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753 lines
24 KiB
753 lines
24 KiB
// Copyright (c) 2017-2018, The Monero Project
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without modification, are
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// permitted provided that the following conditions are met:
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//
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// 1. Redistributions of source code must retain the above copyright notice, this list of
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// conditions and the following disclaimer.
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//
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// 2. Redistributions in binary form must reproduce the above copyright notice, this list
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// of conditions and the following disclaimer in the documentation and/or other
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// materials provided with the distribution.
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//
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// 3. Neither the name of the copyright holder nor the names of its contributors may be
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// used to endorse or promote products derived from this software without specific
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// prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
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// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
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// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
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// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Adapted from Java code by Sarang Noether
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#include <stdlib.h>
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#include <openssl/ssl.h>
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#include <boost/thread/mutex.hpp>
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#include "misc_log_ex.h"
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#include "common/perf_timer.h"
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extern "C"
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{
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#include "crypto/crypto-ops.h"
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}
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#include "rctOps.h"
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#include "bulletproofs.h"
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#undef MONERO_DEFAULT_LOG_CATEGORY
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#define MONERO_DEFAULT_LOG_CATEGORY "bulletproofs"
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//#define DEBUG_BP
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#define PERF_TIMER_START_BP(x) PERF_TIMER_START_UNIT(x, 1000000)
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namespace rct
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{
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static rct::key vector_exponent(const rct::keyV &a, const rct::keyV &b);
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static rct::keyV vector_powers(rct::key x, size_t n);
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static rct::key inner_product(const rct::keyV &a, const rct::keyV &b);
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static constexpr size_t maxN = 64;
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static rct::key Hi[maxN], Gi[maxN];
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static ge_dsmp Gprecomp[64], Hprecomp[64];
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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 } };
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static const rct::keyV oneN = vector_powers(rct::identity(), maxN);
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static const rct::keyV twoN = vector_powers(TWO, maxN);
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static const rct::key ip12 = inner_product(oneN, twoN);
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static boost::mutex init_mutex;
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static rct::key get_exponent(const rct::key &base, size_t idx)
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{
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static const std::string salt("bulletproof");
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std::string hashed = std::string((const char*)base.bytes, sizeof(base)) + salt + tools::get_varint_data(idx);
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return rct::hashToPoint(rct::hash2rct(crypto::cn_fast_hash(hashed.data(), hashed.size())));
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}
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static void init_exponents()
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{
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boost::lock_guard<boost::mutex> lock(init_mutex);
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static bool init_done = false;
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if (init_done)
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return;
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for (size_t i = 0; i < maxN; ++i)
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{
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Hi[i] = get_exponent(rct::H, i * 2);
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rct::precomp(Hprecomp[i], Hi[i]);
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Gi[i] = get_exponent(rct::H, i * 2 + 1);
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rct::precomp(Gprecomp[i], Gi[i]);
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}
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init_done = true;
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}
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/* Given two scalar arrays, construct a vector commitment */
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static rct::key vector_exponent(const rct::keyV &a, const rct::keyV &b)
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{
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CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
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CHECK_AND_ASSERT_THROW_MES(a.size() <= maxN, "Incompatible sizes of a and maxN");
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rct::key res = rct::identity();
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for (size_t i = 0; i < a.size(); ++i)
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{
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rct::key term;
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rct::addKeys3(term, a[i], Gprecomp[i], b[i], Hprecomp[i]);
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rct::addKeys(res, res, term);
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}
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return res;
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}
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/* Compute a custom vector-scalar commitment */
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static rct::key vector_exponent_custom(const rct::keyV &A, const rct::keyV &B, const rct::keyV &a, const rct::keyV &b)
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{
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CHECK_AND_ASSERT_THROW_MES(A.size() == B.size(), "Incompatible sizes of A and B");
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CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
