Electroneum
rctOps.cpp
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1 // Copyright (c) 2016, Electroneum Research Labs
2 //
3 // Author: Shen Noether <shen.noether@gmx.com>
4 //
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30 
31 #include <boost/lexical_cast.hpp>
32 #include "misc_log_ex.h"
34 #include "rctOps.h"
35 using namespace crypto;
36 using namespace std;
37 
38 #undef ELECTRONEUM_DEFAULT_LOG_CATEGORY
39 #define ELECTRONEUM_DEFAULT_LOG_CATEGORY "ringct"
40 
41 #define CHECK_AND_ASSERT_THROW_MES_L1(expr, message) {if(!(expr)) {MWARNING(message); throw std::runtime_error(message);}}
42 
44 static const zero_commitment zero_commitments[] = {
45  { (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}} },
46  { (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}} },
47  { (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}} },
48  { (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}} },
49  { (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}} },
50  { (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}} },
51  { (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}} },
52  { (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}} },
53  { (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}} },
54  { (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}} },
55  { (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}} },
56  { (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}} },
57  { (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}} },
58  { (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}} },
59  { (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}} },
60  { (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}} },
61  { (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}} },
62  { (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}} },
63  { (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}} },
64  { (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}} },
65  { (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}} },
66  { (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}} },
67  { (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}} },
68  { (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}} },
69  { (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}} },
70  { (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}} },
71  { (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}} },
72  { (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}} },
73  { (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}} },
74  { (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}} },
75  { (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}} },
76  { (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}} },
77  { (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}} },
78  { (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}} },
79  { (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}} },
80  { (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}} },
81  { (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}} },
82  { (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}} },
83  { (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}} },
84  { (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}} },
85  { (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}} },
86  { (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}} },
87  { (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}} },
88  { (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}} },
89  { (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}} },
90  { (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}} },
91  { (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}} },
92  { (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}} },
93  { (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}} },
94  { (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}} },
95  { (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}} },
96  { (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}} },
97  { (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}} },
98  { (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}} },
99  { (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}} },
100  { (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}} },
101  { (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}} },
102  { (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}} },
103  { (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}} },
104  { (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}} },
105  { (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}} },
106  { (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}} },
107  { (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}} },
108  { (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}} },
109  { (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}} },
110  { (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}} },
111  { (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}} },
112  { (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}} },
113  { (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}} },
114  { (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}} },
115  { (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}} },
116  { (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}} },
117  { (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}} },
118  { (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}} },
119  { (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}} },
120  { (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}} },
121  { (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}} },
122  { (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}} },
123  { (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}} },
124  { (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}} },
125  { (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}} },
126  { (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}} },
127  { (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}} },
128  { (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}} },
129  { (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}} },
130  { (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}} },
131  { (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}} },
132  { (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}} },
133  { (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}} },
134  { (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}} },
135  { (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}} },
136  { (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}} },
137  { (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}} },
138  { (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}} },
139  { (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}} },
140  { (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}} },
141  { (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}} },
142  { (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}} },
143  { (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}} },
144  { (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}} },
145  { (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}} },
146  { (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}} },
147  { (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}} },
148  { (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}} },
149  { (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}} },
150  { (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}} },
151  { (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}} },
152  { (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}} },
153  { (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}} },
