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/***********************************************************************
* Copyright (c) 2014-2015 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php. *
***********************************************************************/
#ifndef _SECP256K1_SCHNORR_IMPL_H_
#define _SECP256K1_SCHNORR_IMPL_H_
#include <string.h>
#include "schnorr.h"
#include "num.h"
#include "field.h"
#include "group.h"
#include "ecmult.h"
#include "ecmult_gen.h"
/**
* Custom Schnorr-based signature scheme. They support multiparty signing, public key
* recovery and batch validation.
*
* Rationale for verifying R's y coordinate:
* In order to support batch validation and public key recovery, the full R point must
* be known to verifiers, rather than just its x coordinate. In order to not risk
* being more strict in batch validation than normal validation, validators must be
* required to reject signatures with incorrect y coordinate. This is only possible
* by including a (relatively slow) field inverse, or a field square root. However,
* batch validation offers potentially much higher benefits than this cost.
*
* Rationale for having an implicit y coordinate oddness:
* If we commit to having the full R point known to verifiers, there are two mechanism.
* Either include its oddness in the signature, or give it an implicit fixed value.
* As the R y coordinate can be flipped by a simple negation of the nonce, we choose the
* latter, as it comes with nearly zero impact on signing or validation performance, and
* saves a byte in the signature.
*
* Signing:
* Inputs: 32-byte message m, 32-byte scalar key x (!=0), 32-byte scalar nonce k (!=0)
*
* Compute point R = k * G. Reject nonce if R's y coordinate is odd (or negate nonce).
* Compute 32-byte r, the serialization of R's x coordinate.
* Compute scalar h = Hash(r || m). Reject nonce if h == 0 or h >= order.
* Compute scalar s = k - h * x.
* The signature is (r, s).
*
*
* Verification:
* Inputs: 32-byte message m, public key point Q, signature: (32-byte r, scalar s)
*
* Signature is invalid if s >= order.
* Signature is invalid if r >= p.
* Compute scalar h = Hash(r || m). Signature is invalid if h == 0 or h >= order.
* Option 1 (faster for single verification):
* Compute point R = h * Q + s * G. Signature is invalid if R is infinity or R's y coordinate is odd.
* Signature is valid if the serialization of R's x coordinate equals r.
* Option 2 (allows batch validation and pubkey recovery):
* Decompress x coordinate r into point R, with odd y coordinate. Fail if R is not on the curve.
* Signature is valid if R + h * Q + s * G == 0.
*/
static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
secp256k1_gej Rj;
secp256k1_ge Ra;
unsigned char h32[32];
secp256k1_scalar h, s;
int overflow;
secp256k1_scalar n;
if (secp256k1_scalar_is_zero(key) || secp256k1_scalar_is_zero(nonce)) {
return 0;
}
n = *nonce;
secp256k1_ecmult_gen(ctx, &Rj, &n);
if (pubnonce != NULL) {
secp256k1_gej_add_ge(&Rj, &Rj, pubnonce);
}
secp256k1_ge_set_gej(&Ra, &Rj);
secp256k1_fe_normalize(&Ra.y);
if (secp256k1_fe_is_odd(&Ra.y)) {
/* R's y coordinate is odd, which is not allowed (see rationale above).
Force it to be even by negating the nonce. Note that this even works
for multiparty signing, as the R point is known to all participants,
which can all decide to flip the sign in unison, resulting in the
overall R point to be negated too. */
secp256k1_scalar_negate(&n, &n);
}
secp256k1_fe_normalize(&Ra.x);
secp256k1_fe_get_b32(sig64, &Ra.x);
hash(h32, sig64, msg32);
overflow = 0;
secp256k1_scalar_set_b32(&h, h32, &overflow);
if (overflow || secp256k1_scalar_is_zero(&h)) {
secp256k1_scalar_clear(&n);
return 0;
}
secp256k1_scalar_mul(&s, &h, key);
secp256k1_scalar_negate(&s, &s);
secp256k1_scalar_add(&s, &s, &n);
secp256k1_scalar_clear(&n);
secp256k1_scalar_get_b32(sig64 + 32, &s);
return 1;
}
static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
secp256k1_gej Qj, Rj;
secp256k1_ge Ra;
secp256k1_fe Rx;
secp256k1_scalar h, s;
unsigned char hh[32];
int overflow;
if (secp256k1_ge_is_infinity(pubkey)) {
return 0;
}
hash(hh, sig64, msg32);
overflow = 0;
secp256k1_scalar_set_b32(&h, hh, &overflow);
if (overflow || secp256k1_scalar_is_zero(&h)) {
return 0;
}
overflow = 0;
secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
if (overflow) {
return 0;
}
if (!secp256k1_fe_set_b32(&Rx, sig64)) {
return 0;
}
secp256k1_gej_set_ge(&Qj, pubkey);
secp256k1_ecmult(ctx, &Rj, &Qj, &h, &s);
if (secp256k1_gej_is_infinity(&Rj)) {
return 0;
}
secp256k1_ge_set_gej_var(&Ra, &Rj);
secp256k1_fe_normalize_var(&Ra.y);
if (secp256k1_fe_is_odd(&Ra.y)) {
return 0;
}
return secp256k1_fe_equal_var(&Rx, &Ra.x);
}
static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
secp256k1_gej Qj, Rj;
secp256k1_ge Ra;
secp256k1_fe Rx;
secp256k1_scalar h, s;
unsigned char hh[32];
int overflow;
hash(hh, sig64, msg32);
overflow = 0;
secp256k1_scalar_set_b32(&h, hh, &overflow);
if (overflow || secp256k1_scalar_is_zero(&h)) {
return 0;
}
overflow = 0;
secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
if (overflow) {
return 0;
}
if (!secp256k1_fe_set_b32(&Rx, sig64)) {
return 0;
}
if (!secp256k1_ge_set_xo_var(&Ra, &Rx, 0)) {
return 0;
}
secp256k1_gej_set_ge(&Rj, &Ra);
secp256k1_scalar_inverse_var(&h, &h);
secp256k1_scalar_negate(&s, &s);
secp256k1_scalar_mul(&s, &s, &h);
secp256k1_ecmult(ctx, &Qj, &Rj, &h, &s);
if (secp256k1_gej_is_infinity(&Qj)) {
return 0;
}
secp256k1_ge_set_gej(pubkey, &Qj);
return 1;
}
static int secp256k1_schnorr_sig_combine(unsigned char *sig64, size_t n, const unsigned char * const *sig64ins) {
secp256k1_scalar s = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
size_t i;
for (i = 0; i < n; i++) {
secp256k1_scalar si;
int overflow;
secp256k1_scalar_set_b32(&si, sig64ins[i] + 32, &overflow);
if (overflow) {
return -1;
}
if (i) {
if (memcmp(sig64ins[i - 1], sig64ins[i], 32) != 0) {
return -1;
}
}
secp256k1_scalar_add(&s, &s, &si);
}
if (secp256k1_scalar_is_zero(&s)) {
return 0;
}
memcpy(sig64, sig64ins[0], 32);
secp256k1_scalar_get_b32(sig64 + 32, &s);
secp256k1_scalar_clear(&s);
return 1;
}
#endif
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