crypto/ec/curve448/point_448.h

   1 /*
   2  * Copyright 2017 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 __DECAF_POINT_448_H__
  14 # define __DECAF_POINT_448_H__ 1
  15
  16 # include "curve448utils.h"
  17 # include "field.h"
  18
  19 #ifdef __cplusplus
  20 extern "C" {
  21 #endif
  22
  23 # define DECAF_448_SCALAR_LIMBS ((446-1)/DECAF_WORD_BITS+1)
  24
  25 /* The number of bits in a scalar */
  26 # define DECAF_448_SCALAR_BITS 446
  27
  28 /* Number of bytes in a serialized scalar. */
  29 # define DECAF_448_SCALAR_BYTES 56
  30
  31 /* X448 encoding ratio. */
  32 # define DECAF_X448_ENCODE_RATIO 2
  33
  34 /* Number of bytes in an x448 public key */
  35 # define DECAF_X448_PUBLIC_BYTES 56
  36
  37 /* Number of bytes in an x448 private key */
  38 # define DECAF_X448_PRIVATE_BYTES 56
  39
  40 /* Twisted Edwards extended homogeneous coordinates */
  41 typedef struct curve448_point_s {
  42     gf x, y, z, t;
  43 } curve448_point_t[1];
  44
  45 /* Precomputed table based on a point.  Can be trivial implementation. */
  46 struct curve448_precomputed_s;
  47
  48 /* Precomputed table based on a point.  Can be trivial implementation. */
  49 typedef struct curve448_precomputed_s curve448_precomputed_s;
  50
  51 /* Scalar is stored packed, because we don't need the speed. */
  52 typedef struct curve448_scalar_s {
  53     decaf_word_t limb[DECAF_448_SCALAR_LIMBS];
  54 } curve448_scalar_t[1];
  55
  56 /* A scalar equal to 1. */
  57 extern const curve448_scalar_t curve448_scalar_one;
  58
  59 /* A scalar equal to 0. */
  60 extern const curve448_scalar_t curve448_scalar_zero;
  61
  62 /* The identity point on the curve. */
  63 extern const curve448_point_t curve448_point_identity;
  64
  65 /* Precomputed table for the base point on the curve. */
  66 extern const struct curve448_precomputed_s *curve448_precomputed_base;
  67
  68 /*
  69  * Read a scalar from wire format or from bytes.
  70  *
  71  * ser (in): Serialized form of a scalar.
  72  * out (out): Deserialized form.
  73  *
  74  * Returns:
  75  * DECAF_SUCCESS: The scalar was correctly encoded.
  76  * DECAF_FAILURE: The scalar was greater than the modulus, and has been reduced
  77  * modulo that modulus.
  78  */
  79 __owur decaf_error_t curve448_scalar_decode(
  80                             curve448_scalar_t out,
  81                             const unsigned char ser[DECAF_448_SCALAR_BYTES]);
  82
  83 /*
  84  * Read a scalar from wire format or from bytes.  Reduces mod scalar prime.
  85  *
  86  * ser (in): Serialized form of a scalar.
  87  * ser_len (in): Length of serialized form.
  88  * out (out): Deserialized form.
  89  */
  90 void curve448_scalar_decode_long(curve448_scalar_t out,
  91                                  const unsigned char *ser, size_t ser_len);
  92
  93 /*
  94  * Serialize a scalar to wire format.
  95  *
  96  * ser (out): Serialized form of a scalar.
  97  * s (in): Deserialized scalar.
  98  */
  99 void curve448_scalar_encode(unsigned char ser[DECAF_448_SCALAR_BYTES],
 100                             const curve448_scalar_t s);
 101
 102 /*
 103  * Add two scalars. The scalars may use the same memory.
 104  *
 105  * a (in): One scalar.
 106  * b (in): Another scalar.
 107  * out (out): a+b.
 108  */
 109 void curve448_scalar_add(curve448_scalar_t out,
 110                          const curve448_scalar_t a, const curve448_scalar_t b);
 111
 112 /*
 113  * Subtract two scalars.  The scalars may use the same memory.
 114  * a (in): One scalar.
 115  * b (in): Another scalar.
 116  * out (out): a-b.
 117  */
 118 void curve448_scalar_sub(curve448_scalar_t out,
 119                          const curve448_scalar_t a, const curve448_scalar_t b);
 120
 121 /*
 122  * Multiply two scalars. The scalars may use the same memory.
 123  *
 124  * a (in): One scalar.
 125  * b (in): Another scalar.
 126  * out (out): a*b.
 127  */
 128 void curve448_scalar_mul(curve448_scalar_t out,
 129                          const curve448_scalar_t a, const curve448_scalar_t b);
 130
 131 /*
 132 * Halve a scalar.  The scalars may use the same memory.
 133 *
 134 * a (in): A scalar.
 135 * out (out): a/2.
 136 */
 137 void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);
 138
 139 /*
 140  * Copy a scalar.  The scalars may use the same memory, in which case this
 141  * function does nothing.
 142  *
 143  * a (in): A scalar.
 144  * out (out): Will become a copy of a.
 145  */
 146 static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,
 147                                              const curve448_scalar_t a)
 148 {
 149     *out = *a;
 150 }
 151
 152 /*
 153  * Copy a point.  The input and output may alias, in which case this function
 154  * does nothing.
 155  *
 156  * a (out): A copy of the point.
 157  * b (in): Any point.