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CHECK_AND_ASSERT_THROW_MES(a.size() == A.size(), "Incompatible sizes of a and A");
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CHECK_AND_ASSERT_THROW_MES(a.size() <= maxN, "Incompatible sizes of a and maxN");
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rct::key res = rct::identity();
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for (size_t i = 0; i < a.size(); ++i)
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{
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rct::key term;
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#if 0
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// we happen to know where A and B might fall, so don't bother checking the rest
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ge_dsmp *Acache = NULL, *Bcache = NULL;
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ge_dsmp Acache_custom[1], Bcache_custom[1];
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if (Gi[i] == A[i])
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Acache = Gprecomp + i;
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else if (i<32 && Gi[i+32] == A[i])
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Acache = Gprecomp + i + 32;
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else
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{
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rct::precomp(Acache_custom[0], A[i]);
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Acache = Acache_custom;
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}
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if (i == 0 && B[i] == Hi[0])
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Bcache = Hprecomp;
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else
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{
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rct::precomp(Bcache_custom[0], B[i]);
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Bcache = Bcache_custom;
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}
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rct::addKeys3(term, a[i], *Acache, b[i], *Bcache);
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#else
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ge_dsmp Acache, Bcache;
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rct::precomp(Bcache, B[i]);
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rct::addKeys3(term, a[i], A[i], b[i], Bcache);
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#endif
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rct::addKeys(res, res, term);
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}
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return res;
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}
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/* Given a scalar, construct a vector of powers */
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static rct::keyV vector_powers(rct::key x, size_t n)
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{
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rct::keyV res(n);
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if (n == 0)
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return res;
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res[0] = rct::identity();
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if (n == 1)
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return res;
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res[1] = x;
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for (size_t i = 2; i < n; ++i)
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{
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sc_mul(res[i].bytes, res[i-1].bytes, x.bytes);
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}
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return res;
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}
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/* Given two scalar arrays, construct the inner product */
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static rct::key inner_product(const rct::keyV &a, const rct::keyV &b)
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{
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CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
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rct::key res = rct::zero();
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for (size_t i = 0; i < a.size(); ++i)
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{
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sc_muladd(res.bytes, a[i].bytes, b[i].bytes, res.bytes);
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}
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return res;
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}
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/* Given two scalar arrays, construct the Hadamard product */
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static rct::keyV hadamard(const rct::keyV &a, const rct::keyV &b)
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{
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CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
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rct::keyV res(a.size());
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for (size_t i = 0; i < a.size(); ++i)
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{
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sc_mul(res[i].bytes, a[i].bytes, b[i].bytes);
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}
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return res;
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}
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/* Given two curvepoint arrays, construct the Hadamard product */
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static rct::keyV hadamard2(const rct::keyV &a, const rct::keyV &b)
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{
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CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
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rct::keyV res(a.size());
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for (size_t i = 0; i < a.size(); ++i)
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{
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rct::addKeys(res[i], a[i], b[i]);
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}
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return res;
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}
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/* Add two vectors */
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static rct::keyV vector_add(const rct::keyV &a, const rct::keyV &b)
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{
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CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
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rct::keyV res(a.size());
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for (size_t i = 0; i < a.size(); ++i)
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{
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sc_add(res[i].bytes, a[i].bytes, b[i].bytes);
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}
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return res;
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}
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/* Subtract two vectors */
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static rct::keyV vector_subtract(const rct::keyV &a, const rct::keyV &b)
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{
