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 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  * 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
  20 # define C448_SCALAR_LIMBS ((446-1)/C448_WORD_BITS+1)
  21
  22 /* The number of bits in a scalar */
  23 # define C448_SCALAR_BITS 446
  24
  25 /* Number of bytes in a serialized scalar. */
  26 # define C448_SCALAR_BYTES 56
  27
  28 /* X448 encoding ratio. */
  29 # define X448_ENCODE_RATIO 2
  30
  31 /* Number of bytes in an x448 public key */
  32 # define X448_PUBLIC_BYTES 56
  33
  34 /* Number of bytes in an x448 private key */
  35 # define X448_PRIVATE_BYTES 56
  36
  37 /* Twisted Edwards extended homogeneous coordinates */
  38 typedef struct curve448_point_s {
  39     gf x, y, z, t;
  40 } curve448_point_t[1];
  41
  42 /* Precomputed table based on a point.  Can be trivial implementation. */
  43 struct curve448_precomputed_s;
  44
  45 /* Precomputed table based on a point.  Can be trivial implementation. */
  46 typedef struct curve448_precomputed_s curve448_precomputed_s;
  47
  48 /* Scalar is stored packed, because we don't need the speed. */
  49 typedef struct curve448_scalar_s {
  50     c448_word_t limb[C448_SCALAR_LIMBS];
  51 } curve448_scalar_t[1];
  52
  53 /* A scalar equal to 1. */
  54 extern const curve448_scalar_t curve448_scalar_one;
  55
  56 /* A scalar equal to 0. */
  57 extern const curve448_scalar_t curve448_scalar_zero;
  58
  59 /* The identity point on the curve. */
  60 extern const curve448_point_t curve448_point_identity;
  61
  62 /* Precomputed table for the base point on the curve. */
  63 extern const struct curve448_precomputed_s *curve448_precomputed_base;
  64
  65 /*
  66  * Read a scalar from wire format or from bytes.
  67  *
  68  * ser (in): Serialized form of a scalar.
  69  * out (out): Deserialized form.
  70  *
  71  * Returns:
  72  * C448_SUCCESS: The scalar was correctly encoded.
  73  * C448_FAILURE: The scalar was greater than the modulus, and has been reduced
  74  * modulo that modulus.
  75  */
  76 __owur c448_error_t curve448_scalar_decode(
  77                             curve448_scalar_t out,
  78                             const unsigned char ser[C448_SCALAR_BYTES]);
  79
  80 /*
  81  * Read a scalar from wire format or from bytes.  Reduces mod scalar prime.
  82  *
  83  * ser (in): Serialized form of a scalar.
  84  * ser_len (in): Length of serialized form.
  85  * out (out): Deserialized form.
  86  */
  87 void curve448_scalar_decode_long(curve448_scalar_t out,
  88                                  const unsigned char *ser, size_t ser_len);
  89
  90 /*
  91  * Serialize a scalar to wire format.
  92  *
  93  * ser (out): Serialized form of a scalar.
  94  * s (in): Deserialized scalar.
  95  */
  96 void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
  97                             const curve448_scalar_t s);
  98
  99 /*
 100  * Add two scalars. The scalars may use the same memory.
 101  *
 102  * a (in): One scalar.
 103  * b (in): Another scalar.
 104  * out (out): a+b.
 105  */
 106 void curve448_scalar_add(curve448_scalar_t out,
 107                          const curve448_scalar_t a, const curve448_scalar_t b);
 108
 109 /*
 110  * Subtract two scalars.  The scalars may use the same memory.
 111  * a (in): One scalar.
 112  * b (in): Another scalar.
 113  * out (out): a-b.
 114  */
 115 void curve448_scalar_sub(curve448_scalar_t out,
 116                          const curve448_scalar_t a, const curve448_scalar_t b);
 117
 118 /*
 119  * Multiply two scalars. The scalars may use the same memory.
 120  *
 121  * a (in): One scalar.
 122  * b (in): Another scalar.
 123  * out (out): a*b.
 124  */
 125 void curve448_scalar_mul(curve448_scalar_t out,
 126                          const curve448_scalar_t a, const curve448_scalar_t b);
 127
 128 /*
 129 * Halve a scalar.  The scalars may use the same memory.
 130 *
 131 * a (in): A scalar.
 132 * out (out): a/2.
 133 */
 134 void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);
 135
 136 /*
 137  * Copy a scalar.  The scalars may use the same memory, in which case this
 138  * function does nothing.
 139  *
 140  * a (in): A scalar.
 141  * out (out): Will become a copy of a.
 142  */
 143 static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,
 144                                              const curve448_scalar_t a)
 145 {
 146     *out = *a;
 147 }
 148
 149 /*
 150  * Copy a point.  The input and output may alias, in which case this function
 151  * does nothing.
 152  *
 153  * a (out): A copy of the point.
 154  * b (in): Any point.
