * a (out): A copy of the point.
 172  * b (in): Any point.
 173  */
 174 static ossl_inline void curve448_point_copy(curve448_point_t a,
 175                                             const curve448_point_t b)
 176 {
 177     *a = *b;
 178 }
 179
 180 /*
 181  * Test whether two points are equal.  If yes, return C448_TRUE, else return
 182  * C448_FALSE.
 183  *
 184  * a (in): A point.
 185  * b (in): Another point.
 186  *
 187  * Returns:
 188  * C448_TRUE: The points are equal.
 189  * C448_FALSE: The points are not equal.
 190  */
 191 __owur c448_bool_t curve448_point_eq(const curve448_point_t a,
 192                                      const curve448_point_t b);
 193
 194 /*
 195  * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially
 196  * faster.
 197  *
 198  * two_a (out): The sum a+a.
 199  * a (in): A point.
 200  */
 201 void curve448_point_double(curve448_point_t two_a, const curve448_point_t a);
 202
 203 /*
 204  * RFC 7748 Diffie-Hellman scalarmul.  This function uses a different
 205  * (non-Decaf) encoding.
 206  *
 207  * out (out): The scaled point base*scalar
 208  * base (in): The point to be scaled.
 209  * scalar (in): The scalar to multiply by.
 210  *
 211  * Returns:
 212  * C448_SUCCESS: The scalarmul succeeded.
 213  * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a
 214  * small subgroup.
 215  */
 216 __owur c448_error_t x448_int(uint8_t out[X448_PUBLIC_BYTES],
 217                              const uint8_t base[X448_PUBLIC_BYTES],
 218                              const uint8_t scalar[X448_PRIVATE_BYTES]);
 219
 220 /*
 221  * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748.
 222  *
 223  * This function is mainly used internally, but is exported in case
 224  * it will be useful.
 225  *
 226  * The ratio is necessary because the internal representation doesn't
 227  * track the cofactor information, so on output we must clear the cofactor.
 228  * This would multiply by the cofactor, but in fact internally points are always
 229  * even, so it multiplies by half the cofactor instead.
 230  *
 231  * As it happens, this aligns with the base point definitions; that is,
 232  * if you pass the Decaf/Ristretto base point to this function, the result
 233  * will be X448_ENCODE_RATIO times the X448
 234  * base point.
 235  *
 236  * out (out): The scaled and encoded point.
 237  * p (in): The point to be scaled and encoded.
 238  */
 239 void curve448_point_mul_by_ratio_and_encode_like_x448(
 240                                         uint8_t out[X448_PUBLIC_BYTES],
 241                                         const curve448_point_t p);
 242
 243 /*
 244  * RFC 7748 Diffie-Hellman base point scalarmul.  This function uses a different
 245  * (non-Decaf) encoding.
 246  *
 247  * out (out): The scaled point base*scalar
 248  * scalar (in): The scalar to multiply by.
 249  */
 250 void x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES],
 251                             const uint8_t scalar[X448_PRIVATE_BYTES]);
 252
 253 /*
 254  * Multiply a precomputed base point by a scalar: out = scalar*base.
 255  *
 256  * scaled (out): The scaled point base*scalar
 257  * base (in): The point to be scaled.
 258  * scalar (in): The scalar to multiply by.
 259  */
 260 void curve448_precomputed_scalarmul(curve448_point_t scaled,
 261                                     const curve448_precomputed_s * base,
 262                                     const curve448_scalar_t scalar);
 263
 264 /*
 265  * Multiply two base points by two scalars:
 266  * combo = scalar1*curve448_point_base + scalar2*base2.
 267  *
 268  * Otherwise equivalent to curve448_point_double_scalarmul, but may be
 269  * faster at the expense of being variable time.
 270  *
 271  * combo (out): The linear combination scalar1*base + scalar2*base2.
 272  * scalar1 (in): A first scalar to multiply by.
 273  * base2 (in): A second point to be scaled.
 274  * scalar2 (in) A second scalar to multiply by.
 275  *
 276  * Warning: This function takes variable time, and may leak the scalars used.
 277  * It is designed for signature verification.
 278  */
 279 void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
 280                                                const curve448_scalar_t scalar1,
 281                                                const curve448_point_t base2,
 282                                                const curve448_scalar_t scalar2);
 283
 284 /*
 285  * Test that a point is valid, for debugging purposes.
 286  *
 287  * to_test (in): The point to test.
 288  *
 289  * Returns:
 290  * C448_TRUE The point is valid.
 291  * C448_FALSE The point is invalid.
 292  */
 293 __owur c448_bool_t curve448_point_valid(const curve448_point_t to_test);
 294
 295 /* Overwrite scalar with zeros. */
 296 void curve448_scalar_destroy(curve448_scalar_t scalar);
 297
 298 /* Overwrite point with zeros. */
 299 void curve448_point_destroy(curve448_point_t point);
 300
 301 #endif                          /* HEADER_POINT_448_H */