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monero/src/ringct/rctOps.cpp

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// Copyright (c) 2016, Monero Research Labs
//
// Author: Shen Noether <shen.noether@gmx.com>
//
// 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.
#include <boost/lexical_cast.hpp>
#include "misc_log_ex.h"
#include "cryptonote_basic/cryptonote_format_utils.h"
#include "rctOps.h"
using namespace crypto;
using namespace std;
#undef MONERO_DEFAULT_LOG_CATEGORY
#define MONERO_DEFAULT_LOG_CATEGORY "ringct"
#define CHECK_AND_ASSERT_THROW_MES_L1(expr, message) {if(!(expr)) {MWARNING(message); throw std::runtime_error(message);}}
struct zero_commitment { uint64_t amount; rct::key commitment; };
static const zero_commitment zero_commitments[] = {
{ (uint64_t)0ull, {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}} },
{ (uint64_t)1ull, {{0x17, 0x38, 0xeb, 0x7a, 0x67, 0x7c, 0x61, 0x49, 0x22, 0x8a, 0x2b, 0xea, 0xa2, 0x1b, 0xea, 0x9e, 0x33, 0x70, 0x80, 0x2d, 0x72, 0xa3, 0xee, 0xc7, 0x90, 0x11, 0x95, 0x80, 0xe0, 0x2b, 0xd5, 0x22}} },
{ (uint64_t)2ull, {{0x76, 0x24, 0x84, 0x63, 0xa, 0x6, 0x17, 0x17, 0x8d, 0xe, 0x33, 0xf3, 0x2e, 0xe, 0x11, 0x3e, 0xa8, 0x46, 0x86, 0x9d, 0x46, 0x4b, 0xb, 0x6f, 0xf1, 0x3b, 0x29, 0x97, 0x4, 0x9c, 0xda, 0x7d}} },
{ (uint64_t)3ull, {{0xcf, 0xf7, 0x7b, 0x56, 0x62, 0x1c, 0x4f, 0xef, 0x74, 0xcf, 0x37, 0xc1, 0x78, 0xd4, 0xb5, 0x8a, 0xf4, 0xad, 0x8c, 0xd4, 0x35, 0xfc, 0xb9, 0x62, 0x76, 0xbc, 0x15, 0x9c, 0x7c, 0x6a, 0x28, 0x8c}} },
{ (uint64_t)4ull, {{0x9a, 0xb8, 0x6c, 0x31, 0xf4, 0x22, 0xd8, 0x21, 0xb5, 0x22, 0x57, 0x30, 0xd1, 0xbf, 0x73, 0xa, 0x9b, 0x91, 0xd2, 0xee, 0xe3, 0x14, 0xb8, 0x4e, 0xbd, 0x4b, 0x93, 0xa6, 0x81, 0x61, 0x82, 0x66}} },
{ (uint64_t)5ull, {{0x32, 0xee, 0x2f, 0x65, 0x9a, 0xf6, 0x38, 0x58, 0xc2, 0xf7, 0xdc, 0x11, 0x1b, 0x3b, 0xb8, 0xfe, 0xc0, 0x2c, 0xac, 0x42, 0x38, 0x3b, 0xb7, 0x36, 0xde, 0x1, 0x8, 0x6f, 0x38, 0xf0, 0x12, 0x3c}} },
{ (uint64_t)6ull, {{0x47, 0x26, 0x2b, 0x1e, 0xa6, 0x43, 0x1, 0x6e, 0x38, 0x24, 0x17, 0x53, 0xa4, 0xfb, 0x39, 0x92, 0x9e, 0x31, 0xea, 0x9b, 0xd3, 0x41, 0x1a, 0xb1, 0x7f, 0x16, 0x6e, 0x61, 0xf6, 0xc, 0xe5, 0xa7}} },
{ (uint64_t)7ull, {{0xc6, 0x32, 0x93, 0x68, 0x79, 0x9a, 0xd, 0xed, 0x4c, 0x20, 0x25, 0x6b, 0xff, 0xe6, 0x45, 0x47, 0xf1, 0x7b, 0xc4, 0x23, 0x95, 0x4, 0xbe, 0x82, 0x4d, 0xff, 0x8a, 0x2b, 0xe1, 0xaf, 0xe3, 0xcd}} },
{ (uint64_t)8ull, {{0xd5, 0xf1, 0x50, 0x74, 0x33, 0x46, 0x19, 0xf, 0x84, 0x2b, 0x6, 0xb8, 0xfa, 0xe1, 0x20, 0xeb, 0x85, 0x24, 0x7e, 0x9f, 0x6d, 0xec, 0x88, 0xff, 0xa2, 0x23, 0xbf, 0x69, 0x94, 0xe9, 0xc8, 0xc2}} },
{ (uint64_t)9ull, {{0x56, 00, 0x23, 0x32, 0x9e, 0xc0, 0xfa, 0xf3, 0x3b, 0x5e, 0x3a, 0x5c, 0xb4, 0xea, 0xef, 0xee, 0x38, 0xf8, 0x96, 0x1c, 0x88, 0xb6, 0x6a, 0x2f, 0x19, 0xd4, 0x59, 0x51, 0x96, 0x9c, 0x6d, 0x1f}} },
{ (uint64_t)10ull, {{0x3, 0x80, 0xdc, 0x24, 0xcc, 0x97, 0xcc, 0xe6, 0x58, 0xc3, 0xa9, 0x47, 0xc5, 0x10, 0x25, 0xde, 0x1a, 0x69, 0x80, 0x3b, 0xdb, 0x50, 0x5, 0xe3, 0xb7, 0xdd, 0xa9, 0xd, 0x68, 0x59, 0xb0, 0x1c}} },
{ (uint64_t)20ull, {{0x9, 0x3, 0xf6, 0x2e, 0x97, 0x76, 0x47, 0x58, 0xfe, 0xf8, 0x9e, 0x5b, 0xec, 0x29, 0xef, 0x4f, 0xc5, 0xe6, 0x45, 0x4b, 0x2d, 0x47, 0x44, 0x47, 0x36, 0x4, 0x4c, 0x25, 0x2e, 0xe2, 0x8e, 0xba}} },
{ (uint64_t)30ull, {{0xa2, 0x8b, 0x89, 0xe0, 0xb, 0xed, 0x62, 0x31, 0x68, 0x5b, 0xf9, 0x74, 0x36, 0xf2, 0xba, 0x51, 0xa2, 0x51, 0x55, 0x7f, 0x8d, 0x17, 0xa, 0x78, 0xe3, 0x12, 0xd6, 0x24, 0xbf, 0x60, 0xff, 0xfe}} },
{ (uint64_t)40ull, {{0xb5, 0xc6, 0x95, 0x55, 0x6a, 0x28, 0x47, 0xb2, 0xe, 0x1c, 0xbb, 0x26, 0xe6, 0xa9, 0xc6, 0x8a, 0x61, 0xc5, 0x50, 0xce, 0xb7, 0xc3, 0x4, 0xfe, 0x92, 0x28, 0x3d, 0x29, 0xa9, 0xb2, 0x43, 0xcb}} },
{ (uint64_t)50ull, {{0x12, 0x8e, 0xc6, 0xcd, 0xc0, 0x6b, 0x43, 0xc5, 0xd0, 0x9c, 0x3f, 0x65, 0x2a, 0xe3, 0x44, 0x7f, 0x9b, 0x3f, 0x2c, 0x30, 0x91, 0x2d, 0xf0, 0x80, 0x37, 00, 0x85, 0xbc, 0xc, 0x9, 0xef, 0x78}} },
{ (uint64_t)60ull, {{0x1f, 0x9f, 0x40, 0x3a, 0xae, 0xa7, 0x16, 0xfb, 0xe2, 0x98, 0xa8, 0x14, 0xf1, 0xee, 0xbc, 0x1b, 0x73, 0x16, 0x8c, 0x37, 0xfa, 0xe3, 0x16, 0xeb, 0x65, 0x5, 0x81, 0x6f, 0xc2, 0x20, 0xeb, 0xfb}} },
{ (uint64_t)70ull, {{0x10, 0xa2, 0x38, 0xc5, 0xe4, 0x8e, 0x4b, 0x93, 0x99, 0xdb, 0xa6, 0xcb, 0xd9, 0x8e, 0x63, 0x54, 0x41, 0x59, 0xe9, 0x8c, 0x93, 0x5a, 0xc0, 0x60, 0x3d, 0x72, 0xde, 0xf, 0xff, 0x31, 0x53, 0xbb}} },
{ (uint64_t)80ull, {{0x75, 0xab, 0x78, 0xc7, 0x28, 0x1f, 0x69, 0x28, 0xf0, 0x94, 0x86, 0x5, 0x7a, 0x63, 0x64, 0x18, 0x27, 0xc5, 0x74, 0x84, 0xe3, 0xe9, 0x9a, 0x39, 0xf3, 0x12, 0xa4, 0x3a, 0x51, 0x9b, 0xda, 0x8}} },
{ (uint64_t)90ull, {{0xe9, 0x56, 0x7b, 0xa7, 0x88, 0xb8, 0x5b, 0x82, 0xc8, 0x65, 0x7a, 0x15, 0xa5, 0x48, 0x99, 0x5c, 0xf6, 0xb0, 0xbd, 0xd1, 0xc6, 0x2a, 0xda, 0x77, 0x55, 0xf2, 0x32, 0x3a, 0xd8, 0xa4, 0x8, 0x51}} },
{ (uint64_t)100ull, {{0xb6, 0x17, 0x36, 0xd5, 0xf2, 0x8d, 0xef, 0x28, 0x61, 0x6a, 0xfc, 0x47, 0x93, 0xe9, 0x9b, 0x27, 0xcd, 0x3e, 0x89, 0xfb, 0x91, 0xc1, 0x13, 0xd4, 0x30, 0x73, 0x65, 0xfb, 0x75, 0xde, 0xdf, 0x88}} },
{ (uint64_t)200ull, {{0x71, 0x3, 0xeb, 0x72, 0x19, 0x28, 0xd7, 0x91, 0x99, 0x87, 0xf3, 0x50, 0xca, 0xa5, 0x7a, 0xe7, 0xb0, 0x81, 0x57, 0x15, 0x3b, 0x4c, 0x43, 0xd, 0x3e, 0xde, 0xc0, 0xc2, 0x3, 0x7, 0x97, 0x44}} },
{ (uint64_t)300ull, {{0x24, 0x40, 0x9e, 0x92, 0x2e, 0xce, 0xd1, 0xa0, 0x5e, 0x4e, 0xac, 0xa3, 0xdf, 0x91, 0x19, 0xc3, 0x8a, 0x92, 0x2e, 0xb, 0x66, 0xd0, 0x2d, 0x9d, 0xd2, 0xfb, 0x1d, 0xcc, 0x20, 0xb9, 0xaf, 0xc7}} },
{ (uint64_t)400ull, {{0xa7, 0x72, 0x9f, 0xa9, 0x32, 0x81, 0x82, 0x99, 0x34, 0x11, 0x5d, 0x47, 0x5a, 0x67, 0x86, 0xa, 0x14, 0x12, 0xc5, 0xe5, 0x95, 0x12, 0x20, 0xd9, 0x60, 0xc2, 0x41, 0xa0, 0x19, 0x1a, 0x9e, 0x65}} },
{ (uint64_t)500ull, {{0x2e, 0x53, 0xc, 0x6, 0x1c, 0x6d, 0x9e, 0x97, 0xab, 0xaf, 0x46, 0x8c, 0x32, 0xb0, 0xad, 0xa7, 0x49, 0x22, 0x57, 0x72, 0xfc, 0xd1, 0x17, 0x41, 0xcb, 0x5c, 0x3, 0x5c, 0xdd, 0x26, 0x14, 0xe}} },
{ (uint64_t)600ull, {{0xa5, 0xb, 0x91, 0x9, 0x9d, 0xf1, 0xb1, 0x69, 0x4f, 0x30, 0xb5, 0x8f, 0xe6, 0x77, 0x68, 0x50, 0xdb, 0xdb, 0xf4, 0x6c, 0xed, 0x99, 0x7f, 0x52, 0x62, 0xa8, 0x51, 0x59, 0x40, 0x74, 0xa5, 0x9d}} },