154  { (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}} },
155  { (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}} },
156  { (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}} },
157  { (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}} },
158  { (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}} },
159  { (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}} },
160  { (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}} },
161  { (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}} },
162  { (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}} },
163  { (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}} },
164  { (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}} },
165  { (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}} },
166  { (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}} },
167  { (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}} },
168  { (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}} },
169  { (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}} },
170  { (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}} },
171  { (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}} },
172  { (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}} },
173  { (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}} },
174  { (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}} },
175  { (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}} },
176  { (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}} },
177  { (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}} },
178  { (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}} },
179  { (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}} },
180  { (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}} },
181  { (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}} },
182  { (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}} },
183  { (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}} },
184  { (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}} },
185  { (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}} },
186  { (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}} },
187  { (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}} },
188  { (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}} },
189  { (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}} },
190  { (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}} },
191  { (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}} },
192  { (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}} },
193  { (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}} },
194  { (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}} },
195  { (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}} },
196  { (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}} },
197  { (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}} },
198  { (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}} },
199  { (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}} },
200  { (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}} },
201  { (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}} },
202  { (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}} },
203  { (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}} },
204  { (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}} },
205  { (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}} },
206  { (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}} },
207  { (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}} },
208  { (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}} },
209  { (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}} },
210  { (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}} },
211  { (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}} },
212  { (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}} },
213  { (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}} },
214  { (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}} },
215  { (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}} },
216  { (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}} },
217  { (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}} },
218 };
219 
220 namespace rct {
221 
222  //Various key initialization functions
223 
224  //initializes a key matrix;
225  //first parameter is rows,
226  //second is columns
227  keyM keyMInit(size_t rows, size_t cols) {
228  keyM rv(cols);
229  size_t i = 0;
230  for (i = 0 ; i < cols ; i++) {
231  rv[i] = keyV(rows);
232  }
233  return rv;
234  }
235 
236 
237 
238 
239  //Various key generation functions
240 
241  bool toPointCheckOrder(ge_p3 *P, const unsigned char *data)
242  {
243  if (ge_frombytes_vartime(P, data))
244  return false;
245  ge_p2 R;
246  ge_scalarmult(&R, curveOrder().bytes, P);
247  key tmp;
248  ge_tobytes(tmp.bytes, &R);
249  return tmp == identity();
250  }
251 
252  //generates a random scalar which can be used as a secret key or mask
253  void skGen(key &sk) {
255  }
256 
257  //generates a random scalar which can be used as a secret key or mask
258  key skGen() {
259  key sk;
260  skGen(sk);
261  return sk;
262  }
263 
264  //Generates a vector of secret key
265  //Mainly used in testing
266  keyV skvGen(size_t rows ) {
267  CHECK_AND_ASSERT_THROW_MES(rows > 0, "0 keys requested");
268  keyV rv(rows);
269  size_t i = 0;
270  for (i = 0 ; i < rows ; i++) {
271  skGen(rv[i]);
272  }
273  return rv;
274  }
275 
276  //generates a random curve point (for testing)
277  key pkGen() {
278  key sk = skGen();
279  key pk = scalarmultBase(sk);
280  return pk;
281  }
282 
283  //generates a random secret and corresponding public key
284  void skpkGen(key &sk, key &pk) {
285  skGen(sk);
286  scalarmultBase(pk, sk);
287  }
288 
289  //generates a random secret and corresponding public key
290  tuple<key, key> skpkGen() {
291  key sk = skGen();
292  key pk = scalarmultBase(sk);
293  return make_tuple(sk, pk);
294  }
295 
296  //generates C =aG + bH from b, a is given..
297  void genC(key & C, const key & a, etn_amount amount) {
298  addKeys2(C, a, d2h(amount), rct::H);
299  }
300 
301  //generates a <secret , public> / Pedersen commitment to the amount
302  tuple<ctkey, ctkey> ctskpkGen(etn_amount amount) {
303  ctkey sk, pk;
304  skpkGen(sk.dest, pk.dest);
305  skpkGen(sk.mask, pk.mask);
306  key am = d2h(amount);
307  key bH = scalarmultH(am);
308  addKeys(pk.mask, pk.mask, bH);
309  return make_tuple(sk, pk);
310  }
311 
312 
313  //generates a <secret , public> / Pedersen commitment but takes bH as input
314  tuple<ctkey, ctkey> ctskpkGen(const key &bH) {
315  ctkey sk, pk;
316  skpkGen(sk.dest, pk.dest);
317  skpkGen(sk.mask, pk.mask);
318  addKeys(pk.mask, pk.mask, bH);
319  return make_tuple(sk, pk);
320  }
321 
323  const zero_commitment *begin = zero_commitments;
324  const zero_commitment *end = zero_commitments + sizeof(zero_commitments) / sizeof(zero_commitments[0]);
325  const zero_commitment value{amount, rct::zero()};
326  const auto it = std::lower_bound(begin, end, value, [](const zero_commitment &e0, const zero_commitment &e1){ return e0.amount < e1.amount; });
327  if (it != end && it->amount == amount)
328  {
329  return it->commitment;
330  }
331  key am = d2h(amount);
332  key bH = scalarmultH(am);
333  return addKeys(G, bH);
334  }
335 
336  key commit(etn_amount amount, const key &mask) {
337  key c;
338  genC(c, mask, amount);
339  return c;
340  }
341 
342  //generates a random uint long long (for testing)
344  return h2d(skGen()) % (upperlimit);
345  }
346 
347  //Scalar multiplications of curve points
348 
349  //does a * G where a is a scalar and G is the curve basepoint
350  void scalarmultBase(key &aG,const key &a) {
351  ge_p3 point;
352  sc_reduce32copy(aG.bytes, a.bytes); //do this beforehand!
