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monero/src/ringct/bulletproofs.cc
moneromooo-monero 3f1a3fac00
bulletproofs: more robust challenge computation 
Changes from sarang, from a recommendation by an anonymous reviewer
2018-01-31 15:57:01 +00:00

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// Copyright (c) 2017-2018, The Monero Project
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without modification, are
// permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice, this list of
// conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
// of conditions and the following disclaimer in the documentation and/or other
// materials provided with the distribution.
//
// 3. Neither the name of the copyright holder nor the names of its contributors may be
// used to endorse or promote products derived from this software without specific
// prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Adapted from Java code by Sarang Noether
#include <stdlib.h>
#include <openssl/ssl.h>
#include <boost/thread/mutex.hpp>
#include "misc_log_ex.h"
#include "common/perf_timer.h"
extern "C"
{
#include "crypto/crypto-ops.h"
}
#include "rctOps.h"
#include "bulletproofs.h"
#undef MONERO_DEFAULT_LOG_CATEGORY
#define MONERO_DEFAULT_LOG_CATEGORY "bulletproofs"
//#define DEBUG_BP
#define PERF_TIMER_START_BP(x) PERF_TIMER_START_UNIT(x, 1000000)
namespace rct
{
static rct::key vector_exponent(const rct::keyV &a, const rct::keyV &b);
static rct::keyV vector_powers(rct::key x, size_t n);
static rct::key inner_product(const rct::keyV &a, const rct::keyV &b);
static constexpr size_t maxN = 64;
static rct::key Hi[maxN], Gi[maxN];
static ge_dsmp Gprecomp[64], Hprecomp[64];
static const rct::key TWO = { {0x02, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 } };
static const rct::keyV oneN = vector_powers(rct::identity(), maxN);
static const rct::keyV twoN = vector_powers(TWO, maxN);
static const rct::key ip12 = inner_product(oneN, twoN);
static boost::mutex init_mutex;
static rct::key get_exponent(const rct::key &base, size_t idx)
{
static const std::string salt("bulletproof");
std::string hashed = std::string((const char*)base.bytes, sizeof(base)) + salt + tools::get_varint_data(idx);
return rct::hashToPoint(rct::hash2rct(crypto::cn_fast_hash(hashed.data(), hashed.size())));
}
static void init_exponents()
{
boost::lock_guard<boost::mutex> lock(init_mutex);
static bool init_done = false;
if (init_done)
return;
for (size_t i = 0; i < maxN; ++i)
{
Hi[i] = get_exponent(rct::H, i * 2);
rct::precomp(Hprecomp[i], Hi[i]);
Gi[i] = get_exponent(rct::H, i * 2 + 1);
rct::precomp(Gprecomp[i], Gi[i]);
}
init_done = true;
}
/* Given two scalar arrays, construct a vector commitment */
static rct::key vector_exponent(const rct::keyV &a, const rct::keyV &b)
{
CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
CHECK_AND_ASSERT_THROW_MES(a.size() <= maxN, "Incompatible sizes of a and maxN");
rct::key res = rct::identity();
for (size_t i = 0; i < a.size(); ++i)
{
rct::key term;
rct::addKeys3(term, a[i], Gprecomp[i], b[i], Hprecomp[i]);
rct::addKeys(res, res, term);
}
return res;
}