{ (uint64_t)700ull, {{0x51, 0x2c, 0xf, 0xae, 0xcc, 0xbe, 0xf2, 0xfe, 0xe5, 0x75, 0x4c, 0x6a, 0x45, 0xfd, 0xc0, 0x75, 0x2d, 0x4f, 0x15, 0x22, 0xe7, 0x7f, 0xf0, 0xc4, 0x8d, 0xcb, 0x19, 0x91, 0x8a, 0x68, 0x84, 0xe0}} },
{ (uint64_t)800ull, {{0xda, 0xa9, 0xf9, 0xa5, 0xb9, 0x71, 0x33, 0x33, 0xe9, 0x8c, 0x5, 0xac, 0xe7, 0x27, 0xcc, 0xe, 0x7d, 0xc3, 0xf1, 0x59, 0x49, 0xe1, 0xef, 0x4d, 0x94, 0xfa, 0x47, 0xd6, 0x8a, 0x34, 0xc6, 0x75}} },
{ (uint64_t)900ull, {{0xc7, 0x2b, 0x18, 0xc9, 0x17, 0xcd, 0x43, 0xee, 0x78, 0x40, 0x5e, 0x39, 0x83, 0x98, 0xb8, 0x3a, 0xc0, 0x97, 0x7b, 0x25, 0x19, 0x90, 0xd8, 0x13, 0xc, 0x38, 0xba, 0x53, 0xb6, 0x3d, 0xb4, 0xf7}} },
{ (uint64_t)1000ull, {{0x1, 0xdf, 0x60, 0x91, 0xeb, 0x6a, 0x48, 0xe9, 0xe4, 0x22, 0x25, 0xb, 0xe3, 0x83, 0x88, 0xc8, 0x61, 0xb6, 0x55, 0x55, 0xa7, 0x20, 0xad, 0x15, 0x35, 0x86, 0xfe, 0x2b, 0xd2, 0x2f, 0xa2, 0x3d}} },
{ (uint64_t)2000ull, {{0x24, 0xf5, 0xb1, 0x34, 0x78, 0x46, 0xaf, 0x22, 0xb5, 0x6f, 0x41, 0x25, 0xb3, 0xe7, 0x67, 0x8c, 0xf8, 0x4b, 0x4f, 0xd2, 0xf9, 0x2e, 0x1c, 0x40, 0xaa, 0x3a, 0x1b, 0xe0, 0xc7, 0x4d, 0x95, 0xe6}} },
{ (uint64_t)3000ull, {{0xa7, 0x1c, 0x9a, 0x8f, 0x40, 0xc1, 0x25, 0x9c, 0x36, 0x26, 0x27, 0x73, 0xe0, 0x8, 0x20, 0x18, 0x3e, 0x6b, 0x59, 0xe0, 0x71, 0xc9, 0x9b, 0x34, 0x9b, 0xef, 0x8f, 0x7e, 0xd2, 0xc6, 0xad, 0xb9}} },
{ (uint64_t)4000ull, {{0x98, 0xdc, 0x74, 0xaf, 0x19, 0x89, 0xd3, 0x4b, 0x64, 0x2e, 0xb3, 0x6, 0x2d, 0xbc, 0x9d, 0xca, 0xd8, 0x1, 0xc5, 0x65, 0x27, 0x6, 0x93, 0x99, 0xe7, 0xc4, 0x11, 0xad, 0x14, 0x28, 0x82, 0xf6}} },
{ (uint64_t)5000ull, {{0x61, 0x76, 0xac, 0x4a, 0xc0, 0x6, 0x5e, 0x49, 0xd6, 0xc4, 0x41, 0xcf, 0x40, 0x4f, 0xad, 0xda, 0xad, 0x44, 0x93, 0xe, 0xf0, 0x3c, 0x68, 0x9, 0xad, 0xd7, 0x77, 0xe4, 0x2f, 0xee, 0x7f, 0x10}} },
{ (uint64_t)6000ull, {{0x78, 0x79, 0x4, 0x65, 0xf6, 0x60, 0x5b, 0x5a, 0x84, 0x77, 0x36, 0x5a, 0xa6, 0xc2, 0xa4, 0xa5, 0x84, 0x91, 0xc, 0x23, 0x95, 0x2, 0x92, 0x97, 0x52, 0x49, 0xa1, 0xad, 0x7d, 0xf0, 0xf7, 0xe8}} },
{ (uint64_t)7000ull, {{0x20, 0xa5, 0x60, 0x6b, 0x60, 0x23, 0x95, 0xd6, 0x8e, 0x2f, 0xad, 0x8e, 0xc6, 0x7f, 0x92, 0xde, 0x89, 0xc6, 0x3e, 0x1e, 0x7f, 0xc1, 0xdd, 0x7f, 0x92, 0xff, 0xed, 0xb8, 0xf6, 0x55, 0xfb, 0xd}} },
{ (uint64_t)8000ull, {{0x9a, 0x78, 0x97, 0x43, 0x98, 0x65, 0x17, 0xd9, 0x5f, 0x4e, 0x80, 0x8b, 0xeb, 0xe6, 0x52, 0xd, 0xe6, 0xcf, 0x8c, 0x51, 0x35, 0xab, 0x36, 0x8, 0x7e, 0x87, 0xe2, 0x76, 0xac, 0x6a, 0x34, 0x1}} },
{ (uint64_t)9000ull, {{0x5f, 0xc7, 0xaa, 0x48, 0xbb, 0x19, 0x13, 0x58, 0xc7, 0xe3, 0x4d, 0x24, 0xcf, 0x9c, 0x31, 0x16, 0x74, 0x12, 0x7a, 0xb2, 0x45, 0xd0, 0x8f, 0x4e, 0x2c, 0xfd, 0xbf, 0x8f, 0x5, 0xc9, 0x5b, 0xf5}} },
{ (uint64_t)10000ull, {{0x61, 0x20, 0xe7, 0x76, 0xe9, 0x12, 0xab, 0x10, 0x5a, 0x49, 0xf9, 0xda, 0x2, 0xa6, 0x75, 0x17, 0xc0, 0xa9, 0xb, 0x2b, 0x3e, 0x2d, 0xa3, 0xd, 0xff, 0x34, 0x39, 0x93, 0xdb, 0xec, 0x95, 0x97}} },
{ (uint64_t)20000ull, {{0x77, 0xbf, 0xb5, 0x37, 0xac, 0xa, 0xbc, 0x41, 0xaa, 0x21, 0xd0, 0xec, 0xd9, 0x18, 0x13, 0x34, 0xd8, 0x6b, 0xa7, 0x86, 0x5a, 0x94, 0x47, 0xf5, 0xc1, 0x58, 0x9a, 0x81, 0xd7, 0xef, 0xb3, 0xbb}} },
{ (uint64_t)30000ull, {{0x35, 0xf4, 0x5, 0xa9, 0x5f, 0x75, 0x19, 0x2a, 0xe9, 0xc0, 0xd4, 0xf5, 0x88, 0x84, 0x47, 0x14, 0xf6, 0x85, 0x1b, 0x97, 0xce, 0xbd, 0x9f, 0x7c, 0x2, 0xc5, 0xdd, 0xd7, 0xbf, 0x58, 0xff, 0x31}} },
{ (uint64_t)40000ull, {{0x77, 0x55, 0xbb, 0x3f, 0x38, 0x7c, 0x21, 0xb8, 0xa0, 0xf4, 0x48, 0x1f, 0xbf, 0xa8, 0x8a, 0xbe, 0xee, 0xce, 0xc7, 0x56, 0x53, 0xfc, 0xa1, 0x89, 0x58, 0x39, 0xc1, 0xba, 0x6, 0x47, 0x9f, 0x96}} },
{ (uint64_t)50000ull, {{0x8b, 0x7e, 0x84, 0xa3, 0x37, 0xb7, 0xb9, 0xcd, 0x5d, 0xb3, 0x63, 0x33, 0x8, 0xad, 0x51, 0x86, 0xa3, 0x59, 0xd, 0xff, 0xb8, 0x23, 0x1e, 0x2f, 0x31, 0xfd, 0x20, 0x42, 0x54, 0x9f, 0xfb, 0xe2}} },
{ (uint64_t)60000ull, {{0xef, 0xfd, 0xa6, 0x25, 0x15, 0xea, 0xb1, 0xbc, 0x1e, 0xbd, 0x74, 0x92, 0x94, 0x9b, 0x1, 0x22, 0xc3, 0x9f, 0x71, 0xa, 0x65, 0x16, 0xec, 0x66, 0x8c, 0x37, 0x61, 0xe6, 0xcc, 0x36, 0x1f, 0x25}} },
{ (uint64_t)70000ull, {{0x16, 0xba, 0x89, 00, 0xf3, 0x6f, 0xf, 0x6c, 0x46, 0x1c, 0xb, 0xe7, 0x64, 0xae, 0xee, 0x48, 0x86, 0x6, 0xb0, 0x53, 0xed, 0xdc, 0x10, 0xb5, 0x9a, 0x3e, 0xde, 0xcd, 0x23, 0xd4, 0x4f, 0xc0}} },
{ (uint64_t)80000ull, {{0x4d, 0xd4, 0x70, 0x3b, 0x7b, 0x7f, 0xcf, 0xe7, 0x2a, 0x2e, 0x4f, 0x31, 0xa4, 0x34, 0x17, 0xf9, 0xc0, 0xda, 0x64, 0x2f, 0xd0, 0xa9, 0x29, 0xb8, 0xf5, 0xed, 0xd8, 0x3, 0x7f, 0x93, 0xc5, 0xb3}} },
{ (uint64_t)90000ull, {{0x8e, 0xfc, 0x3, 0x20, 0x40, 0xbd, 0x90, 0x41, 0xda, 0x3d, 0xb0, 0x9b, 0xa1, 0x3d, 0xa2, 0xa5, 0xd1, 0xb8, 0x12, 0x3, 0xa, 0x5a, 0x36, 0x7c, 0x58, 0x94, 0xbd, 0x54, 0x11, 0x9, 0xe7, 0x30}} },
{ (uint64_t)100000ull, {{0xbd, 0x2e, 0xb1, 0x97, 0x83, 0x57, 0x1c, 0xf2, 0x22, 0x2c, 0x81, 0xb, 0x69, 0xf, 0xc7, 0x66, 0x64, 0x57, 0xae, 0x20, 0x92, 0x5b, 0x90, 0x5, 0xce, 0xe6, 0x1d, 0xf2, 0x66, 0x6f, 0xdc, 0xb7}} },
{ (uint64_t)200000ull, {{0x83, 0xd4, 0xcd, 0xdd, 0xc1, 0x44, 0x87, 0x32, 0xf2, 0x97, 0x7c, 0x41, 0xaa, 0xa7, 0x1f, 0xe6, 0xde, 0x9c, 0x17, 0x6d, 0xa8, 0x99, 0xee, 0xbf, 0xfc, 0x1b, 0xb, 0xa9, 0xea, 0x92, 0x97, 0x90}} },
{ (uint64_t)300000ull, {{0xcc, 0xc0, 0x6b, 0x44, 0xc3, 0x1, 0x38, 0x6, 0x30, 0x45, 0xed, 0x1, 0xd2, 0x45, 0xd8, 0x14, 0x3, 0xb6, 0x36, 0x52, 0xeb, 0xc4, 0xf9, 0x96, 0x7f, 0xd, 0x7f, 0x38, 0x69, 0x7f, 0x46, 0x16}} },
{ (uint64_t)400000ull, {{0x1b, 0xbf, 0xe7, 0xe, 0xca, 0xf1, 0xdd, 0xd7, 0xf1, 0x2, 0x36, 0xf6, 0x8a, 0x41, 00, 0xb, 0x5d, 0xab, 0x2d, 0x47, 0x5c, 0xb9, 0x2f, 0x62, 0xc2, 0xd6, 0x84, 0xcf, 0x57, 0x69, 0xfb, 0x84}} },
{ (uint64_t)500000ull, {{0xf1, 0xb1, 0xcd, 0xaa, 0x78, 0x14, 0x95, 0x36, 0xf, 0x53, 0x31, 0x81, 0xaa, 0x58, 0xc8, 0xbd, 0xae, 0x6a, 0x77, 0x98, 0xd0, 0x2d, 0xab, 0x6d, 0x56, 0x26, 0x81, 0x27, 0x67, 0x9, 0xe7, 0x1}} },
{ (uint64_t)600000ull, {{0xd5, 0x26, 0x7d, 0x60, 0xd4, 0xfe, 0x9b, 0xc5, 0xfe, 0xfa, 0x7d, 0x3f, 0xe0, 0x7c, 0xd1, 0xfa, 0xd4, 0x55, 0x73, 0xd5, 0xae, 0x19, 0x10, 0xda, 0x7, 0x3e, 0x6d, 0x2d, 0xf9, 0xe2, 0x4, 0x39}} },
{ (uint64_t)700000ull, {{0xb, 0x58, 0x11, 0x25, 0xc2, 0xc4, 0x83, 0xc9, 0xa3, 0xd8, 0xbc, 0x8, 0x32, 0x2f, 0x26, 0xaa, 0x1f, 0xc5, 0xe, 0x41, 0x53, 0x2c, 0x1b, 0x9d, 0xf6, 0x26, 0xb0, 0x9, 0xd7, 0x88, 0x67, 0xcf}} },