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CHECK_AND_ASSERT_THROW_MES(a.size() == b.size(), "Incompatible sizes of a and b");
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rct::keyV res(a.size());
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for (size_t i = 0; i < a.size(); ++i)
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{
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sc_sub(res[i].bytes, a[i].bytes, b[i].bytes);
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}
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return res;
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}
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/* Multiply a scalar and a vector */
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static rct::keyV vector_scalar(const rct::keyV &a, const rct::key &x)
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{
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rct::keyV res(a.size());
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for (size_t i = 0; i < a.size(); ++i)
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{
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sc_mul(res[i].bytes, a[i].bytes, x.bytes);
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}
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return res;
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}
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/* Exponentiate a curve vector by a scalar */
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static rct::keyV vector_scalar2(const rct::keyV &a, const rct::key &x)
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{
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rct::keyV res(a.size());
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for (size_t i = 0; i < a.size(); ++i)
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{
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rct::scalarmultKey(res[i], a[i], x);
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}
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return res;
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}
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static rct::key switch_endianness(rct::key k)
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{
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std::reverse(k.bytes, k.bytes + sizeof(k));
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return k;
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}
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/* Compute the inverse of a scalar, the stupid way */
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static rct::key invert(const rct::key &x)
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{
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rct::key inv;
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BN_CTX *ctx = BN_CTX_new();
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BIGNUM *X = BN_new();
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BIGNUM *L = BN_new();
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BIGNUM *I = BN_new();
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BN_bin2bn(switch_endianness(x).bytes, sizeof(rct::key), X);
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BN_bin2bn(switch_endianness(rct::curveOrder()).bytes, sizeof(rct::key), L);
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CHECK_AND_ASSERT_THROW_MES(BN_mod_inverse(I, X, L, ctx), "Failed to invert");
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const int len = BN_num_bytes(I);
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CHECK_AND_ASSERT_THROW_MES((size_t)len <= sizeof(rct::key), "Invalid number length");
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inv = rct::zero();
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BN_bn2bin(I, inv.bytes);
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std::reverse(inv.bytes, inv.bytes + len);
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BN_free(I);
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BN_free(L);
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BN_free(X);
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BN_CTX_free(ctx);
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#ifdef DEBUG_BP
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rct::key tmp;
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sc_mul(tmp.bytes, inv.bytes, x.bytes);
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CHECK_AND_ASSERT_THROW_MES(tmp == rct::identity(), "invert failed");
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#endif
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return inv;
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}
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/* Compute the slice of a vector */
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static rct::keyV slice(const rct::keyV &a, size_t start, size_t stop)
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{
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CHECK_AND_ASSERT_THROW_MES(start < a.size(), "Invalid start index");
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CHECK_AND_ASSERT_THROW_MES(stop <= a.size(), "Invalid stop index");
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CHECK_AND_ASSERT_THROW_MES(start < stop, "Invalid start/stop indices");
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rct::keyV res(stop - start);
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for (size_t i = start; i < stop; ++i)
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{
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res[i - start] = a[i];
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}
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return res;
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}
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static rct::key hash_cache_mash(rct::key &hash_cache, const rct::key &mash0, const rct::key &mash1)
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{
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rct::keyV data;
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data.reserve(3);
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data.push_back(hash_cache);
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data.push_back(mash0);
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data.push_back(mash1);
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return hash_cache = rct::hash_to_scalar(data);
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}
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static rct::key hash_cache_mash(rct::key &hash_cache, const rct::key &mash0, const rct::key &mash1, const rct::key &mash2)
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{
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rct::keyV data;
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data.reserve(4);
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data.push_back(hash_cache);
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data.push_back(mash0);
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data.push_back(mash1);
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data.push_back(mash2);
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return hash_cache = rct::hash_to_scalar(data);
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}
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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)
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{
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rct::keyV data;
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data.reserve(5);
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data.push_back(hash_cache);
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data.push_back(mash0);