353  ge_scalarmult_base(&point, aG.bytes);
354  ge_p3_tobytes(aG.bytes, &point);
355  }
356 
357  //does a * G where a is a scalar and G is the curve basepoint
358  key scalarmultBase(const key & a) {
359  ge_p3 point;
360  key aG;
361  sc_reduce32copy(aG.bytes, a.bytes); //do this beforehand
362  ge_scalarmult_base(&point, aG.bytes);
363  ge_p3_tobytes(aG.bytes, &point);
364  return aG;
365  }
366 
367  //does a * P where a is a scalar and P is an arbitrary point
368  void scalarmultKey(key & aP, const key &P, const key &a) {
369  ge_p3 A;
370  ge_p2 R;
371  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
372  ge_scalarmult(&R, a.bytes, &A);
373  ge_tobytes(aP.bytes, &R);
374  }
375 
376  //does a * P where a is a scalar and P is an arbitrary point
377  key scalarmultKey(const key & P, const key & a) {
378  ge_p3 A;
379  ge_p2 R;
380  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
381  ge_scalarmult(&R, a.bytes, &A);
382  key aP;
383  ge_tobytes(aP.bytes, &R);
384  return aP;
385  }
386 
387 
388  //Computes aH where H= toPoint(cn_fast_hash(G)), G the basepoint
389  key scalarmultH(const key & a) {
390  ge_p2 R;
391  ge_scalarmult(&R, a.bytes, &ge_p3_H);
392  key aP;
393  ge_tobytes(aP.bytes, &R);
394  return aP;
395  }
396 
397  //Computes 8P
398  key scalarmult8(const key & P) {
399  ge_p3 p3;
400  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&p3, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
401  ge_p2 p2;
402  ge_p3_to_p2(&p2, &p3);
403  ge_p1p1 p1;
404  ge_mul8(&p1, &p2);
405  ge_p1p1_to_p2(&p2, &p1);
406  rct::key res;
407  ge_tobytes(res.bytes, &p2);
408  return res;
409  }
410 
411  //Computes lA where l is the curve order
412  bool isInMainSubgroup(const key & A) {
413  ge_p3 p3;
414  return toPointCheckOrder(&p3, A.bytes);
415  }
416 
417  //Curve addition / subtractions
418 
419  //for curve points: AB = A + B
420  void addKeys(key &AB, const key &A, const key &B) {
421  ge_p3 B2, A2;
422  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
423  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
424  ge_cached tmp2;
425  ge_p3_to_cached(&tmp2, &B2);
426  ge_p1p1 tmp3;
427  ge_add(&tmp3, &A2, &tmp2);
428  ge_p1p1_to_p3(&A2, &tmp3);
429  ge_p3_tobytes(AB.bytes, &A2);
430  }
431 
432  rct::key addKeys(const key &A, const key &B) {
433  key k;
434  addKeys(k, A, B);
435  return k;
436  }
437 
438  rct::key addKeys(const keyV &A) {
439  if (A.empty())
440  return rct::identity();
441  ge_p3 p3, tmp;
442  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__));
443  for (size_t i = 1; i < A.size(); ++i)
444  {
445  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__));
446  ge_cached p2;
447  ge_p3_to_cached(&p2, &tmp);
448  ge_p1p1 p1;
449  ge_add(&p1, &p3, &p2);
450  ge_p1p1_to_p3(&p3, &p1);
451  }
452  rct::key res;
453  ge_p3_tobytes(res.bytes, &p3);
454  return res;
455  }
456 
457  //addKeys1