{ (uint64_t)800000ull, {{0xf5, 0xb3, 0xd1, 0x8f, 0x66, 0xd0, 0xf9, 0x17, 0x5c, 0x30, 0x83, 0xb5, 0xf8, 0x7, 0x8e, 0xaf, 0xa8, 0x9e, 0xf8, 0x1d, 0xe7, 0x15, 0x8, 0xbc, 0x25, 0x1f, 0x5c, 0x5f, 0xe7, 0x25, 0x2e, 0x6}} },
{ (uint64_t)900000ull, {{0x1, 0xde, 0x40, 0x2c, 0x4b, 00, 0x43, 0x4, 0x2e, 0xae, 0x9e, 0xde, 0xa1, 0x49, 0x2b, 0x9d, 0x82, 0xb7, 0xbc, 0x36, 0x68, 0xe9, 0xb5, 0x84, 0xb0, 0x31, 0x3d, 0x44, 0x50, 0x53, 0x40, 0x74}} },
{ (uint64_t)1000000ull, {{0x53, 0x4b, 0x85, 0xc7, 0x89, 0x3f, 0x66, 0xf0, 0x26, 0xb6, 0x5e, 0xd7, 0xe7, 0xa4, 0xb8, 0xc9, 0xf4, 0xb, 0xe3, 0x1b, 0xcd, 0xa, 0x3d, 0xcd, 0x27, 0xc4, 0x71, 0x2, 0x56, 0x51, 0x65, 0x3}} },
{ (uint64_t)2000000ull, {{0xcd, 0xb5, 0xda, 0xfa, 0x53, 0x10, 0xf5, 0x26, 0x2f, 0xfc, 0x9, 0x26, 0xd0, 0xdf, 0x6e, 0xeb, 0xee, 0x2d, 0x52, 0xa9, 0x8d, 0xc6, 0x9f, 0xd, 0xc5, 0xe4, 0xeb, 0xf0, 0xc1, 0xa8, 0x77, 0x2e}} },
{ (uint64_t)3000000ull, {{0x9e, 0x75, 0x63, 0xf0, 0x33, 0x59, 0xea, 0x31, 0xe2, 0x91, 0xe7, 0xf0, 0xb8, 0x74, 0x17, 0xbc, 0xf5, 0xb2, 0x34, 0xee, 0x8b, 0x7e, 0x5b, 0x4, 0x41, 0x73, 0xbf, 00, 0x46, 0x86, 0x7c, 0x57}} },
{ (uint64_t)4000000ull, {{0xfd, 0x2a, 0xeb, 0xd, 0x5e, 0xe5, 0x3b, 0x77, 0xf2, 0xb1, 0xe3, 0xac, 0x75, 0x2d, 0x19, 0x38, 0x9f, 0xc5, 0xba, 0xa0, 0xf8, 0xd7, 0x64, 0x48, 0xa5, 0x9f, 0x99, 0x85, 0xa4, 0x8d, 0xa, 0x25}} },
{ (uint64_t)5000000ull, {{0xc0, 0xbe, 0x4f, 0xb8, 0x77, 0xb9, 0xce, 0x50, 0x87, 0x71, 0x32, 0x3b, 0xcf, 0x1f, 0xb9, 0x48, 0x47, 0x10, 0xee, 0x23, 0x2, 00, 0x6, 0xc3, 0xe8, 0xca, 0xac, 0x6e, 0x4f, 0x2, 0xfa, 0xbf}} },
{ (uint64_t)6000000ull, {{0xfc, 0x44, 0x5c, 0xa3, 0x84, 0xf3, 0x3e, 0x55, 0x8d, 0xc1, 0x56, 0x44, 0x9d, 0x3f, 0xba, 0x6a, 0xfd, 0x54, 0xc3, 0x42, 0xe6, 0x35, 0x11, 0xf, 0xe7, 0x9c, 0x16, 0xc7, 0x17, 0xf7, 0xd4, 0xf7}} },
{ (uint64_t)7000000ull, {{0xd8, 0x9, 0x2b, 0x8d, 0x45, 0xdb, 0x54, 0xa5, 0x6d, 0x64, 0xe8, 0x9, 0x4a, 0x6, 0x22, 0xe2, 0x6e, 0x8a, 0x2e, 0xec, 0xb9, 0x3, 0xb2, 0xe1, 0xf7, 0x5a, 0x83, 0x7b, 0x3a, 0xd8, 0x55, 0x4a}} },
{ (uint64_t)8000000ull, {{0x10, 0x4, 0x5c, 0x91, 0xdb, 0xad, 0x8a, 0x6a, 0x81, 0x62, 0x4a, 0xe0, 0xcf, 0x20, 0x5d, 0xb9, 0x97, 0x3e, 0xe8, 0x42, 0x3e, 0x97, 0xaf, 0x58, 0xa6, 0x1c, 0xfa, 0x7a, 0x78, 0x66, 0xf4, 0x1}} },
{ (uint64_t)9000000ull, {{0x11, 0x5c, 0x20, 0x9e, 0xe1, 0xde, 0xf3, 0x10, 0xce, 0xc9, 0xa6, 0xd1, 0x6c, 0xe6, 0x27, 0xec, 0xbd, 0xb9, 0xff, 0x2c, 0x23, 0x9, 0x3c, 0x24, 0xc8, 0x6c, 0x1b, 0xf2, 0x50, 0xd4, 0xb5, 0x85}} },
{ (uint64_t)10000000ull, {{0x2f, 0x99, 0xd9, 0x74, 0x44, 0x18, 0x66, 0x9, 0x49, 0xba, 0x43, 0x35, 0x61, 0xc6, 0x5, 0xb6, 0xf7, 0xbe, 0x8f, 0x82, 0xa, 0x93, 0xcb, 0x2a, 0xed, 0xa9, 0x7c, 0x87, 0x32, 0x92, 0x56, 0x49}} },
{ (uint64_t)20000000ull, {{0xc6, 0x77, 0x1f, 0xab, 0x14, 0xb, 0x75, 0xf4, 0xef, 0xd0, 0x97, 0xfc, 0xe1, 0x82, 0x6b, 0x80, 0xba, 0xe3, 0x16, 0xbc, 0xec, 0x28, 0x86, 0x9b, 0x3a, 0x1b, 0xf1, 0xbc, 0x6e, 0x4d, 0x20, 0x43}} },
{ (uint64_t)30000000ull, {{0xa1, 0xe9, 0xed, 0x3e, 0xf6, 0x5a, 0x9d, 0x52, 0x6c, 0xc2, 0x62, 0x5, 0x88, 0x12, 0x1, 0xd8, 0xa8, 0xf2, 0xc4, 0x40, 0x9f, 0xa3, 0x64, 0x10, 0x72, 0x96, 0xb9, 0xf9, 0x6a, 0x61, 0xb3, 0x58}} },
{ (uint64_t)40000000ull, {{0xb5, 0x31, 0x2d, 0xc7, 0x72, 0x94, 0xab, 0x9b, 0xc8, 0xbf, 0xd1, 0x39, 0x1e, 0x9a, 0xca, 0x92, 0x45, 0xe2, 0x28, 0xf7, 0x4b, 0x49, 0x74, 0xfc, 0x29, 0xad, 0x1c, 0x31, 0xcb, 0xe3, 0xe6, 0xa3}} },
{ (uint64_t)50000000ull, {{0xb8, 0xab, 0xc9, 0xff, 0xf6, 0x84, 0x1d, 0x2e, 0xa0, 0x13, 0x5a, 0x21, 0x72, 0xd3, 0xa7, 0xb, 0xfc, 0x2b, 0x70, 0x22, 0x8, 0xcd, 0x4a, 0x43, 0xc6, 0x30, 0xbe, 0xb1, 0xb8, 0xa0, 0x32, 0x8b}} },
{ (uint64_t)60000000ull, {{0x63, 0x90, 0xe1, 0xdb, 0x81, 0xb0, 0xea, 0x5c, 0xe2, 0x73, 0x94, 0x14, 0xe5, 0x2b, 0x7, 0x98, 0xd8, 0x2e, 0xb8, 0xe9, 0xae, 0xc5, 0x6d, 0xfe, 0x7e, 0x2c, 0x64, 0x11, 0xab, 0x79, 0x41, 0x87}} },
{ (uint64_t)70000000ull, {{0x7e, 0x51, 0xaf, 0xee, 0x5b, 0xc9, 0x71, 0x52, 0x9d, 0x64, 0x4d, 0xcd, 0x7f, 0x2a, 0x2a, 0xb0, 0x26, 0x69, 0xce, 0x2c, 0xb5, 0x7, 0xa6, 0x2d, 0xfc, 0x93, 0x17, 0x6c, 0xb6, 0xdf, 0x41, 0x38}} },
{ (uint64_t)80000000ull, {{0xf3, 0x7b, 0x94, 0x6b, 0x8b, 0x24, 0x88, 0xeb, 0xee, 0x1c, 0x6, 0xc1, 0x27, 0xfb, 0xe5, 0xfa, 0x5e, 0xfd, 0x62, 0x36, 0x9d, 0xd5, 0xaa, 0xda, 0xed, 0xd8, 0x88, 0x50, 0x1d, 0x3b, 0x7e, 0x3b}} },
{ (uint64_t)90000000ull, {{0x46, 0xcb, 0x76, 0x57, 0xf6, 0x1c, 0x83, 0x7c, 0xec, 0x80, 0x74, 0xbb, 0xb0, 0xf5, 0x2e, 0x7f, 0xc5, 0x9a, 0xd, 0x94, 0xe0, 0x17, 00, 0x9a, 0xbe, 0x25, 0x65, 0x2e, 0x4a, 0xd2, 0xe5, 0x3d}} },
{ (uint64_t)100000000ull, {{0x66, 0x7b, 0x8e, 0x6f, 0x6a, 0x4b, 0x91, 0x89, 0x76, 0xd9, 0x73, 0x5a, 0x43, 0x36, 0x7d, 0xc7, 0x59, 0x2c, 0x87, 0xd0, 0xa1, 0xf8, 0x15, 0xc6, 0xe8, 0x7d, 0xf1, 0x1a, 0x13, 0x50, 0x9f, 0xb2}} },
{ (uint64_t)200000000ull, {{0x3b, 0xcb, 0x51, 0x48, 0x1, 0x64, 0x1b, 0x62, 0x55, 0x93, 0x8c, 0xc5, 0x3, 0x76, 0x2d, 0x35, 0xce, 0x6, 0xd7, 0x5f, 0xe9, 0x50, 0x95, 0x9a, 0x1a, 0xab, 0x21, 0x4b, 0x50, 0x9b, 0x10, 0xb}} },
{ (uint64_t)300000000ull, {{0xa5, 0x92, 0x6f, 0x3, 0x1e, 0x6b, 0x15, 0xeb, 0x86, 0x23, 0x51, 0x8, 0xab, 0xb1, 0xaf, 0x90, 0xc5, 0xb1, 0x62, 0xc3, 0x99, 0x8c, 0x8b, 0xbb, 0x3f, 0xfb, 0xb0, 0x72, 0x9d, 0xa9, 0x45, 0x7b}} },
{ (uint64_t)400000000ull, {{0xfe, 0x35, 0xb6, 0x99, 0x44, 0x41, 0xe, 0xaf, 0x81, 0x5b, 0xdc, 0xd0, 0xa4, 0xd7, 0x1e, 0xf9, 0xfc, 0x66, 0x86, 0x48, 0xad, 0x43, 0x74, 0x3b, 0x3, 0x5a, 0xed, 0x2c, 0x17, 0xc1, 0x38, 0x7a}} },
{ (uint64_t)500000000ull, {{0x22, 0x22, 0xd6, 0x70, 0xb8, 0x7d, 0x9b, 0x47, 0xb8, 0xb9, 0x5c, 0x8c, 0x39, 0x7b, 0xc5, 0x2e, 0x2b, 0x46, 0xa6, 0x48, 0xb0, 0x2, 0xa0, 0x48, 0x5a, 0x37, 0x5c, 0xd8, 0x1f, 0x4a, 0x54, 0x5f}} },
{ (uint64_t)600000000ull, {{0xd3, 0x23, 0x8a, 0x4a, 0x8b, 0x71, 0xab, 0x46, 0xd1, 0x53, 0x4, 0xac, 0xfa, 0x2f, 0x40, 0xbf, 0x5e, 0xa6, 0x3b, 0x3d, 0x86, 0x4a, 0x79, 0xfa, 0x84, 0x25, 0xd2, 0x65, 0x5a, 0xe7, 0x7, 0x6f}} },
{ (uint64_t)700000000ull, {{0xa8, 0xff, 0x28, 0x3f, 0xcf, 0xf0, 0x53, 0xd3, 0x44, 0xc8, 0xf7, 0x56, 0x4f, 0x40, 0x24, 0xb6, 0x6b, 0xfa, 0x45, 0x9f, 0x47, 0x6f, 0xd, 0x73, 0xc, 0x91, 0x39, 0x90, 0x8b, 0x2d, 0x64, 0x7e}} },
