1  /***********************************************************************
 2   * Copyright (c) 2013, 2014 Pieter Wuille                              *
 3   * Distributed under the MIT software license, see the accompanying    *
 4   * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
 5   ***********************************************************************/
 6  
 7  #ifndef SECP256K1_FIELD_REPR_H
 8  #define SECP256K1_FIELD_REPR_H
 9  
10  #include <stdint.h>
11  
12  /** This field implementation represents the value as 10 uint32_t limbs in base
13   *  2^26. */
14  typedef struct {
15     /* A field element f represents the sum(i=0..9, f.n[i] << (i*26)) mod p,
16      * where p is the field modulus, 2^256 - 2^32 - 977.
17      *
18      * The individual limbs f.n[i] can exceed 2^26; the field's magnitude roughly
19      * corresponds to how much excess is allowed. The value
20      * sum(i=0..9, f.n[i] << (i*26)) may exceed p, unless the field element is
21      * normalized. */
22      uint32_t n[10];
23      /*
24       * Magnitude m requires:
25       *     n[i] <= 2 * m * (2^26 - 1) for i=0..8
26       *     n[9] <= 2 * m * (2^22 - 1)
27       *
28       * Normalized requires:
29       *     n[i] <= (2^26 - 1) for i=0..8
30       *     sum(i=0..9, n[i] << (i*26)) < p
31       *     (together these imply n[9] <= 2^22 - 1)
32       */
33      SECP256K1_FE_VERIFY_FIELDS
34  } secp256k1_fe;
35  
36  /* Unpacks a constant into a overlapping multi-limbed FE element. */
37  #define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
38      (d0) & 0x3FFFFFFUL, \
39      (((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \
40      (((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \
41      (((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \
42      (((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \
43      (((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \
44      (((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \
45      (((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \
46      (((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \
47      (((uint32_t)d7) >> 10) \
48  }
49  
50  typedef struct {
51      uint32_t n[8];
52  } secp256k1_fe_storage;
53  
54  #define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }}
55  #define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0]
56  
57  #endif /* SECP256K1_FIELD_REPR_H */