/* Compute a custom vector-scalar commitment */
static rct::key vector_exponent_custom(const rct::keyV &A, const rct::keyV &B, const rct::keyV &a, const rct::keyV &b)
{
CHECK_AND_ASSERT_THROW_MES(A.size() == B.size(), "Incompatible sizes of A and B");
CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
CHECK_AND_ASSERT_THROW_MES(a.size() == A.size(), "Incompatible sizes of a and A");
CHECK_AND_ASSERT_THROW_MES(a.size() <= maxN, "Incompatible sizes of a and maxN");
rct::key res = rct::identity();
for (size_t i = 0; i < a.size(); ++i)
{
rct::key term;
#if 0
// we happen to know where A and B might fall, so don't bother checking the rest
ge_dsmp *Acache = NULL, *Bcache = NULL;
ge_dsmp Acache_custom[1], Bcache_custom[1];
if (Gi[i] == A[i])
Acache = Gprecomp + i;
else if (i<32 && Gi[i+32] == A[i])
Acache = Gprecomp + i + 32;
else
{
rct::precomp(Acache_custom[0], A[i]);
Acache = Acache_custom;
}
if (i == 0 && B[i] == Hi[0])
Bcache = Hprecomp;
else
{
rct::precomp(Bcache_custom[0], B[i]);
Bcache = Bcache_custom;
}
rct::addKeys3(term, a[i], *Acache, b[i], *Bcache);
#else
ge_dsmp Acache, Bcache;
rct::precomp(Bcache, B[i]);
rct::addKeys3(term, a[i], A[i], b[i], Bcache);
#endif
rct::addKeys(res, res, term);
}
return res;
}
/* Given a scalar, construct a vector of powers */
static rct::keyV vector_powers(rct::key x, size_t n)
{
rct::keyV res(n);
if (n == 0)
return res;
res[0] = rct::identity();
if (n == 1)
return res;
res[1] = x;
for (size_t i = 2; i < n; ++i)
{
sc_mul(res[i].bytes, res[i-1].bytes, x.bytes);
}
return res;
}
/* Given two scalar arrays, construct the inner product */
static rct::key inner_product(const rct::keyV &a, const rct::keyV &b)
{
CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
rct::key res = rct::zero();
for (size_t i = 0; i < a.size(); ++i)
{
sc_muladd(res.bytes, a[i].bytes, b[i].bytes, res.bytes);
}
return res;
}
/* Given two scalar arrays, construct the Hadamard product */
static rct::keyV hadamard(const rct::keyV &a, const rct::keyV &b)
{
CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
rct::keyV res(a.size());
for (size_t i = 0; i < a.size(); ++i)
{
sc_mul(res[i].bytes, a[i].bytes, b[i].bytes);
}
return res;
}
/* Given two curvepoint arrays, construct the Hadamard product */
static rct::keyV hadamard2(const rct::keyV &a, const rct::keyV &b)
{
CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
rct::keyV res(a.size());
for (size_t i = 0; i < a.size(); ++i)
{
rct::addKeys(res[i], a[i], b[i]);
}
return res;
}
/* Add two vectors */
static rct::keyV vector_add(const rct::keyV &a, const rct::keyV &b)
{
CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
rct::keyV res(a.size());
for (size_t i = 0; i < a.size(); ++i)
{
sc_add(res[i].bytes, a[i].bytes, b[i].bytes);
}
return res;
}
/* Subtract two vectors */
static rct::keyV vector_subtract(const rct::keyV &a, const rct::keyV &b)
{
CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
rct::keyV res(a.size());
for (size_t i = 0; i < a.size(); ++i)
{
sc_sub(res[i].bytes, a[i].bytes, b[i].bytes);
}
return res;
}
/* Multiply a scalar and a vector */
static rct::keyV vector_scalar(const rct::keyV &a, const rct::key &x)