{ (uint64_t)800000000ull, {{0xf2, 0xda, 0xf8, 0x88, 0xc4, 0x46, 0x57, 0x1, 0xc0, 0xe6, 0x1e, 0x12, 0xc3, 0xfb, 0xd4, 0xea, 0x79, 0xc7, 0xec, 0xb4, 0xf0, 0xc4, 0xb1, 0x54, 0xc5, 0x1a, 0x24, 0xd1, 0xe9, 0x21, 0x28, 0xba}} },
{ (uint64_t)900000000ull, {{0x11, 0x6a, 0xe5, 0xd2, 0x9c, 0xec, 0x72, 0xaa, 0xc5, 0x57, 0xcb, 0x14, 0xe2, 0xcd, 0xd5, 0x53, 0xe5, 0x88, 0xff, 0x8b, 0x81, 0x78, 0x26, 0x1, 0x99, 0xc4, 0xc, 0xae, 0xa2, 0x12, 0xcb, 0x63}} },
{ (uint64_t)1000000000ull, {{0x8c, 0xe6, 0x48, 0x33, 0xce, 0xc9, 00, 0xcb, 0x6d, 0x5a, 0xc4, 0x6f, 0xc0, 0x23, 0x7d, 0x8f, 0x24, 0x39, 0xc3, 0xdf, 0xa2, 0x38, 0xba, 0xf9, 0xcc, 0x94, 0x16, 0x6a, 0xd2, 0xe8, 0x98, 0x87}} },
{ (uint64_t)2000000000ull, {{0x37, 0x8d, 0x3c, 0x5d, 0xbb, 0xa4, 0x82, 0x3d, 0x33, 0x12, 0xbb, 0x61, 0xfc, 0x6, 0x75, 0xa1, 0xbb, 0x39, 0x89, 0xf3, 0x97, 0x1, 0xeb, 0xd, 0x5c, 0xe4, 0xde, 0x5b, 0xd, 0x90, 0x74, 0x72}} },
{ (uint64_t)3000000000ull, {{0x7f, 0xa2, 0xd0, 0xa5, 0x99, 0xe7, 0x97, 0x2e, 0x74, 0xcb, 0x75, 0xf9, 0x8a, 0xf4, 0x84, 0xfc, 0x85, 0x19, 0xcb, 0x7e, 0x25, 0xb9, 0x84, 0xa7, 0x6d, 0x8b, 0xc2, 0xba, 0x8d, 0xaf, 0xde, 0xd8}} },
{ (uint64_t)4000000000ull, {{0xda, 0x3a, 0xcb, 00, 0xab, 0x2d, 0x8d, 0xcc, 0xac, 0xec, 0x8f, 0x77, 0x59, 0x21, 0xc4, 0xe, 0x26, 0xb1, 0xff, 0xbe, 0xca, 0x9e, 0xb7, 0xe6, 0x57, 0x25, 0x6f, 0x59, 0x68, 0xf2, 0x34, 0x1c}} },
{ (uint64_t)5000000000ull, {{0x34, 0x6, 0xd7, 0x9a, 0x50, 0xd8, 0x14, 0xa9, 0xcc, 0xed, 0x3b, 0x24, 0x4, 0xed, 0x3e, 0x1b, 0x8d, 0xa6, 0x21, 0x98, 0x8c, 0x43, 0xb1, 0x93, 0x69, 0x42, 0xf4, 0x94, 0xa, 0xc5, 0xbf, 0x6a}} },
{ (uint64_t)6000000000ull, {{0xf8, 0x3e, 0xe8, 0xc1, 0x62, 0xfc, 0x52, 0xa0, 0x8, 0x9f, 0x46, 0xe8, 0x29, 0xc2, 0xea, 0xf6, 0xa1, 0x9f, 0xd5, 0x96, 0xcd, 0x12, 0xb3, 0xe8, 0x19, 0xd5, 0x67, 0x69, 0x44, 0xf, 0x7b, 0x4e}} },
{ (uint64_t)7000000000ull, {{0x8c, 0x72, 0x7d, 0x24, 0x57, 0xf3, 0x4b, 0x2f, 0xdb, 0x6a, 0xdf, 0x69, 0x1a, 0xb3, 0x5f, 0xaa, 0xe4, 0xff, 0x23, 0x4c, 0x28, 0xb4, 0x4e, 0x9f, 0xd3, 0x71, 0x8e, 0xef, 0xec, 0x41, 0x75, 0x80}} },
{ (uint64_t)8000000000ull, {{0x4a, 0x2e, 0x2f, 0x76, 0xe3, 0x5d, 0xcb, 0xa8, 0x97, 0xa3, 0xae, 0x72, 0xc4, 0x27, 0xd, 0x9c, 0x13, 0x17, 0x14, 0xed, 0x19, 0x1b, 0x55, 0x5c, 0x5e, 0x1, 0xe4, 0x75, 0x7c, 0xba, 0xe7, 0x2c}} },
{ (uint64_t)9000000000ull, {{0x3f, 0x9f, 0xc, 0x4, 0xc0, 0xb9, 0xec, 0x9b, 0x4d, 0x11, 0x7c, 0x5f, 0xc9, 0xf1, 0x8a, 0x20, 0xf2, 0xb3, 0xfa, 0xcc, 0xa4, 0xc8, 0xae, 0x41, 0xaf, 0x7c, 0x8, 0xe9, 0xe0, 0xef, 0xb9, 0x81}} },
{ (uint64_t)10000000000ull, {{0x97, 0xc9, 0x2a, 0x29, 0x1, 0x5e, 0xcb, 0x49, 0xf8, 0x9, 0x5, 0x45, 0xe0, 0x1f, 0xf9, 0x78, 0x6c, 0xae, 0x40, 0x57, 0x73, 0x47, 0x61, 0x18, 0x24, 0xf4, 0xb6, 0x59, 0x9f, 0xf5, 0xd3, 0x64}} },
{ (uint64_t)20000000000ull, {{0x9, 0xba, 0xed, 0x9a, 0x3c, 0x44, 0xb2, 0x22, 0x85, 0xa0, 0xae, 0xa4, 0x14, 0x8c, 0xa7, 0xde, 0x9b, 0xea, 0x96, 0x3c, 0xf6, 0x96, 0x23, 0xb6, 0x83, 0x44, 0x5c, 0xa, 0x10, 0xa5, 0x86, 0x77}} },
{ (uint64_t)30000000000ull, {{0x45, 0xac, 0xaf, 0x1d, 0xe2, 0x89, 0x6d, 0xe8, 0x72, 0x84, 0xff, 0xed, 0x57, 0x8b, 0x77, 0x14, 0xf5, 0x18, 0xa6, 0x18, 0xe2, 0xae, 0x6f, 0x90, 0xae, 0x4f, 0x70, 0x13, 0xa2, 0x8e, 0x99, 0xe0}} },
{ (uint64_t)40000000000ull, {{0x8, 0xb8, 0x47, 0x36, 0x42, 0x24, 0xe2, 0x9c, 0xe3, 0x36, 0x63, 0x93, 0xc2, 0xe1, 0x1e, 0xfc, 0x75, 0x55, 0xde, 0xe1, 0xa0, 0x5f, 0x91, 0xa7, 0x2e, 0x61, 0x11, 0x76, 0x84, 0xdd, 0xbe, 0x29}} },
{ (uint64_t)50000000000ull, {{0x6c, 0x8e, 0xe, 0x4a, 0x63, 0x4f, 0x85, 0x9a, 0x31, 0xab, 0x2f, 0x7a, 0x78, 0xc0, 0xc4, 0xa5, 0x93, 0x8c, 0xb7, 0x7f, 0x3, 0x35, 0x50, 0xa4, 0x7d, 0x7e, 0x31, 0x81, 0xb6, 0xb2, 0x6e, 0xc0}} },
{ (uint64_t)60000000000ull, {{0x66, 0xc2, 0xa0, 0x9, 0x65, 0xf9, 0xbf, 0xcb, 0xb1, 0x1e, 0xa0, 0x3c, 0xf1, 0xd6, 0x31, 0xb0, 0xe, 0x8a, 0x1e, 0xf7, 0xa6, 0xb, 0x1b, 0xe4, 0xa5, 0xac, 0x9, 0x23, 0xb, 0xf8, 0x17, 0x3f}} },
{ (uint64_t)70000000000ull, {{0x63, 0x51, 0xd7, 0x74, 0xc0, 0x2c, 0x5a, 0x9d, 0xee, 0xcf, 0xdb, 0xab, 0x70, 0x96, 0x68, 0x59, 0x8c, 0x47, 0xe4, 0xb1, 0x78, 0x2c, 0xe5, 0xae, 0x31, 0x6a, 0xf7, 0x40, 0xa6, 0x6f, 0x7e, 0x30}} },
{ (uint64_t)80000000000ull, {{0x5a, 0xcc, 0xfd, 0x16, 0x22, 0x79, 0xa5, 0x1c, 0x8b, 0x3b, 0xd5, 0xd3, 0x67, 0x9e, 0x91, 0x89, 0x67, 0xa2, 0x64, 0xea, 0x6, 0x3d, 0x37, 0xdf, 0xf5, 0xe3, 0x45, 0x7e, 0xc3, 0x7, 0xd4, 0x57}} },
{ (uint64_t)90000000000ull, {{0xb7, 0x47, 0xfc, 0x1, 0xc6, 0xf0, 0xc7, 0x49, 0x67, 0x3a, 0x29, 0x10, 0x25, 0xc, 0x2e, 0x23, 0xcb, 0x38, 0x27, 0x4d, 0x63, 0xb4, 0x2f, 0x52, 0x1b, 0x84, 0x63, 0x56, 0xe4, 0x13, 0x61, 0x8f}} },
{ (uint64_t)100000000000ull, {{0x9, 0x42, 0x84, 0x3d, 0x6f, 0x69, 0xe1, 0xcf, 0x3d, 0x99, 0xc9, 0x9f, 0xc, 0x97, 0xc0, 0xe6, 0xe5, 0x78, 0x93, 0x5a, 0xf6, 0xa8, 0xbd, 0xb8, 0xf8, 0x1d, 0x5b, 0x90, 0xbd, 0xe7, 0xcc, 0x10}} },
{ (uint64_t)200000000000ull, {{0x56, 0x4c, 0x64, 0xea, 0x50, 0xe4, 0xbd, 0x20, 0xdb, 0x58, 0x5d, 0xb5, 0x87, 0xb1, 0xf7, 0x64, 0xa2, 0x62, 0xd8, 0x46, 0xa6, 0xb0, 0xa2, 0x4b, 0x43, 0x27, 0x60, 0xd2, 0xf9, 0xde, 0x66, 0x5b}} },
{ (uint64_t)300000000000ull, {{0xac, 0x65, 0x83, 0x41, 0x5b, 0xd6, 0x4c, 0x3, 0x35, 0x97, 0xf9, 0x28, 0xa4, 0xb5, 0xd4, 0xf4, 0x78, 0x9e, 0xa8, 0xb2, 0x87, 0x82, 0x73, 0x89, 0xa8, 0x1e, 0xb6, 0x62, 0x9e, 0xc5, 0xb8, 0x50}} },
{ (uint64_t)400000000000ull, {{0x52, 0xf4, 0x9d, 0x89, 0xcf, 0x74, 0x13, 0x2f, 0xc7, 0x43, 0x2e, 0x6a, 0x6b, 0xef, 0xcf, 0xf3, 0xfd, 0x13, 0xd6, 0x3b, 0x51, 0x60, 0xab, 0x1c, 0xe6, 0x4a, 0xb0, 0xd1, 0x21, 0xcd, 0xa9, 0x9a}} },
{ (uint64_t)500000000000ull, {{0xe9, 0xaa, 0x7c, 0x81, 0xcd, 0xb5, 0xb3, 0x14, 0x8f, 0xb7, 0x62, 0x80, 0x63, 0xcd, 0x7a, 0x7, 0xd1, 0xad, 0xd1, 0x64, 0x3c, 0xed, 0xd3, 0xfa, 0x34, 0x47, 0x9d, 0x85, 0x9c, 0xc5, 0x62, 0x65}} },
{ (uint64_t)600000000000ull, {{0x98, 0x27, 0xae, 0x31, 0xe5, 0xc2, 0xa7, 0x78, 0x39, 0xf6, 0xb, 0x83, 0xab, 0x45, 0x78, 0xe2, 0xa0, 0x1e, 0xfa, 0x4b, 0x3b, 0x14, 0xcc, 0x72, 0x73, 0x14, 0xff, 0xd7, 0x15, 0x53, 0x63, 0xbf}} },
{ (uint64_t)700000000000ull, {{0x72, 0x91, 0x6a, 0x79, 0x27, 0xff, 0x13, 0x24, 0xd4, 0x98, 0x40, 0xec, 0xc0, 0x98, 0x68, 0xb8, 0xf3, 0x15, 0xe4, 0xf1, 0xf6, 0xd4, 0x45, 0x8d, 0x37, 0x5e, 0xc7, 0x45, 0xfc, 0x2e, 0x63, 0x53}} },
