1  /***********************************************************************
 2   * Copyright (c) 2020 Peter Dettman                                    *
 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_MODINV64_H
 8  #define SECP256K1_MODINV64_H
 9  
10  #include "util.h"
11  
12  #ifndef SECP256K1_WIDEMUL_INT128
13  #error "modinv64 requires 128-bit wide multiplication support"
14  #endif
15  
16  /* A signed 62-bit limb representation of integers.
17   *
18   * Its value is sum(v[i] * 2^(62*i), i=0..4). */
19  typedef struct {
20      int64_t v[5];
21  } secp256k1_modinv64_signed62;
22  
23  typedef struct {
24      /* The modulus in signed62 notation, must be odd and in [3, 2^256]. */
25      secp256k1_modinv64_signed62 modulus;
26  
27      /* modulus^{-1} mod 2^62 */
28      uint64_t modulus_inv62;
29  } secp256k1_modinv64_modinfo;
30  
31  /* Replace x with its modular inverse mod modinfo->modulus. x must be in range [0, modulus).
32   * If x is zero, the result will be zero as well. If not, the inverse must exist (i.e., the gcd of
33   * x and modulus must be 1). These rules are automatically satisfied if the modulus is prime.
34   *
35   * On output, all of x's limbs will be in [0, 2^62).
36   */
37  static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
38  
39  /* Same as secp256k1_modinv64_var, but constant time in x (not in the modulus). */
40  static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
41  
42  /* Compute the Jacobi symbol for (x | modinfo->modulus). x must be coprime with modulus (and thus
43   * cannot be 0, as modulus >= 3). All limbs of x must be non-negative. Returns 0 if the result
44   * cannot be computed. */
45  static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
46  
47  #endif /* SECP256K1_MODINV64_H */