{
rct::keyV res(a.size());
for (size_t i = 0; i < a.size(); ++i)
{
sc_mul(res[i].bytes, a[i].bytes, x.bytes);
}
return res;
}
/* Exponentiate a curve vector by a scalar */
static rct::keyV vector_scalar2(const rct::keyV &a, const rct::key &x)
{
rct::keyV res(a.size());
for (size_t i = 0; i < a.size(); ++i)
{
rct::scalarmultKey(res[i], a[i], x);
}
return res;
}
static rct::key switch_endianness(rct::key k)
{
std::reverse(k.bytes, k.bytes + sizeof(k));
return k;
}
/* Compute the inverse of a scalar, the stupid way */
static rct::key invert(const rct::key &x)
{
rct::key inv;
BN_CTX *ctx = BN_CTX_new();
BIGNUM *X = BN_new();
BIGNUM *L = BN_new();
BIGNUM *I = BN_new();
BN_bin2bn(switch_endianness(x).bytes, sizeof(rct::key), X);
BN_bin2bn(switch_endianness(rct::curveOrder()).bytes, sizeof(rct::key), L);
CHECK_AND_ASSERT_THROW_MES(BN_mod_inverse(I, X, L, ctx), "Failed to invert");
const int len = BN_num_bytes(I);
CHECK_AND_ASSERT_THROW_MES((size_t)len <= sizeof(rct::key), "Invalid number length");
inv = rct::zero();
BN_bn2bin(I, inv.bytes);
std::reverse(inv.bytes, inv.bytes + len);
BN_free(I);
BN_free(L);
BN_free(X);
BN_CTX_free(ctx);
#ifdef DEBUG_BP
rct::key tmp;
sc_mul(tmp.bytes, inv.bytes, x.bytes);
CHECK_AND_ASSERT_THROW_MES(tmp == rct::identity(), "invert failed");
#endif
return inv;
}
/* Compute the slice of a vector */
static rct::keyV slice(const rct::keyV &a, size_t start, size_t stop)
{
CHECK_AND_ASSERT_THROW_MES(start < a.size(), "Invalid start index");
CHECK_AND_ASSERT_THROW_MES(stop <= a.size(), "Invalid stop index");
CHECK_AND_ASSERT_THROW_MES(start < stop, "Invalid start/stop indices");
rct::keyV res(stop - start);
for (size_t i = start; i < stop; ++i)
{
res[i - start] = a[i];
}
return res;
}
static rct::key hash_cache_mash(rct::key &hash_cache, const rct::key &mash0, const rct::key &mash1)
{
rct::keyV data;
data.reserve(3);
data.push_back(hash_cache);
data.push_back(mash0);
data.push_back(mash1);
return hash_cache = rct::hash_to_scalar(data);
}
static rct::key hash_cache_mash(rct::key &hash_cache, const rct::key &mash0, const rct::key &mash1, const rct::key &mash2)
{
rct::keyV data;
data.reserve(4);
data.push_back(hash_cache);
data.push_back(mash0);
data.push_back(mash1);
data.push_back(mash2);
return hash_cache = rct::hash_to_scalar(data);
}
static rct::key hash_cache_mash(rct::key &hash_cache, const rct::key &mash0, const rct::key &mash1, const rct::key &mash2, const rct::key &mash3)
{
rct::keyV data;
data.reserve(5);
data.push_back(hash_cache);
data.push_back(mash0);
data.push_back(mash1);
data.push_back(mash2);
data.push_back(mash3);
return hash_cache = rct::hash_to_scalar(data);
}
/* Given a value v (0..2^N-1) and a mask gamma, construct a range proof */
Bulletproof bulletproof_PROVE(const rct::key &sv, const rct::key &gamma)
{
init_exponents();
PERF_TIMER_UNIT(PROVE, 1000000);
constexpr size_t logN = 6; // log2(64)
constexpr size_t N = 1<<logN;
rct::key V;
rct::keyV aL(N), aR(N);
PERF_TIMER_START_BP(PROVE_v);
rct::addKeys2(V, gamma, sv, rct::H);
PERF_TIMER_STOP(PROVE_v);
PERF_TIMER_START_BP(PROVE_aLaR);
for (size_t i = N; i-- > 0; )
{