 155  */
 156 static ossl_inline void curve448_point_copy(curve448_point_t a,
 157                                             const curve448_point_t b)
 158 {
 159     *a = *b;
 160 }
 161
 162 /*
 163  * Test whether two points are equal.  If yes, return C448_TRUE, else return
 164  * C448_FALSE.
 165  *
 166  * a (in): A point.
 167  * b (in): Another point.
 168  *
 169  * Returns:
 170  * C448_TRUE: The points are equal.
 171  * C448_FALSE: The points are not equal.
 172  */
 173 __owur c448_bool_t curve448_point_eq(const curve448_point_t a,
 174                                      const curve448_point_t b);
 175
 176 /*
 177  * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially
 178  * faster.
 179  *
 180  * two_a (out): The sum a+a.
 181  * a (in): A point.
 182  */
 183 void curve448_point_double(curve448_point_t two_a, const curve448_point_t a);
 184
 185 /*
 186  * RFC 7748 Diffie-Hellman scalarmul.  This function uses a different
 187  * (non-Decaf) encoding.
 188  *
 189  * out (out): The scaled point base*scalar
 190  * base (in): The point to be scaled.
 191  * scalar (in): The scalar to multiply by.
 192  *
 193  * Returns:
 194  * C448_SUCCESS: The scalarmul succeeded.
 195  * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a
 196  * small subgroup.
 197  */
 198 __owur c448_error_t x448_int(uint8_t out[X448_PUBLIC_BYTES],
 199                              const uint8_t base[X448_PUBLIC_BYTES],
 200                              const uint8_t scalar[X448_PRIVATE_BYTES]);
 201
 202 /*
 203  * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748.
 204  *
 205  * This function is mainly used internally, but is exported in case
 206  * it will be useful.
 207  *
 208  * The ratio is necessary because the internal representation doesn't
 209  * track the cofactor information, so on output we must clear the cofactor.
 210  * This would multiply by the cofactor, but in fact internally points are always
 211  * even, so it multiplies by half the cofactor instead.
 212  *
 213  * As it happens, this aligns with the base point definitions; that is,
 214  * if you pass the Decaf/Ristretto base point to this function, the result
 215  * will be X448_ENCODE_RATIO times the X448
 216  * base point.
 217  *
 218  * out (out): The scaled and encoded point.
 219  * p (in): The point to be scaled and encoded.
 220  */
 221 void curve448_point_mul_by_ratio_and_encode_like_x448(
 222                                         uint8_t out[X448_PUBLIC_BYTES],
 223                                         const curve448_point_t p);
 224
 225 /*
 226  * RFC 7748 Diffie-Hellman base point scalarmul.  This function uses a different
 227  * (non-Decaf) encoding.
 228  *
 229  * out (out): The scaled point base*scalar
 230  * scalar (in): The scalar to multiply by.
 231  */
 232 void x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES],
 233                             const uint8_t scalar[X448_PRIVATE_BYTES]);
 234
 235 /*
 236  * Multiply a precomputed base point by a scalar: out = scalar*base.
 237  *
 238  * scaled (out): The scaled point base*scalar
 239  * base (in): The point to be scaled.
 240  * scalar (in): The scalar to multiply by.
 241  */
 242 void curve448_precomputed_scalarmul(curve448_point_t scaled,
 243                                     const curve448_precomputed_s * base,
 244                                     const curve448_scalar_t scalar);
 245
 246 /*
 247  * Multiply two base points by two scalars:
 248  * combo = scalar1*curve448_point_base + scalar2*base2.
 249  *
 250  * Otherwise equivalent to curve448_point_double_scalarmul, but may be
 251  * faster at the expense of being variable time.
 252  *
 253  * combo (out): The linear combination scalar1*base + scalar2*base2.
 254  * scalar1 (in): A first scalar to multiply by.
 255  * base2 (in): A second point to be scaled.
 256  * scalar2 (in) A second scalar to multiply by.
 257  *
 258  * Warning: This function takes variable time, and may leak the scalars used.
 259  * It is designed for signature verification.
 260  */
 261 void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
 262                                                const curve448_scalar_t scalar1,
 263                                                const curve448_point_t base2,
 264                                                const curve448_scalar_t scalar2);
 265
 266 /*
 267  * Test that a point is valid, for debugging purposes.
 268  *
 269  * to_test (in): The point to test.
 270  *
 271  * Returns:
 272  * C448_TRUE The point is valid.
 273  * C448_FALSE The point is invalid.
 274  */
 275 __owur c448_bool_t curve448_point_valid(const curve448_point_t to_test);
 276
 277 /* Overwrite scalar with zeros. */
 278 void curve448_scalar_destroy(curve448_scalar_t scalar);
 279
 280 /* Overwrite point with zeros. */
 281 void curve448_point_destroy(curve448_point_t point);
 282
 283 #endif                          /* HEADER_POINT_448_H */