{ (uint64_t)800000000000ull, {{0x66, 0x76, 0xe0, 0x4, 0xf, 0xa4, 0xb8, 0x22, 0x9c, 0x61, 0x69, 0xc, 0x71, 0x32, 0x22, 0xcf, 0x3d, 0x37, 0xb9, 0x49, 0x3b, 0x49, 0x6, 0x80, 0xbb, 0x48, 0xd8, 0xd5, 0x1a, 0xde, 0x95, 0xf2}} },
{ (uint64_t)900000000000ull, {{0x41, 0x54, 0xb3, 0x46, 0x5a, 0x43, 0x72, 0x67, 0x1e, 0xa9, 0xe0, 0x64, 0xa7, 0xca, 0xa6, 0x6e, 0x14, 0xb4, 0x98, 0x6a, 0x46, 0x68, 0x91, 0x8a, 0xfa, 0x57, 0x9b, 0xf1, 0xed, 0x25, 0x6, 0xdd}} },
{ (uint64_t)1000000000000ull, {{0xbb, 0x6f, 0x70, 0x62, 0xca, 0x30, 0x6d, 0x67, 0x2a, 0x73, 0xe, 0x2a, 0x2f, 0x21, 0x9b, 0xdb, 0xe4, 0xc, 0x9f, 0xb3, 0xfe, 0x4d, 0x60, 0x13, 0x69, 0x2a, 0xf9, 0x3c, 0xdb, 0x2e, 0xc, 0xd1}} },
{ (uint64_t)2000000000000ull, {{0xbc, 0xe, 0xae, 0x5b, 0x9c, 0x6a, 0xd6, 0x38, 0x7a, 0x41, 0x19, 0x3c, 0x46, 0xf3, 0xc1, 0xd0, 0x71, 0x6d, 0x77, 0xd6, 0x4e, 0x22, 0xb2, 0xe0, 0x7b, 0x4b, 0xce, 0x75, 0x67, 0x65, 0xa2, 0xb}} },
{ (uint64_t)3000000000000ull, {{0x10, 0xc, 0x6f, 0x13, 0x42, 0xb7, 0x1b, 0x73, 0xed, 0xdd, 0xc5, 0x49, 0x2b, 0xe9, 0x23, 0x18, 0x2f, 00, 0xa6, 0x83, 0x48, 0x8e, 0xc3, 0xa2, 0xa1, 0xc7, 0xa9, 0x49, 0xcb, 0xe5, 0x77, 0x68}} },
{ (uint64_t)4000000000000ull, {{0x41, 0x9f, 0x7c, 0x94, 0x91, 0x4, 0x34, 0xf, 0xd3, 0xce, 0x85, 0x94, 0x8d, 0x2e, 0xf9, 0xf0, 0xdd, 0x4b, 0xb3, 0xd9, 0x2f, 0x5a, 0x78, 0x2c, 0x5f, 0x78, 0x4, 0xb7, 0x52, 0x9a, 0x13, 0xc6}} },
{ (uint64_t)5000000000000ull, {{0x40, 0x65, 0x34, 0x98, 0xbe, 0xa0, 0x22, 0xe3, 0x36, 0x5a, 0x3, 0xe5, 0x75, 0x25, 0xba, 0x65, 0x96, 0x53, 0x76, 0x24, 0x4f, 0xff, 0x10, 0x73, 0xe, 0xd9, 0x7a, 0x73, 0xb7, 0x53, 0x1, 0x91}} },
{ (uint64_t)6000000000000ull, {{0xdb, 0x1c, 0x7c, 0xf6, 0x8, 0x91, 0xf9, 0x65, 0xeb, 0xa9, 0xc6, 0x2, 0x24, 00, 0x63, 0xe, 00, 0x47, 0x95, 0x34, 0xe6, 0xf5, 0xb5, 0x33, 0xdc, 0xfc, 0x83, 0x19, 0x38, 0x52, 0x2c, 0x78}} },
{ (uint64_t)7000000000000ull, {{0x59, 0xa0, 0x3a, 0x31, 0x53, 0xa9, 0x94, 0xd7, 0x23, 0x27, 0xe4, 0xd9, 0x24, 0x21, 0xd3, 0xe3, 0x29, 0x1b, 0x1f, 0xa1, 0xb2, 0x40, 0xde, 0x44, 0xb9, 0x2d, 0x7f, 0x62, 0xec, 0x1, 0x28, 0xf1}} },
{ (uint64_t)8000000000000ull, {{0xb2, 0x80, 0xb9, 0x3b, 0x1e, 0x43, 0x88, 00, 0x73, 0xea, 0x4a, 0xa0, 0xef, 0x11, 0x4, 0xf8, 0x24, 0xbd, 0x12, 0x7a, 0x4a, 0x3d, 0xa2, 0x13, 0x92, 0x65, 0xf, 0xe8, 0xc6, 0x55, 0xb6, 0xc5}} },
{ (uint64_t)9000000000000ull, {{0xda, 0xf0, 0xd3, 0xe9, 0x32, 0x17, 0xd8, 0xe9, 0x5a, 0xbf, 0xdd, 0xf1, 0x3b, 0x7f, 0xd4, 0x8e, 0x34, 0x47, 0xad, 0x9, 0x23, 0x26, 0xb8, 0x99, 0xed, 0x58, 0x1f, 0xd5, 0xf8, 0x6, 0xc5, 0x6}} },
{ (uint64_t)10000000000000ull, {{0x16, 0x3d, 0xd6, 0x82, 0xec, 0x97, 0x7c, 0xdd, 0xa5, 0x95, 0x31, 0xda, 0x3f, 0xfa, 0x72, 0x99, 0x8a, 0x6f, 0x88, 0x37, 0xab, 0xad, 0xc6, 0x36, 0xaa, 0xed, 0xc8, 0xbe, 0x19, 0xb2, 0xd7, 0xc7}} },
{ (uint64_t)20000000000000ull, {{0x2, 0xfa, 0x35, 0x3a, 0xa8, 0x4e, 0xa8, 0xc4, 0x4c, 0x80, 0x23, 0x6, 0x5d, 0x79, 0x41, 0x60, 0x6b, 0x1f, 0xa5, 0xc2, 0x64, 0xdc, 0xcf, 0x46, 0xdc, 0x64, 0x94, 0xeb, 0xe9, 0x60, 0x6f, 0x20}} },
{ (uint64_t)30000000000000ull, {{0x87, 0x5, 0xd, 0xab, 0xf5, 0xb2, 0x3e, 0x8b, 0x79, 0x81, 0x3f, 0x4e, 0xd7, 0x6a, 0xa4, 0xad, 0xd2, 0x25, 0xdd, 0x2a, 0x50, 0x89, 0xaf, 0x6, 0x7d, 0xa7, 0x7c, 0xcb, 0x6e, 0xc5, 0x59, 0x46}} },
{ (uint64_t)40000000000000ull, {{0xaa, 0xe6, 0xb2, 0xc8, 0xa2, 0x9e, 0x4d, 0xbc, 0x63, 0x76, 0xc1, 0x72, 0x5, 0xfb, 0x2, 0x85, 0xe7, 0xd7, 0xd3, 0x25, 0x32, 0x3c, 0xd5, 0x26, 0xf, 0x98, 0xad, 0xff, 0xf7, 0xd4, 0xd4, 0xfb}} },
{ (uint64_t)50000000000000ull, {{0x9d, 0x79, 0x28, 0x82, 0x12, 0xa1, 0xe2, 0x3c, 0x9, 0x9f, 0xb2, 0xd8, 0xf0, 0xd0, 0xdb, 0xd3, 0xc2, 0xec, 0xd7, 0x58, 0xb9, 0xe6, 0xb5, 0xb4, 0xf2, 0x90, 0x60, 0x7, 0x9f, 0x19, 0x66, 0x9f}} },
{ (uint64_t)60000000000000ull, {{0x18, 0x90, 0x10, 0x6f, 0x1b, 0x97, 0xbc, 0x2d, 0xa, 0xe3, 0x96, 0xe5, 0xe5, 0x5e, 0xbf, 0xcc, 0x8e, 0xf6, 0x91, 0x7f, 0xb1, 0x96, 0xcb, 0x2b, 0x1e, 0x80, 0x25, 0x5d, 0x54, 0xb6, 0x87, 0x10}} },
{ (uint64_t)70000000000000ull, {{0x57, 0xd3, 0x4e, 0xf7, 0x54, 0x3b, 0xe4, 0x7b, 0x7b, 0xf4, 0x97, 0xce, 0x4a, 0x17, 0x6e, 0x78, 0xc6, 0xd6, 0x5c, 0xd3, 0x27, 0xf6, 0x4b, 0xa7, 0x5c, 0x27, 0xd1, 0x57, 0xb3, 0x37, 0x12, 0x5d}} },
{ (uint64_t)80000000000000ull, {{0x5e, 0xcb, 0x10, 0x15, 0x4b, 0x96, 0xca, 0xb5, 0x5e, 0x9, 0x46, 0x83, 0xf8, 0xdb, 0xff, 0x7f, 0x56, 0x63, 0x5f, 0xa6, 0x64, 0x97, 0xee, 0x9e, 0x24, 0xe, 0x83, 0x63, 0x7c, 0x7c, 0x87, 0x72}} },
{ (uint64_t)90000000000000ull, {{0x42, 0x32, 0x69, 0x98, 0x51, 0x30, 0xf1, 0x66, 0x51, 0x6a, 0x5b, 0xa8, 0x61, 0x9, 0x6d, 0x72, 0xec, 0xcc, 0x67, 0xad, 0xab, 0xa4, 0x5e, 0xb3, 0x73, 0x9a, 0xe, 0xbc, 0x61, 0xa3, 0x20, 0xae}} },
{ (uint64_t)100000000000000ull, {{0xa8, 0xd1, 0x60, 0x95, 0x91, 0x49, 0x8f, 0xa7, 0xc2, 0x94, 0x27, 0xad, 0x89, 0x31, 0xaf, 0x36, 0xc5, 0x2d, 0xc9, 0x7b, 0x4a, 0x11, 0xe7, 0x47, 0xa9, 0x56, 0xc2, 0x8c, 0x42, 0x54, 0xcf, 0xd4}} },
{ (uint64_t)200000000000000ull, {{0x23, 0x14, 0x49, 00, 0xa8, 0x66, 0xe8, 0xc1, 0xbf, 0x40, 0x98, 0xda, 0xa9, 0x48, 0xb9, 0x86, 0xf3, 0x84, 0xe, 0x5a, 0x7d, 0x21, 0x5e, 0xf0, 0xd5, 0x64, 0xef, 0xd8, 0xbe, 0xc6, 0x83, 0x15}} },
{ (uint64_t)300000000000000ull, {{0x6a, 0x51, 0x47, 0x3c, 0x86, 0xed, 0xad, 0x53, 0x51, 0x4b, 0x3f, 0x95, 0x97, 0xed, 0x21, 0xae, 00, 0x81, 0x51, 0xa0, 0x9e, 0x43, 0xad, 0xdd, 0x45, 0xd1, 0x74, 0x63, 0xc5, 0x34, 0x3, 0x97}} },
{ (uint64_t)400000000000000ull, {{0x8, 0xbd, 0xd4, 0xc3, 0xe4, 0x53, 0x1b, 0x29, 0x7a, 0x70, 00, 0x1e, 0xb8, 0xa4, 0xf1, 0x98, 0xdc, 0x3b, 0xd4, 0xf1, 0xf5, 0x60, 0x9a, 0xda, 0x98, 0xf6, 0xd9, 0x5f, 0x9a, 0x1a, 0x30, 0x2e}} },
{ (uint64_t)500000000000000ull, {{0x97, 0x55, 0x70, 0xea, 0x12, 0xde, 0x5a, 0xf5, 0xc5, 0x36, 0xbd, 0xb6, 0x83, 0x54, 0xfb, 0xc8, 0x32, 0x21, 0x50, 0xfc, 0x56, 0x83, 0x7c, 0x4b, 0x78, 0xa9, 0x85, 0x76, 0x5d, 0x2a, 0x70, 0x99}} },
{ (uint64_t)600000000000000ull, {{0xa7, 0xa6, 0x39, 0x93, 0x41, 0xcb, 0x4d, 0x67, 0x76, 0xcd, 0x94, 0xd, 0x1d, 0x6a, 0xb0, 0xac, 0xa, 0xbf, 0x56, 0x93, 0x6a, 0x35, 0x31, 0xdf, 0xe9, 0x6c, 0x23, 0x69, 0x97, 0x8e, 0x49, 0xfa}} },
{ (uint64_t)700000000000000ull, {{0x55, 0x9, 0x3e, 0x5e, 0xeb, 0xca, 0x3, 0x88, 0x48, 0xdc, 0x99, 0x7e, 0x31, 0x95, 0xec, 0xc5, 0x8f, 0xb4, 0xa5, 0x71, 0xb9, 0x52, 0x56, 0xc0, 0xff, 0x49, 0xbe, 0xd0, 0xf1, 0x65, 0x22, 0xbd}} },