if (sv[i/8] & (((uint64_t)1)<<(i%8)))
{
aL[i] = rct::identity();
}
else
{
aL[i] = rct::zero();
}
sc_sub(aR[i].bytes, aL[i].bytes, rct::identity().bytes);
}
PERF_TIMER_STOP(PROVE_aLaR);
rct::key hash_cache = rct::hash_to_scalar(V);
// DEBUG: Test to ensure this recovers the value
#ifdef DEBUG_BP
uint64_t test_aL = 0, test_aR = 0;
for (size_t i = 0; i < N; ++i)
{
if (aL[i] == rct::identity())
test_aL += ((uint64_t)1)<<i;
if (aR[i] == rct::zero())
test_aR += ((uint64_t)1)<<i;
}
uint64_t v_test = 0;
for (int n = 0; n < 8; ++n) v_test |= (((uint64_t)sv[n]) << (8*n));
CHECK_AND_ASSERT_THROW_MES(test_aL == v_test, "test_aL failed");
CHECK_AND_ASSERT_THROW_MES(test_aR == v_test, "test_aR failed");
#endif
PERF_TIMER_START_BP(PROVE_step1);
// PAPER LINES 38-39
rct::key alpha = rct::skGen();
rct::key ve = vector_exponent(aL, aR);
rct::key A;
rct::addKeys(A, ve, rct::scalarmultBase(alpha));
// PAPER LINES 40-42
rct::keyV sL = rct::skvGen(N), sR = rct::skvGen(N);
rct::key rho = rct::skGen();
ve = vector_exponent(sL, sR);
rct::key S;
rct::addKeys(S, ve, rct::scalarmultBase(rho));
// PAPER LINES 43-45
rct::key y = hash_cache_mash(hash_cache, A, S);
rct::key z = hash_cache = rct::hash_to_scalar(y);
// Polynomial construction before PAPER LINE 46
rct::key t0 = rct::zero();
rct::key t1 = rct::zero();
rct::key t2 = rct::zero();
const auto yN = vector_powers(y, N);
rct::key ip1y = inner_product(oneN, yN);
rct::key tmp;
sc_muladd(t0.bytes, z.bytes, ip1y.bytes, t0.bytes);
rct::key zsq;
sc_mul(zsq.bytes, z.bytes, z.bytes);
sc_muladd(t0.bytes, zsq.bytes, sv.bytes, t0.bytes);
rct::key k = rct::zero();
sc_mulsub(k.bytes, zsq.bytes, ip1y.bytes, k.bytes);
rct::key zcu;
sc_mul(zcu.bytes, zsq.bytes, z.bytes);
sc_mulsub(k.bytes, zcu.bytes, ip12.bytes, k.bytes);
sc_add(t0.bytes, t0.bytes, k.bytes);
// DEBUG: Test the value of t0 has the correct form
#ifdef DEBUG_BP
rct::key test_t0 = rct::zero();
rct::key iph = inner_product(aL, hadamard(aR, yN));
sc_add(test_t0.bytes, test_t0.bytes, iph.bytes);
rct::key ips = inner_product(vector_subtract(aL, aR), yN);
sc_muladd(test_t0.bytes, z.bytes, ips.bytes, test_t0.bytes);
rct::key ipt = inner_product(twoN, aL);
sc_muladd(test_t0.bytes, zsq.bytes, ipt.bytes, test_t0.bytes);
sc_add(test_t0.bytes, test_t0.bytes, k.bytes);
CHECK_AND_ASSERT_THROW_MES(t0 == test_t0, "t0 check failed");
#endif
PERF_TIMER_STOP(PROVE_step1);
PERF_TIMER_START_BP(PROVE_step2);
const auto HyNsR = hadamard(yN, sR);
const auto vpIz = vector_scalar(oneN, z);
const auto vp2zsq = vector_scalar(twoN, zsq);
const auto aL_vpIz = vector_subtract(aL, vpIz);
const auto aR_vpIz = vector_add(aR, vpIz);
rct::key ip1 = inner_product(aL_vpIz, HyNsR);
sc_add(t1.bytes, t1.bytes, ip1.bytes);
rct::key ip2 = inner_product(sL, vector_add(hadamard(yN, aR_vpIz), vp2zsq));
sc_add(t1.bytes, t1.bytes, ip2.bytes);
rct::key ip3 = inner_product(sL, HyNsR);
sc_add(t2.bytes, t2.bytes, ip3.bytes);
// PAPER LINES 47-48
rct::key tau1 = rct::skGen(), tau2 = rct::skGen();
rct::key T1 = rct::addKeys(rct::scalarmultKey(rct::H, t1), rct::scalarmultBase(tau1));
rct::key T2 = rct::addKeys(rct::scalarmultKey(rct::H, t2), rct::scalarmultBase(tau2));