 158  */
 159 static ossl_inline void curve448_point_copy(curve448_point_t a,
 160                                             const curve448_point_t b)
 161 {
 162     *a = *b;
 163 }
 164
 165 /*
 166  * Test whether two points are equal.  If yes, return DECAF_TRUE, else return
 167  * DECAF_FALSE.
 168  *
 169  * a (in): A point.
 170  * b (in): Another point.
 171  *
 172  * Returns:
 173  * DECAF_TRUE: The points are equal.
 174  * DECAF_FALSE: The points are not equal.
 175  */
 176 __owur decaf_bool_t curve448_point_eq(const curve448_point_t a,
 177                                       const curve448_point_t b);
 178
 179 /*
 180  * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially
 181  * faster.
 182  *
 183  * two_a (out): The sum a+a.
 184  * a (in): A point.
 185  */
 186 void curve448_point_double(curve448_point_t two_a, const curve448_point_t a);
 187
 188 /*
 189  * RFC 7748 Diffie-Hellman scalarmul.  This function uses a different
 190  * (non-Decaf) encoding.
 191  *
 192  * out (out): The scaled point base*scalar
 193  * base (in): The point to be scaled.
 194  * scalar (in): The scalar to multiply by.
 195  *
 196  * Returns:
 197  * DECAF_SUCCESS: The scalarmul succeeded.
 198  * DECAF_FAILURE: The scalarmul didn't succeed, because the base point is in a
 199  * small subgroup.
 200  */
 201 __owur decaf_error_t decaf_x448(uint8_t out[DECAF_X448_PUBLIC_BYTES],
 202                                 const uint8_t base[DECAF_X448_PUBLIC_BYTES],
 203                                 const uint8_t scalar[DECAF_X448_PRIVATE_BYTES]);
 204
 205 /*
 206  * Multiply a point by DECAF_X448_ENCODE_RATIO, then encode it like RFC 7748.
 207  *
 208  * This function is mainly used internally, but is exported in case
 209  * it will be useful.
 210  *
 211  * The ratio is necessary because the internal representation doesn't
 212  * track the cofactor information, so on output we must clear the cofactor.
 213  * This would multiply by the cofactor, but in fact internally libdecaf's
 214  * points are always even, so it multiplies by half the cofactor instead.
 215  *
 216  * As it happens, this aligns with the base point definitions; that is,
 217  * if you pass the Decaf/Ristretto base point to this function, the result
 218  * will be DECAF_X448_ENCODE_RATIO times the X448
 219  * base point.
 220  *
 221  * out (out): The scaled and encoded point.
 222  * p (in): The point to be scaled and encoded.
 223  */
 224 void curve448_point_mul_by_ratio_and_encode_like_x448(
 225                                         uint8_t out[DECAF_X448_PUBLIC_BYTES],
 226                                         const curve448_point_t p);
 227
 228 /*
 229  * RFC 7748 Diffie-Hellman base point scalarmul.  This function uses a different
 230  * (non-Decaf) encoding.
 231  *
 232  * out (out): The scaled point base*scalar
 233  * scalar (in): The scalar to multiply by.
 234  */
 235 void decaf_x448_derive_public_key(
 236                                 uint8_t out[DECAF_X448_PUBLIC_BYTES],
 237                                 const uint8_t scalar[DECAF_X448_PRIVATE_BYTES]);
 238
 239 /*
 240  * Multiply a precomputed base point by a scalar: out = scalar*base.
 241  *
 242  * scaled (out): The scaled point base*scalar
 243  * base (in): The point to be scaled.
 244  * scalar (in): The scalar to multiply by.
 245  */
 246 void curve448_precomputed_scalarmul(curve448_point_t scaled,
 247                                     const curve448_precomputed_s * base,
 248                                     const curve448_scalar_t scalar);
 249
 250 /*
 251  * Multiply two base points by two scalars:
 252  * combo = scalar1*curve448_point_base + scalar2*base2.
 253  *
 254  * Otherwise equivalent to curve448_point_double_scalarmul, but may be
 255  * faster at the expense of being variable time.
 256  *
 257  * combo (out): The linear combination scalar1*base + scalar2*base2.
 258  * scalar1 (in): A first scalar to multiply by.
 259  * base2 (in): A second point to be scaled.
 260  * scalar2 (in) A second scalar to multiply by.
 261  *
 262  * Warning: This function takes variable time, and may leak the scalars used.
 263  * It is designed for signature verification.
 264  */
 265 void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
 266                                                const curve448_scalar_t scalar1,
 267                                                const curve448_point_t base2,
 268                                                const curve448_scalar_t scalar2);
 269
 270 /*
 271  * Test that a point is valid, for debugging purposes.
 272  *
 273  * to_test (in): The point to test.
 274  *
 275  * Returns:
 276  * DECAF_TRUE The point is valid.
 277  * DECAF_FALSE The point is invalid.
 278  */
 279 __owur decaf_bool_t curve448_point_valid(const curve448_point_t to_test);
 280
 281 /* Overwrite scalar with zeros. */
 282 void curve448_scalar_destroy(curve448_scalar_t scalar);
 283
 284 /* Overwrite point with zeros. */
 285 void curve448_point_destroy(curve448_point_t point);
 286
 287 #ifdef __cplusplus
 288 } /* extern "C" */
 289 #endif
 290
 291 #endif                          /* __DECAF_POINT_448_H__ */