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data.push_back(mash1);
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data.push_back(mash2);
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data.push_back(mash3);
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return hash_cache = rct::hash_to_scalar(data);
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}
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/* Given a value v (0..2^N-1) and a mask gamma, construct a range proof */
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Bulletproof bulletproof_PROVE(const rct::key &sv, const rct::key &gamma)
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{
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init_exponents();
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PERF_TIMER_UNIT(PROVE, 1000000);
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constexpr size_t logN = 6; // log2(64)
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constexpr size_t N = 1<<logN;
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rct::key V;
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rct::keyV aL(N), aR(N);
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PERF_TIMER_START_BP(PROVE_v);
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rct::addKeys2(V, gamma, sv, rct::H);
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PERF_TIMER_STOP(PROVE_v);
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PERF_TIMER_START_BP(PROVE_aLaR);
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for (size_t i = N; i-- > 0; )
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{
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if (sv[i/8] & (((uint64_t)1)<<(i%8)))
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{
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aL[i] = rct::identity();
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}
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else
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{
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aL[i] = rct::zero();
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}
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sc_sub(aR[i].bytes, aL[i].bytes, rct::identity().bytes);
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}
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PERF_TIMER_STOP(PROVE_aLaR);
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rct::key hash_cache = rct::hash_to_scalar(V);
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// DEBUG: Test to ensure this recovers the value
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#ifdef DEBUG_BP
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uint64_t test_aL = 0, test_aR = 0;
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for (size_t i = 0; i < N; ++i)
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{
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if (aL[i] == rct::identity())
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test_aL += ((uint64_t)1)<<i;
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if (aR[i] == rct::zero())
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test_aR += ((uint64_t)1)<<i;
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}
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uint64_t v_test = 0;
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for (int n = 0; n < 8; ++n) v_test |= (((uint64_t)sv[n]) << (8*n));
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CHECK_AND_ASSERT_THROW_MES(test_aL == v_test, "test_aL failed");
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CHECK_AND_ASSERT_THROW_MES(test_aR == v_test, "test_aR failed");
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#endif
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PERF_TIMER_START_BP(PROVE_step1);
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// PAPER LINES 38-39
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rct::key alpha = rct::skGen();
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rct::key ve = vector_exponent(aL, aR);
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rct::key A;
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rct::addKeys(A, ve, rct::scalarmultBase(alpha));
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// PAPER LINES 40-42
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rct::keyV sL = rct::skvGen(N), sR = rct::skvGen(N);
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rct::key rho = rct::skGen();
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ve = vector_exponent(sL, sR);
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rct::key S;
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rct::addKeys(S, ve, rct::scalarmultBase(rho));
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// PAPER LINES 43-45
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rct::key y = hash_cache_mash(hash_cache, A, S);
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rct::key z = hash_cache = rct::hash_to_scalar(y);
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// Polynomial construction before PAPER LINE 46
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rct::key t0 = rct::zero();
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rct::key t1 = rct::zero();
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rct::key t2 = rct::zero();
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const auto yN = vector_powers(y, N);
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rct::key ip1y = inner_product(oneN, yN);
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rct::key tmp;
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sc_muladd(t0.bytes, z.bytes, ip1y.bytes, t0.bytes);
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rct::key zsq;
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sc_mul(zsq.bytes, z.bytes, z.bytes);
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sc_muladd(t0.bytes, zsq.bytes, sv.bytes, t0.bytes);
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rct::key k = rct::zero();
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sc_mulsub(k.bytes, zsq.bytes, ip1y.bytes, k.bytes);
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rct::key zcu;
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sc_mul(zcu.bytes, zsq.bytes, z.bytes);
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sc_mulsub(k.bytes, zcu.bytes, ip12.bytes, k.bytes);
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sc_add(t0.bytes, t0.bytes, k.bytes);
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// DEBUG: Test the value of t0 has the correct form
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#ifdef DEBUG_BP
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rct::key test_t0 = rct::zero();
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rct::key iph = inner_product(aL, hadamard(aR, yN));
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sc_add(test_t0.bytes, test_t0.bytes, iph.bytes);
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rct::key ips = inner_product(vector_subtract(aL, aR), yN);
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sc_muladd(test_t0.bytes, z.bytes, ips.bytes, test_t0.bytes);
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rct::key ipt = inner_product(twoN, aL);
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sc_muladd(test_t0.bytes, zsq.bytes, ipt.bytes, test_t0.bytes);
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sc_add(test_t0.bytes, test_t0.bytes, k.bytes);
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CHECK_AND_ASSERT_THROW_MES(t0 == test_t0, "t0 check failed");
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#endif
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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;
|
|
}
|
|
|
|
}
|