// PAPER LINES 49-51
rct::key x = hash_cache_mash(hash_cache, z, T1, T2);
// PAPER LINES 52-53
rct::key taux = rct::zero();
sc_mul(taux.bytes, tau1.bytes, x.bytes);
rct::key xsq;
sc_mul(xsq.bytes, x.bytes, x.bytes);
sc_muladd(taux.bytes, tau2.bytes, xsq.bytes, taux.bytes);
sc_muladd(taux.bytes, gamma.bytes, zsq.bytes, taux.bytes);
rct::key mu;
sc_muladd(mu.bytes, x.bytes, rho.bytes, alpha.bytes);
// PAPER LINES 54-57
rct::keyV l = vector_add(aL_vpIz, vector_scalar(sL, x));
rct::keyV r = vector_add(hadamard(yN, vector_add(aR_vpIz, vector_scalar(sR, x))), vp2zsq);
PERF_TIMER_STOP(PROVE_step2);
PERF_TIMER_START_BP(PROVE_step3);
rct::key t = inner_product(l, r);
// DEBUG: Test if the l and r vectors match the polynomial forms
#ifdef DEBUG_BP
rct::key test_t;
sc_muladd(test_t.bytes, t1.bytes, x.bytes, t0.bytes);
sc_muladd(test_t.bytes, t2.bytes, xsq.bytes, test_t.bytes);
CHECK_AND_ASSERT_THROW_MES(test_t == t, "test_t check failed");
#endif
// PAPER LINES 32-33
rct::key x_ip = hash_cache_mash(hash_cache, x, taux, mu, t);
// These are used in the inner product rounds
size_t nprime = N;
rct::keyV Gprime(N);
rct::keyV Hprime(N);
rct::keyV aprime(N);
rct::keyV bprime(N);
const rct::key yinv = invert(y);
rct::key yinvpow = rct::identity();
for (size_t i = 0; i < N; ++i)
{
Gprime[i] = Gi[i];
Hprime[i] = scalarmultKey(Hi[i], yinvpow);
sc_mul(yinvpow.bytes, yinvpow.bytes, yinv.bytes);
aprime[i] = l[i];
bprime[i] = r[i];
}
rct::keyV L(logN);
rct::keyV R(logN);
int round = 0;
rct::keyV w(logN); // this is the challenge x in the inner product protocol
PERF_TIMER_STOP(PROVE_step3);
PERF_TIMER_START_BP(PROVE_step4);
// PAPER LINE 13
while (nprime > 1)
{
// PAPER LINE 15
nprime /= 2;
// PAPER LINES 16-17
rct::key cL = inner_product(slice(aprime, 0, nprime), slice(bprime, nprime, bprime.size()));
rct::key cR = inner_product(slice(aprime, nprime, aprime.size()), slice(bprime, 0, nprime));
// PAPER LINES 18-19
L[round] = vector_exponent_custom(slice(Gprime, nprime, Gprime.size()), slice(Hprime, 0, nprime), slice(aprime, 0, nprime), slice(bprime, nprime, bprime.size()));
sc_mul(tmp.bytes, cL.bytes, x_ip.bytes);
rct::addKeys(L[round], L[round], rct::scalarmultKey(rct::H, tmp));
R[round] = vector_exponent_custom(slice(Gprime, 0, nprime), slice(Hprime, nprime, Hprime.size()), slice(aprime, nprime, aprime.size()), slice(bprime, 0, nprime));
sc_mul(tmp.bytes, cR.bytes, x_ip.bytes);
rct::addKeys(R[round], R[round], rct::scalarmultKey(rct::H, tmp));
// PAPER LINES 21-22
w[round] = hash_cache_mash(hash_cache, L[round], R[round]);
// PAPER LINES 24-25
const rct::key winv = invert(w[round]);
Gprime = hadamard2(vector_scalar2(slice(Gprime, 0, nprime), winv), vector_scalar2(slice(Gprime, nprime, Gprime.size()), w[round]));
Hprime = hadamard2(vector_scalar2(slice(Hprime, 0, nprime), w[round]), vector_scalar2(slice(Hprime, nprime, Hprime.size()), winv));
// PAPER LINES 28-29
aprime = vector_add(vector_scalar(slice(aprime, 0, nprime), w[round]), vector_scalar(slice(aprime, nprime, aprime.size()), winv));
bprime = vector_add(vector_scalar(slice(bprime, 0, nprime), winv), vector_scalar(slice(bprime, nprime, bprime.size()), w[round]));