{ (uint64_t)800000000000000ull, {{0xbb, 0xc6, 0x18, 0x2, 0x24, 0xaf, 0xd3, 0x38, 0xa6, 0xf4, 0xa0, 0x6b, 0x11, 0x98, 0x40, 0x68, 0xeb, 0x36, 0x35, 0xe7, 0xe5, 0x47, 0x66, 0x69, 0x78, 0x83, 0xaf, 0xbd, 0xce, 0xad, 0x2f, 0x31}} },
{ (uint64_t)900000000000000ull, {{0x61, 0x3a, 0xa1, 0x2c, 0xc0, 0xa1, 0x9b, 0xc8, 0x43, 0x63, 0x50, 0xbb, 0xc0, 0xf6, 0x16, 0x32, 0x6e, 0x64, 0x85, 0x83, 0x33, 0x4a, 0x32, 0x65, 0x16, 0x29, 0xe9, 0x5, 0xc5, 0x20, 0x62, 0x69}} },
{ (uint64_t)1000000000000000ull, {{0x52, 0xdd, 0xf8, 0x81, 0x13, 0xa0, 0xfc, 0xf2, 0x12, 0x90, 0x95, 0xc6, 0x18, 0x91, 0xbe, 0x88, 0x5c, 0x9, 0x30, 0x8, 0xeb, 0xc4, 0x65, 0xc, 0xb0, 0xee, 0xa5, 0x60, 0xcd, 0x4d, 0x75, 0x1b}} },
{ (uint64_t)2000000000000000ull, {{0x75, 0xbd, 0xfc, 0x35, 0xa6, 0xdf, 0x76, 0xe5, 0x98, 0x8e, 0xd9, 0xe3, 0x10, 0xa5, 0x89, 0x16, 0xae, 0xf0, 0xc5, 0xf0, 0x5b, 0x89, 0x22, 0xea, 0xae, 0x2c, 0xf9, 0x8f, 0x58, 0x42, 0x3c, 0xe3}} },
{ (uint64_t)3000000000000000ull, {{0x88, 0x98, 0x93, 0xe8, 0x7d, 0x56, 0x9f, 0x14, 0xb2, 0x48, 0xd1, 0xed, 0x93, 0xe8, 0xce, 0x60, 0xbb, 0xe3, 0x73, 0x69, 0xb0, 0xd6, 0xc7, 0xa1, 0x86, 0x89, 0x33, 0xd3, 0xc3, 0xda, 0x9a, 0x72}} },
{ (uint64_t)4000000000000000ull, {{0x88, 0x3e, 0xf3, 0x4b, 0xa2, 0xc1, 0x91, 0xf4, 0x9d, 0x3c, 0xc6, 0xad, 0xa0, 0xaf, 0xf1, 0xcf, 0xb1, 0x77, 0xbd, 0x9e, 0xd4, 0xb3, 0xa5, 0x37, 0x84, 0xb7, 0xf1, 0x62, 0x9b, 0xed, 0x17, 0x41}} },
{ (uint64_t)5000000000000000ull, {{0xa2, 0x90, 0x7c, 0x39, 0x84, 0xb1, 0x4a, 0xb1, 0xf4, 0xda, 0x58, 0xc2, 0xc8, 0x2d, 0x6b, 0x24, 0xf1, 0x29, 0x49, 0x9, 0x75, 0xfc, 0x4a, 0x33, 0x3d, 0x25, 0xa1, 0xf9, 0x2b, 0xc4, 0x32, 0xb6}} },
{ (uint64_t)6000000000000000ull, {{0xa0, 0x7d, 0x9f, 0x18, 0x95, 0x1f, 0xf2, 0x32, 0xcf, 0x4e, 0xc0, 0xee, 0x2f, 0xbc, 0xc3, 0xe1, 0x1b, 0x2c, 0xaf, 0xc9, 0x57, 0x65, 0x82, 0x10, 0x38, 0x1e, 0x3e, 0xe4, 0xed, 0xec, 0x2e, 0x7a}} },
{ (uint64_t)7000000000000000ull, {{0x66, 0x80, 0x21, 0xd5, 0xde, 0x8c, 0xa4, 0xc1, 0x8f, 0x5a, 0x74, 0xf2, 0x78, 0x69, 0xc4, 0xd6, 0xd4, 0x93, 0xa3, 0x30, 0x39, 0x3c, 0xf0, 0x26, 0x41, 0xff, 0xa8, 0x56, 0x7b, 0xa5, 0x36, 0x20}} },
{ (uint64_t)8000000000000000ull, {{0xe0, 0x48, 0x7a, 0xc4, 0x5a, 0x82, 0x59, 0xe3, 0xe5, 0xf2, 0xd9, 0xb8, 0xf6, 0xb8, 0xfa, 0x26, 0x9a, 0x63, 0x49, 0x71, 0xa2, 0xf7, 0xc2, 0x1a, 0x54, 0x17, 0x76, 0x81, 0xeb, 0x2, 0xbd, 0x4a}} },
{ (uint64_t)9000000000000000ull, {{0x98, 0x92, 0x6a, 0x3a, 0xf0, 0x5b, 0xf4, 0xa9, 0x8d, 0xf9, 0xf6, 0x4a, 0xe7, 0xb9, 0xda, 0x45, 0xa7, 0x6, 0xc3, 0xf8, 0x39, 0x5e, 0x47, 0x1f, 0x96, 0xed, 0x3c, 0x6, 0x6, 0xbe, 0xbb, 0x71}} },
{ (uint64_t)10000000000000000ull, {{0x80, 0xad, 0xb7, 0xd, 0x46, 0xf6, 0x3a, 0x75, 0x64, 0xa3, 0xf6, 0x71, 0xd9, 0xba, 0x95, 0x71, 0xb7, 0xf7, 0x95, 0xa9, 0x63, 0x38, 0x2a, 0x4d, 0x9f, 0xaf, 0x2d, 0x54, 0xf6, 0xc6, 0x84, 0x29}} },
{ (uint64_t)20000000000000000ull, {{0xae, 0xbd, 0x97, 0x42, 0x1f, 0x3f, 0xca, 0xe8, 0x95, 0x18, 0x60, 0xe6, 0xd9, 0xd1, 0xf3, 0xec, 0x59, 0x73, 0xa2, 0xf7, 0x66, 0x88, 0x4b, 0xfe, 0x17, 0x50, 0x79, 0x51, 0xe4, 0x62, 0xc6, 0x63}} },
{ (uint64_t)30000000000000000ull, {{0x61, 0x2, 0x6c, 0x84, 0x2a, 0x6a, 0x22, 0x25, 0x74, 0x6b, 0x19, 0x6b, 0x56, 0x89, 0xe1, 0x18, 0xf5, 0x41, 0x34, 0x15, 0x98, 0x1d, 0x7, 0x73, 0x62, 0xb2, 0xe7, 0xb9, 0xac, 0xa5, 0x28, 0x16}} },
{ (uint64_t)40000000000000000ull, {{0x52, 0x54, 0xb5, 0x78, 0xe8, 0x57, 0x9a, 0x27, 0x3b, 0x89, 0x8e, 0x65, 0x9d, 0xd3, 0xe1, 0xa1, 0xcf, 0xba, 0x12, 0x47, 0x26, 0x64, 0xbd, 0x4e, 0x7f, 0x9a, 0x13, 0xb1, 0xfc, 0xee, 0x2, 0x93}} },
{ (uint64_t)50000000000000000ull, {{0x7b, 0x2a, 0xb, 00, 0xcf, 0xdc, 0xa9, 0x51, 0x46, 0xcf, 0x80, 0x95, 0xdd, 0x2b, 0x82, 0x90, 0x91, 0xb0, 0xf2, 0xd5, 0xbb, 0xc, 0x33, 0x82, 0x2d, 0x8b, 0x43, 0x42, 0x69, 0xcd, 0x2a, 0x42}} },
{ (uint64_t)60000000000000000ull, {{0x21, 0x57, 0x4f, 0xed, 0x15, 0x1a, 0x2f, 0x9f, 0x64, 0xa4, 0x5b, 0xe2, 0x8a, 0x3a, 0xf5, 0x88, 0xe9, 0xf2, 0xd1, 0x71, 0x35, 0xa3, 0x53, 0x7f, 0x7, 0xfd, 0x6a, 0xef, 0xa2, 0x9f, 0x2, 0xaf}} },
{ (uint64_t)70000000000000000ull, {{0x1a, 0xf2, 0x41, 0xe1, 0x38, 0x27, 0x98, 0x29, 0xac, 0x6a, 0xe6, 0x2f, 0xf, 0x33, 0x20, 0x4b, 0xb2, 0x8a, 0xfd, 0x6, 0x5c, 0x42, 0x59, 0x3b, 0xdc, 0x79, 0x14, 0x85, 0x97, 0x5b, 0x26, 0x95}} },
{ (uint64_t)80000000000000000ull, {{0xa8, 0xc8, 0xb8, 0x7b, 0x51, 0x2d, 0xef, 0x9b, 0x5e, 0x50, 0xe, 0xb4, 0x98, 0xaf, 0x86, 0xaa, 0xd2, 0x46, 0x4a, 0xea, 0xe7, 0x6d, 0xb1, 0xf6, 0x5d, 0x23, 0x26, 0xce, 0x90, 0x26, 0xec, 0x69}} },
{ (uint64_t)90000000000000000ull, {{0x3d, 0x78, 0x73, 0x63, 0x95, 0xf1, 0xd7, 0xde, 0x8e, 0x16, 0xc0, 0xb5, 0xa9, 0x9f, 0x4d, 0xc4, 0xeb, 0x8f, 0x22, 0xac, 0xc1, 0x5b, 0x21, 0x42, 0x44, 0x1d, 0xbd, 0x8d, 0x2c, 0x31, 0xb9, 0xce}} },
{ (uint64_t)100000000000000000ull, {{0x27, 0x27, 0xd4, 0x93, 0x2f, 0x98, 0x39, 0xe4, 0x3b, 0x6b, 0xf5, 0xfb, 0x29, 0xa3, 0xbe, 0x4c, 0x9, 0xb, 0x6e, 0xb9, 0x31, 00, 0xbb, 0x92, 0x58, 0x1a, 0xdb, 0x8d, 0xd2, 0xb6, 0x61, 0x54}} },
{ (uint64_t)200000000000000000ull, {{0xae, 0x96, 0x78, 0x2e, 0xf2, 0xc4, 0xdf, 0x7d, 0x2e, 0x4, 0xcc, 0xf9, 0xef, 0x76, 0x23, 0x7f, 0x17, 0xc, 0x97, 0x3, 0xb4, 0x92, 0xc0, 0x78, 0x52, 0x6e, 0xb1, 0xf6, 0x85, 0x3d, 0xb1, 0x33}} },
{ (uint64_t)300000000000000000ull, {{0x17, 0x43, 0xfe, 0xab, 0x12, 0xad, 0xe5, 0xfe, 0x12, 0x53, 0x22, 0x27, 0x2f, 0xd1, 0x40, 0x6b, 0x74, 0xe8, 0x19, 0x70, 0x32, 0x68, 0x46, 0x22, 0xee, 0x79, 0xab, 0xcd, 0x94, 0x93, 0x66, 0x4c}} },
{ (uint64_t)400000000000000000ull, {{0x7, 0x9b, 0xf2, 0xa9, 0x6e, 0x16, 0x6e, 0xf9, 0xe6, 0xb2, 0x23, 0x1d, 0xb9, 0x85, 0x8b, 0x99, 0x98, 0x7f, 0x49, 0x33, 0x87, 0xde, 0xeb, 0xd5, 0x17, 0x48, 0x54, 0x9a, 0xd, 0xf7, 0xdc, 0x44}} },
{ (uint64_t)500000000000000000ull, {{0xca, 0xba, 0x97, 0x98, 0x51, 0x6d, 0xad, 0x3, 0x38, 0xd0, 0x6e, 0x10, 0x6d, 0x76, 0xa2, 0x1, 0x93, 0x7a, 0xce, 0x4c, 0x91, 0x53, 0x9e, 0x61, 0x7d, 0x89, 0x28, 0x73, 0x6, 0xa3, 0x92, 0xb1}} },
{ (uint64_t)600000000000000000ull, {{0x6b, 0x8, 0x7f, 0x48, 0xb3, 0xd7, 0xaa, 0xc9, 0x57, 0xc4, 0x52, 0xe5, 0x1a, 0x18, 0xd7, 0x26, 0xb, 0xf8, 0xc8, 0x56, 0xc4, 0xc7, 0x1e, 0x48, 0xf6, 0x49, 0xae, 00, 0x4a, 0xf6, 0x8f, 0x13}} },
