secp256k1_ellswift.h

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#ifndef SECP256K1_ELLSWIFT_H
#define SECP256K1_ELLSWIFT_H
 
#include "secp256k1.h"
 
#ifdef __cplusplus
extern "C" {
#endif
 
/* This module provides an implementation of ElligatorSwift as well as a
 * version of x-only ECDH using it (including compatibility with BIP324).
 *
 * ElligatorSwift is described in https://eprint.iacr.org/2022/759 by
 * Chavez-Saab, Rodriguez-Henriquez, and Tibouchi. It permits encoding
 * uniformly chosen public keys as 64-byte arrays which are indistinguishable
 * from uniformly random arrays.
 *
 * Let f be the function from pairs of field elements to point X coordinates,
 * defined as follows (all operations modulo p = 2^256 - 2^32 - 977)
 * f(u,t):
 * - Let C = 0xa2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f852,
 *   a square root of -3.
 * - If u=0, set u=1 instead.
 * - If t=0, set t=1 instead.
 * - If u^3 + t^2 + 7 = 0, multiply t by 2.
 * - Let X = (u^3 + 7 - t^2) / (2 * t)
 * - Let Y = (X + t) / (C * u)
 * - Return the first in [u + 4 * Y^2, (-X/Y - u) / 2, (X/Y - u) / 2] that is an
 *   X coordinate on the curve (at least one of them is, for any u and t).
 *
 * Then an ElligatorSwift encoding of x consists of the 32-byte big-endian
 * encodings of field elements u and t concatenated, where f(u,t) = x.
 * The encoding algorithm is described in the paper, and effectively picks a
 * uniformly random pair (u,t) among those which encode x.
 *
 * If the Y coordinate is relevant, it is given the same parity as t.
 *
 * Changes w.r.t. the the paper:
 * - The u=0, t=0, and u^3+t^2+7=0 conditions result in decoding to the point
 *   at infinity in the paper. Here they are remapped to finite points.
 * - The paper uses an additional encoding bit for the parity of y. Here the
 *   parity of t is used (negating t does not affect the decoded x coordinate,
 *   so this is possible).
 *
 * For mathematical background about the scheme, see the doc/ellswift.md file.
 */
 
typedef int (*secp256k1_ellswift_xdh_hash_function)(
    unsigned char *output,
    const unsigned char *x32,
    const unsigned char *ell_a64,
    const unsigned char *ell_b64,
    void *data
);
 
SECP256K1_API const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_prefix;
 
SECP256K1_API const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_bip324;
 
SECP256K1_API int secp256k1_ellswift_encode(
    const secp256k1_context *ctx,
    unsigned char *ell64,
    const secp256k1_pubkey *pubkey,
    const unsigned char *rnd32
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
 
SECP256K1_API int secp256k1_ellswift_decode(
    const secp256k1_context *ctx,
    secp256k1_pubkey *pubkey,
    const unsigned char *ell64
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ellswift_create(
    const secp256k1_context *ctx,
    unsigned char *ell64,
    const unsigned char *seckey32,
    const unsigned char *auxrnd32
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ellswift_xdh(
  const secp256k1_context *ctx,
  unsigned char *output,
  const unsigned char *ell_a64,
  const unsigned char *ell_b64,
  const unsigned char *seckey32,
  int party,
  secp256k1_ellswift_xdh_hash_function hashfp,
  void *data
) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(7);
 
#ifdef __cplusplus
}
#endif
 
#endif /* SECP256K1_ELLSWIFT_H */