++round;
}
PERF_TIMER_STOP(PROVE_step4);
// PAPER LINE 58 (with inclusions from PAPER LINE 8 and PAPER LINE 20)
return Bulletproof(V, A, S, T1, T2, taux, mu, L, R, aprime[0], bprime[0], t);
}
Bulletproof bulletproof_PROVE(uint64_t v, const rct::key &gamma)
{
// vG + gammaH
PERF_TIMER_START_BP(PROVE_v);
rct::key sv = rct::zero();
sv.bytes[0] = v & 255;
sv.bytes[1] = (v >> 8) & 255;
sv.bytes[2] = (v >> 16) & 255;
sv.bytes[3] = (v >> 24) & 255;
sv.bytes[4] = (v >> 32) & 255;
sv.bytes[5] = (v >> 40) & 255;
sv.bytes[6] = (v >> 48) & 255;
sv.bytes[7] = (v >> 56) & 255;
PERF_TIMER_STOP(PROVE_v);
return bulletproof_PROVE(sv, gamma);
}
/* Given a range proof, determine if it is valid */
bool bulletproof_VERIFY(const Bulletproof &proof)
{
init_exponents();
CHECK_AND_ASSERT_MES(proof.V.size() == 1, false, "V does not have exactly one element");
CHECK_AND_ASSERT_MES(proof.L.size() == proof.R.size(), false, "Mismatched L and R sizes");
CHECK_AND_ASSERT_MES(proof.L.size() > 0, false, "Empty proof");
CHECK_AND_ASSERT_MES(proof.L.size() == 6, false, "Proof is not for 64 bits");
const size_t logN = proof.L.size();
const size_t N = 1 << logN;
// Reconstruct the challenges
PERF_TIMER_START_BP(VERIFY);
PERF_TIMER_START_BP(VERIFY_start);
rct::key hash_cache = rct::hash_to_scalar(proof.V[0]);
rct::key y = hash_cache_mash(hash_cache, proof.A, proof.S);
rct::key z = hash_cache = rct::hash_to_scalar(y);
rct::key x = hash_cache_mash(hash_cache, z, proof.T1, proof.T2);
PERF_TIMER_STOP(VERIFY_start);
PERF_TIMER_START_BP(VERIFY_line_60);
// Reconstruct the challenges
rct::key x_ip = hash_cache_mash(hash_cache, x, proof.taux, proof.mu, proof.t);
PERF_TIMER_STOP(VERIFY_line_60);
PERF_TIMER_START_BP(VERIFY_line_61);
// PAPER LINE 61
rct::key L61Left = rct::addKeys(rct::scalarmultBase(proof.taux), rct::scalarmultKey(rct::H, proof.t));
rct::key k = rct::zero();
const auto yN = vector_powers(y, N);
rct::key ip1y = inner_product(oneN, yN);
rct::key zsq;
sc_mul(zsq.bytes, z.bytes, z.bytes);
rct::key tmp, tmp2;
sc_mulsub(k.bytes, zsq.bytes, ip1y.bytes, k.bytes);
rct::key zcu;
sc_mul(zcu.bytes, zsq.bytes, z.bytes);
sc_mulsub(k.bytes, zcu.bytes, ip12.bytes, k.bytes);
PERF_TIMER_STOP(VERIFY_line_61);
PERF_TIMER_START_BP(VERIFY_line_61rl);
sc_muladd(tmp.bytes, z.bytes, ip1y.bytes, k.bytes);
rct::key L61Right = rct::scalarmultKey(rct::H, tmp);
CHECK_AND_ASSERT_MES(proof.V.size() == 1, false, "proof.V does not have exactly one element");
tmp = rct::scalarmultKey(proof.V[0], zsq);
rct::addKeys(L61Right, L61Right, tmp);
tmp = rct::scalarmultKey(proof.T1, x);
rct::addKeys(L61Right, L61Right, tmp);
rct::key xsq;
sc_mul(xsq.bytes, x.bytes, x.bytes);
tmp = rct::scalarmultKey(proof.T2, xsq);
rct::addKeys(L61Right, L61Right, tmp);
PERF_TIMER_STOP(VERIFY_line_61rl);
if (!(L61Right == L61Left))
{
MERROR("Verification failure at step 1");
return false;
}
PERF_TIMER_START_BP(VERIFY_line_62);
// PAPER LINE 62
rct::key P = rct::addKeys(proof.A, rct::scalarmultKey(proof.S, x));
PERF_TIMER_STOP(VERIFY_line_62);
// Compute the number of rounds for the inner product
const size_t rounds = proof.L.size();