{ (uint64_t)700000000000000000ull, {{0x9e, 0xed, 0x8b, 0x23, 0x1f, 0x79, 0x4c, 0x46, 0x5c, 0xbe, 0x88, 0x40, 0xd0, 0xf1, 0x6f, 0x7b, 0x9f, 0x9c, 0x6e, 0xb4, 0x9c, 0x20, 0x7d, 0xe9, 0xd8, 0x55, 0x11, 0x83, 0xd0, 0xc7, 0x6e, 0x43}} },
{ (uint64_t)800000000000000000ull, {{0x58, 0x4a, 0x78, 0x93, 0x13, 0x7e, 0xbd, 0x2, 0x8b, 0xa7, 0x59, 0x82, 0xc3, 0x39, 0xb7, 0x66, 0xaa, 0xda, 0xad, 0xf9, 0x14, 0x50, 0xf9, 0x40, 0x7d, 0x2a, 0x97, 0xd7, 0xf6, 0xb1, 0x93, 0x5e}} },
{ (uint64_t)900000000000000000ull, {{0x7, 0xce, 0x54, 0xb1, 0x18, 0x26, 0xa1, 0x75, 0x23, 0x13, 0x55, 0x1a, 00, 0x20, 0xfd, 0x79, 0x8a, 00, 0x9e, 0x20, 0xcd, 0xb2, 0x40, 0x1d, 0x52, 0x51, 0xc1, 0x55, 0x8e, 0xea, 0xd2, 0x6c}} },
{ (uint64_t)1000000000000000000ull, {{0x39, 0x80, 0x7f, 0x3d, 0xce, 0xb0, 0xa6, 0xfe, 0x34, 0xa7, 0xa1, 0xed, 0xc6, 0x9b, 0x78, 0xff, 0xbe, 0xd5, 0xa7, 0x8c, 0x6c, 0x87, 0x5d, 0xda, 0x96, 0x69, 0xdb, 0xb2, 0x95, 0x70, 0xf0, 0xf4}} },
{ (uint64_t)2000000000000000000ull, {{0xda, 0x74, 00, 0x86, 0xf1, 0x5c, 0xe8, 0x21, 0xe9, 0xd, 0x50, 0xaf, 0xcf, 0x80, 0x9c, 0x7e, 0x18, 0x51, 0x90, 0x1b, 0xa3, 0x5f, 0x9f, 0x63, 0x78, 0xd6, 0x40, 0x7c, 0xb9, 0xc7, 0xa2, 0x75}} },
{ (uint64_t)3000000000000000000ull, {{0x7, 0xa1, 0x75, 0x63, 0xae, 0xf5, 0xcf, 0xd0, 0x36, 0xfa, 0x64, 0xd4, 0xb1, 0x97, 0xa9, 0x51, 0xc0, 0xd2, 0x87, 0x2b, 0xd, 0xb6, 0xf9, 0xbe, 0x47, 0xe6, 0x7c, 0xa6, 0xb5, 0x35, 0xe2, 0x6e}} },
{ (uint64_t)4000000000000000000ull, {{0xe3, 0x49, 0xf7, 0xeb, 0xe5, 0x11, 0x39, 0xfe, 0xd5, 0x69, 0x40, 0x37, 0xd1, 0x14, 0xb7, 0xbd, 0x45, 0xdd, 0xa, 0x6a, 0xf0, 0x4b, 0x62, 0xec, 0xa4, 0xd8, 0xcd, 0x55, 0x2a, 0x14, 0xe3, 0xfb}} },
{ (uint64_t)5000000000000000000ull, {{0x8d, 0x59, 0x7e, 0xa9, 0xf5, 0x79, 0x9a, 0x4d, 0x15, 0x3d, 0x82, 0xd6, 0xf7, 0xbe, 0xa0, 0x2e, 0x52, 0x40, 0xa2, 0xc8, 0x9b, 0x4, 0x1e, 0x6, 0x2f, 0x37, 0xbc, 0x7b, 0x82, 0xa0, 0xac, 0x55}} },
{ (uint64_t)6000000000000000000ull, {{0xa3, 0x43, 0xa7, 0xe1, 0x14, 0x4d, 0x33, 0x50, 0xf, 0x3e, 0xfd, 0x38, 0x15, 0x82, 0xdd, 0xc5, 0xd0, 0x18, 0x3e, 0x5d, 0xcf, 0x8a, 0xfa, 0x64, 0xbb, 0x67, 0x6c, 0x97, 0x3e, 0x3d, 0x1a, 0xb1}} },
{ (uint64_t)7000000000000000000ull, {{0x89, 0xe9, 0x3e, 0xe9, 0xf2, 0x4d, 0x72, 0x61, 0xe5, 0x44, 0xca, 0x8f, 0x9, 0xa7, 0x40, 0x4e, 0xe3, 0xa9, 0xe, 0xe2, 0x50, 0x7d, 0xda, 0xcf, 0x41, 0x2a, 0x58, 0xc, 0x9, 0x65, 0x1c, 0x53}} },
{ (uint64_t)8000000000000000000ull, {{0xc5, 0x94, 0x10, 0x81, 0x54, 0x69, 0xf4, 0x59, 0xd1, 0x5a, 0x6f, 0xe3, 0xf2, 0xa1, 0x1b, 0xa6, 0x31, 0x12, 0xfa, 0xaa, 0xc5, 0x3d, 0xbc, 0x52, 0x5d, 0x3c, 0xfa, 0xb1, 0xfa, 0x9c, 0x3d, 0xdb}} },
{ (uint64_t)9000000000000000000ull, {{0x9d, 0xe7, 0xcb, 0xb, 0x8d, 0x7b, 0xac, 0x47, 0xff, 0xd3, 0x93, 0x1b, 0xcd, 0x82, 0xcd, 0xd5, 0x35, 0xc, 0x29, 0x34, 0xb1, 0x6e, 0xb, 0x64, 0x32, 0xab, 0xf7, 0xcb, 0x4b, 0x5c, 0x37, 0x6d}} },
{ (uint64_t)10000000000000000000ull, {{0x65, 0x8d, 0x1, 0x37, 0x6d, 0x18, 0x63, 0xe7, 0x7b, 0x9, 0x6f, 0x98, 0xe6, 0xe5, 0x13, 0xc2, 0x4, 0x10, 0xf5, 0xc7, 0xfb, 0x18, 0xa6, 0xe5, 0x9a, 0x52, 0x66, 0x84, 0x5c, 0xd9, 0xb1, 0xe3}} },
};
namespace rct {
//Various key initialization functions
//initializes a key matrix;
//first parameter is rows,
//second is columns
keyM keyMInit(size_t rows, size_t cols) {
keyM rv(cols);
size_t i = 0;
for (i = 0 ; i < cols ; i++) {
rv[i] = keyV(rows);
}
return rv;
}
//Various key generation functions
bool toPointCheckOrder(ge_p3 *P, const unsigned char *data)
{
if (ge_frombytes_vartime(P, data))
return false;
ge_p2 R;
ge_scalarmult(&R, curveOrder().bytes, P);
key tmp;
ge_tobytes(tmp.bytes, &R);
return tmp == identity();
}
//generates a random scalar which can be used as a secret key or mask
void skGen(key &sk) {
random32_unbiased(sk.bytes);
}
//generates a random scalar which can be used as a secret key or mask
key skGen() {
key sk;
skGen(sk);
return sk;
}
//Generates a vector of secret key
//Mainly used in testing
keyV skvGen(size_t rows ) {
CHECK_AND_ASSERT_THROW_MES(rows > 0, "0 keys requested");
keyV rv(rows);
size_t i = 0;
for (i = 0 ; i < rows ; i++) {
skGen(rv[i]);
}
return rv;
}
//generates a random curve point (for testing)
key pkGen() {
key sk = skGen();
key pk = scalarmultBase(sk);
return pk;
}
//generates a random secret and corresponding public key
void skpkGen(key &sk, key &pk) {
skGen(sk);
scalarmultBase(pk, sk);
}
//generates a random secret and corresponding public key
tuple<key, key> skpkGen() {
key sk = skGen();
key pk = scalarmultBase(sk);
return make_tuple(sk, pk);
}
//generates C =aG + bH from b, a is given..
void genC(key & C, const key & a, xmr_amount amount) {
addKeys2(C, a, d2h(amount), rct::H);
}
//generates a <secret , public> / Pedersen commitment to the amount
tuple<ctkey, ctkey> ctskpkGen(xmr_amount amount) {
ctkey sk, pk;
skpkGen(sk.dest, pk.dest);
skpkGen(sk.mask, pk.mask);
key am = d2h(amount);
key bH = scalarmultH(am);
addKeys(pk.mask, pk.mask, bH);
return make_tuple(sk, pk);
}
//generates a <secret , public> / Pedersen commitment but takes bH as input
tuple<ctkey, ctkey> ctskpkGen(const key &bH) {
ctkey sk, pk;
skpkGen(sk.dest, pk.dest);
skpkGen(sk.mask, pk.mask);
addKeys(pk.mask, pk.mask, bH);
return make_tuple(sk, pk);
}
key zeroCommit(xmr_amount amount) {
const zero_commitment *begin = zero_commitments;
const zero_commitment *end = zero_commitments + sizeof(zero_commitments) / sizeof(zero_commitments[0]);
const zero_commitment value{amount, rct::zero()};
const auto it = std::lower_bound(begin, end, value, [](const zero_commitment &e0, const zero_commitment &e1){ return e0.amount < e1.amount; });
if (it != end && it->amount == amount)
{
return it->commitment;
}
key am = d2h(amount);
key bH = scalarmultH(am);
return addKeys(G, bH);
}
key commit(xmr_amount amount, const key &mask) {
key c;
genC(c, mask, amount);
return c;
}
//generates a random uint long long (for testing)
xmr_amount randXmrAmount(xmr_amount upperlimit) {
return h2d(skGen()) % (upperlimit);
}
//Scalar multiplications of curve points
//does a * G where a is a scalar and G is the curve basepoint
void scalarmultBase(key &aG,const key &a) {
ge_p3 point;
sc_reduce32copy(aG.bytes, a.bytes); //do this beforehand!