CHECK_AND_ASSERT_MES(rounds > 0, false, "Zero rounds");
PERF_TIMER_START_BP(VERIFY_line_21_22);
// PAPER LINES 21-22
// The inner product challenges are computed per round
rct::keyV w(rounds);
for (size_t i = 0; i < rounds; ++i)
{
w[i] = hash_cache_mash(hash_cache, proof.L[i], proof.R[i]);
}
PERF_TIMER_STOP(VERIFY_line_21_22);
PERF_TIMER_START_BP(VERIFY_line_24_25);
// Basically PAPER LINES 24-25
// Compute the curvepoints from G[i] and H[i]
rct::key inner_prod = rct::identity();
rct::key yinvpow = rct::identity();
rct::key ypow = rct::identity();
PERF_TIMER_START_BP(VERIFY_line_24_25_invert);
const rct::key yinv = invert(y);
rct::keyV winv(rounds);
for (size_t i = 0; i < rounds; ++i)
winv[i] = invert(w[i]);
PERF_TIMER_STOP(VERIFY_line_24_25_invert);
for (size_t i = 0; i < N; ++i)
{
// Convert the index to binary IN REVERSE and construct the scalar exponent
rct::key g_scalar = proof.a;
rct::key h_scalar;
sc_mul(h_scalar.bytes, proof.b.bytes, yinvpow.bytes);
for (size_t j = rounds; j-- > 0; )
{
size_t J = w.size() - j - 1;
if ((i & (((size_t)1)<<j)) == 0)
{
sc_mul(g_scalar.bytes, g_scalar.bytes, winv[J].bytes);
sc_mul(h_scalar.bytes, h_scalar.bytes, w[J].bytes);
}
else
{
sc_mul(g_scalar.bytes, g_scalar.bytes, w[J].bytes);
sc_mul(h_scalar.bytes, h_scalar.bytes, winv[J].bytes);
}
}
// Adjust the scalars using the exponents from PAPER LINE 62
sc_add(g_scalar.bytes, g_scalar.bytes, z.bytes);
sc_mul(tmp.bytes, zsq.bytes, twoN[i].bytes);
sc_muladd(tmp.bytes, z.bytes, ypow.bytes, tmp.bytes);
sc_mulsub(h_scalar.bytes, tmp.bytes, yinvpow.bytes, h_scalar.bytes);
// Now compute the basepoint's scalar multiplication
// Each of these could be written as a multiexp operation instead
rct::addKeys3(tmp, g_scalar, Gprecomp[i], h_scalar, Hprecomp[i]);
rct::addKeys(inner_prod, inner_prod, tmp);
if (i != N-1)
{
sc_mul(yinvpow.bytes, yinvpow.bytes, yinv.bytes);
sc_mul(ypow.bytes, ypow.bytes, y.bytes);
}
}
PERF_TIMER_STOP(VERIFY_line_24_25);
PERF_TIMER_START_BP(VERIFY_line_26);
// PAPER LINE 26
rct::key pprime;
sc_sub(tmp.bytes, rct::zero().bytes, proof.mu.bytes);
rct::addKeys(pprime, P, rct::scalarmultBase(tmp));
for (size_t i = 0; i < rounds; ++i)
{
sc_mul(tmp.bytes, w[i].bytes, w[i].bytes);
sc_mul(tmp2.bytes, winv[i].bytes, winv[i].bytes);
#if 1
ge_dsmp cacheL, cacheR;
rct::precomp(cacheL, proof.L[i]);
rct::precomp(cacheR, proof.R[i]);
rct::addKeys3(tmp, tmp, cacheL, tmp2, cacheR);
rct::addKeys(pprime, pprime, tmp);
#else
rct::addKeys(pprime, pprime, rct::scalarmultKey(proof.L[i], tmp));
rct::addKeys(pprime, pprime, rct::scalarmultKey(proof.R[i], tmp2));
#endif
}
sc_mul(tmp.bytes, proof.t.bytes, x_ip.bytes);
rct::addKeys(pprime, pprime, rct::scalarmultKey(rct::H, tmp));
PERF_TIMER_STOP(VERIFY_line_26);
PERF_TIMER_START_BP(VERIFY_step2_check);
sc_mul(tmp.bytes, proof.a.bytes, proof.b.bytes);
sc_mul(tmp.bytes, tmp.bytes, x_ip.bytes);
tmp = rct::scalarmultKey(rct::H, tmp);
rct::addKeys(tmp, tmp, inner_prod);
PERF_TIMER_STOP(VERIFY_step2_check);
if (!(pprime == tmp))
{
MERROR("Verification failure at step 2");
return false;
}
PERF_TIMER_STOP(VERIFY);
return true;
}
}
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