ge_scalarmult_base(&point, aG.bytes);
ge_p3_tobytes(aG.bytes, &point);
}
//does a * G where a is a scalar and G is the curve basepoint
key scalarmultBase(const key & a) {
ge_p3 point;
key aG;
sc_reduce32copy(aG.bytes, a.bytes); //do this beforehand
ge_scalarmult_base(&point, aG.bytes);
ge_p3_tobytes(aG.bytes, &point);
return aG;
}
//does a * P where a is a scalar and P is an arbitrary point
void scalarmultKey(key & aP, const key &P, const key &a) {
ge_p3 A;
ge_p2 R;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_scalarmult(&R, a.bytes, &A);
ge_tobytes(aP.bytes, &R);
}
//does a * P where a is a scalar and P is an arbitrary point
key scalarmultKey(const key & P, const key & a) {
ge_p3 A;
ge_p2 R;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_scalarmult(&R, a.bytes, &A);
key aP;
ge_tobytes(aP.bytes, &R);
return aP;
}
//Computes aH where H= toPoint(cn_fast_hash(G)), G the basepoint
key scalarmultH(const key & a) {
ge_p2 R;
ge_scalarmult(&R, a.bytes, &ge_p3_H);
key aP;
ge_tobytes(aP.bytes, &R);
return aP;
}
//Computes 8P
key scalarmult8(const key & P) {
ge_p3 p3;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&p3, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_p2 p2;
ge_p3_to_p2(&p2, &p3);
ge_p1p1 p1;
ge_mul8(&p1, &p2);
ge_p1p1_to_p2(&p2, &p1);
rct::key res;
ge_tobytes(res.bytes, &p2);
return res;
}
//Computes lA where l is the curve order
bool isInMainSubgroup(const key & A) {
ge_p3 p3;
return toPointCheckOrder(&p3, A.bytes);
}
//Curve addition / subtractions
//for curve points: AB = A + B
void addKeys(key &AB, const key &A, const key &B) {
ge_p3 B2, A2;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_cached tmp2;
ge_p3_to_cached(&tmp2, &B2);
ge_p1p1 tmp3;
ge_add(&tmp3, &A2, &tmp2);
ge_p1p1_to_p3(&A2, &tmp3);
ge_p3_tobytes(AB.bytes, &A2);
}
rct::key addKeys(const key &A, const key &B) {
key k;
addKeys(k, A, B);
return k;
}
rct::key addKeys(const keyV &A) {
if (A.empty())
return rct::identity();
ge_p3 p3, tmp;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&p3, A[0].bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
for (size_t i = 1; i < A.size(); ++i)
{
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&tmp, A[i].bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_cached p2;
ge_p3_to_cached(&p2, &tmp);
ge_p1p1 p1;
ge_add(&p1, &p3, &p2);
ge_p1p1_to_p3(&p3, &p1);
}
rct::key res;
ge_p3_tobytes(res.bytes, &p3);
return res;
}
//addKeys1
//aGB = aG + B where a is a scalar, G is the basepoint, and B is a point
void addKeys1(key &aGB, const key &a, const key & B) {
key aG = scalarmultBase(a);
addKeys(aGB, aG, B);
}
//addKeys2
//aGbB = aG + bB where a, b are scalars, G is the basepoint and B is a point
void addKeys2(key &aGbB, const key &a, const key &b, const key & B) {
ge_p2 rv;
ge_p3 B2;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_double_scalarmult_base_vartime(&rv, b.bytes, &B2, a.bytes);
ge_tobytes(aGbB.bytes, &rv);
}
//Does some precomputation to make addKeys3 more efficient
// input B a curve point and output a ge_dsmp which has precomputation applied
void precomp(ge_dsmp rv, const key & B) {
ge_p3 B2;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_dsm_precomp(rv, &B2);
}
//addKeys3
//aAbB = a*A + b*B where a, b are scalars, A, B are curve points
//B must be input after applying "precomp"
void addKeys3(key &aAbB, const key &a, const key &A, const key &b, const ge_dsmp B) {
ge_p2 rv;
ge_p3 A2;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_double_scalarmult_precomp_vartime(&rv, a.bytes, &A2, b.bytes, B);
ge_tobytes(aAbB.bytes, &rv);
}
//addKeys3
//aAbB = a*A + b*B where a, b are scalars, A, B are curve points
//A and B must be input after applying "precomp"
void addKeys3(key &aAbB, const key &a, const ge_dsmp A, const key &b, const ge_dsmp B) {
ge_p2 rv;
ge_double_scalarmult_precomp_vartime2(&rv, a.bytes, A, b.bytes, B);
ge_tobytes(aAbB.bytes, &rv);
}
//subtract Keys (subtracts curve points)
//AB = A - B where A, B are curve points
void subKeys(key & AB, const key &A, const key &B) {
ge_p3 B2, A2;
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_cached tmp2;
ge_p3_to_cached(&tmp2, &B2);
ge_p1p1 tmp3;
ge_sub(&tmp3, &A2, &tmp2);
ge_p1p1_to_p3(&A2, &tmp3);
ge_p3_tobytes(AB.bytes, &A2);
}
//checks if A, B are equal in terms of bytes (may say no if one is a non-reduced scalar)
//without doing curve operations
bool equalKeys(const key & a, const key & b) {
bool rv = true;
for (int i = 0; i < 32; ++i) {
if (a.bytes[i] != b.bytes[i]) {
rv = false;
}
}
return rv;
}
//Hashing - cn_fast_hash
//be careful these are also in crypto namespace
//cn_fast_hash for arbitrary multiples of 32 bytes
void cn_fast_hash(key &hash, const void * data, const std::size_t l) {
keccak((const uint8_t *)data, l, hash.bytes, 32);
}
void hash_to_scalar(key &hash, const void * data, const std::size_t l) {
cn_fast_hash(hash, data, l);
sc_reduce32(hash.bytes);
}
//cn_fast_hash for a 32 byte key
void cn_fast_hash(key & hash, const key & in) {
keccak((const uint8_t *)in.bytes, 32, hash.bytes, 32);
}
void hash_to_scalar(key & hash, const key & in) {
cn_fast_hash(hash, in);
sc_reduce32(hash.bytes);
}
//cn_fast_hash for a 32 byte key
key cn_fast_hash(const key & in) {
key hash;
keccak((const uint8_t *)in.bytes, 32, hash.bytes, 32);
return hash;
}
key hash_to_scalar(const key & in) {
key hash = cn_fast_hash(in);
sc_reduce32(hash.bytes);
return hash;
}
//cn_fast_hash for a 128 byte unsigned char
key cn_fast_hash128(const void * in) {
key hash;
keccak((const uint8_t *)in, 128, hash.bytes, 32);
return hash;
}
key hash_to_scalar128(const void * in) {
key hash = cn_fast_hash128(in);
sc_reduce32(hash.bytes);
return hash;
}
//cn_fast_hash for multisig purpose
//This takes the outputs and commitments
//and hashes them into a 32 byte sized key
key cn_fast_hash(const ctkeyV &PC) {
if (PC.empty()) return rct::hash2rct(crypto::cn_fast_hash("", 0));
key rv;
cn_fast_hash(rv, &PC[0], 64*PC.size());
return rv;
}
key hash_to_scalar(const ctkeyV &PC) {
key rv = cn_fast_hash(PC);
sc_reduce32(rv.bytes);
return rv;
}
//cn_fast_hash for a key-vector of arbitrary length
//this is useful since you take a number of keys
//put them in the key vector and it concatenates them
//and then hashes them
key cn_fast_hash(const keyV &keys) {
if (keys.empty()) return rct::hash2rct(crypto::cn_fast_hash("", 0));
key rv;
cn_fast_hash(rv, &keys[0], keys.size() * sizeof(keys[0]));
//dp(rv);
return rv;
}
key hash_to_scalar(const keyV &keys) {
key rv = cn_fast_hash(keys);
sc_reduce32(rv.bytes);
return rv;
}
key cn_fast_hash(const key64 keys) {
key rv;
cn_fast_hash(rv, &keys[0], 64 * sizeof(keys[0]));
//dp(rv);
return rv;
}
key hash_to_scalar(const key64 keys) {
key rv = cn_fast_hash(keys);
sc_reduce32(rv.bytes);
return rv;
}
key hashToPointSimple(const key & hh) {
key pointk;
ge_p1p1 point2;
ge_p2 point;
ge_p3 res;
key h = cn_fast_hash(hh);
CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&res, h.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_p3_to_p2(&point, &res);
ge_mul8(&point2, &point);
ge_p1p1_to_p3(&res, &point2);
ge_p3_tobytes(pointk.bytes, &res);
return pointk;
}
key hashToPoint(const key & hh) {
key pointk;
ge_p2 point;
ge_p1p1 point2;
ge_p3 res;
key h = cn_fast_hash(hh);
ge_fromfe_frombytes_vartime(&point, h.bytes);
ge_mul8(&point2, &point);
ge_p1p1_to_p3(&res, &point2);
ge_p3_tobytes(pointk.bytes, &res);
return pointk;
}
void hashToPoint(key & pointk, const key & hh) {
ge_p2 point;
ge_p1p1 point2;
ge_p3 res;
key h = cn_fast_hash(hh);
ge_fromfe_frombytes_vartime(&point, h.bytes);
ge_mul8(&point2, &point);
ge_p1p1_to_p3(&res, &point2);
ge_p3_tobytes(pointk.bytes, &res);
}
//sums a vector of curve points (for scalars use sc_add)
void sumKeys(key & Csum, const keyV & Cis) {
identity(Csum);
size_t i = 0;
for (i = 0; i < Cis.size(); i++) {
addKeys(Csum, Csum, Cis[i]);
}
}
//Elliptic Curve Diffie Helman: encodes and decodes the amount b and mask a
// where C= aG + bH
static key ecdhHash(const key &k)
{
char data[38];
rct::key hash;
memcpy(data, "amount", 6);
memcpy(data + 6, &k, sizeof(k));
cn_fast_hash(hash, data, sizeof(data));
return hash;
}
static void xor8(key &v, const key &k)
{
for (int i = 0; i < 8; ++i)
v.bytes[i] ^= k.bytes[i];
}
key genCommitmentMask(const key &sk)
{
char data[15 + sizeof(key)];
memcpy(data, "commitment_mask", 15);
memcpy(data + 15, &sk, sizeof(sk));
key scalar;
hash_to_scalar(scalar, data, sizeof(data));
return scalar;
}
void ecdhEncode(ecdhTuple & unmasked, const key & sharedSec, bool v2) {
//encode
if (v2)
{
unmasked.mask = zero();
xor8(unmasked.amount, ecdhHash(sharedSec));
}
else
{
key sharedSec1 = hash_to_scalar(sharedSec);
key sharedSec2 = hash_to_scalar(sharedSec1);
sc_add(unmasked.mask.bytes, unmasked.mask.bytes, sharedSec1.bytes);
sc_add(unmasked.amount.bytes, unmasked.amount.bytes, sharedSec2.bytes);
}
}
void ecdhDecode(ecdhTuple & masked, const key & sharedSec, bool v2) {
//decode
if (v2)
{
masked.mask = genCommitmentMask(sharedSec);
xor8(masked.amount, ecdhHash(sharedSec));
}
else
{
key sharedSec1 = hash_to_scalar(sharedSec);
key sharedSec2 = hash_to_scalar(sharedSec1);
sc_sub(masked.mask.bytes, masked.mask.bytes, sharedSec1.bytes);
sc_sub(masked.amount.bytes, masked.amount.bytes, sharedSec2.bytes);
}
}
}
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