458  //aGB = aG + B where a is a scalar, G is the basepoint, and B is a point
459  void addKeys1(key &aGB, const key &a, const key & B) {
460  key aG = scalarmultBase(a);
461  addKeys(aGB, aG, B);
462  }
463 
464  //addKeys2
465  //aGbB = aG + bB where a, b are scalars, G is the basepoint and B is a point
466  void addKeys2(key &aGbB, const key &a, const key &b, const key & B) {
467  ge_p2 rv;
468  ge_p3 B2;
469  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
470  ge_double_scalarmult_base_vartime(&rv, b.bytes, &B2, a.bytes);
471  ge_tobytes(aGbB.bytes, &rv);
472  }
473 
474  //Does some precomputation to make addKeys3 more efficient
475  // input B a curve point and output a ge_dsmp which has precomputation applied
476  void precomp(ge_dsmp rv, const key & B) {
477  ge_p3 B2;
478  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
479  ge_dsm_precomp(rv, &B2);
480  }
481 
482  //addKeys3
483  //aAbB = a*A + b*B where a, b are scalars, A, B are curve points
484  //B must be input after applying "precomp"
485  void addKeys3(key &aAbB, const key &a, const key &A, const key &b, const ge_dsmp B) {
486  ge_p2 rv;
487  ge_p3 A2;
488  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
489  ge_double_scalarmult_precomp_vartime(&rv, a.bytes, &A2, b.bytes, B);
490  ge_tobytes(aAbB.bytes, &rv);
491  }
492 
493  //addKeys3
494  //aAbB = a*A + b*B where a, b are scalars, A, B are curve points
495  //A and B must be input after applying "precomp"
496  void addKeys3(key &aAbB, const key &a, const ge_dsmp A, const key &b, const ge_dsmp B) {
497  ge_p2 rv;
498  ge_double_scalarmult_precomp_vartime2(&rv, a.bytes, A, b.bytes, B);
499  ge_tobytes(aAbB.bytes, &rv);
500  }
501 
502 
503  //subtract Keys (subtracts curve points)
504  //AB = A - B where A, B are curve points
505  void subKeys(key & AB, const key &A, const key &B) {
506  ge_p3 B2, A2;
507  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
508  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
509  ge_cached tmp2;
510  ge_p3_to_cached(&tmp2, &B2);
511  ge_p1p1 tmp3;
512  ge_sub(&tmp3, &A2, &tmp2);
513  ge_p1p1_to_p3(&A2, &tmp3);
514  ge_p3_tobytes(AB.bytes, &A2);
515  }
516 
517  //checks if A, B are equal in terms of bytes (may say no if one is a non-reduced scalar)
518  //without doing curve operations
519  bool equalKeys(const key & a, const key & b) {
520  bool rv = true;
521  for (int i = 0; i < 32; ++i) {
522  if (a.bytes[i] != b.bytes[i]) {
523  rv = false;
524  }
525  }
526  return rv;
527  }
528 
529  //Hashing - cn_fast_hash
530  //be careful these are also in crypto namespace
531  //cn_fast_hash for arbitrary multiples of 32 bytes
532  void cn_fast_hash(key &hash, const void * data, const std::size_t l) {
533  keccak((const uint8_t *)data, l, hash.bytes, 32);
534  }
535 
536  void hash_to_scalar(key &hash, const void * data, const std::size_t l) {
537  cn_fast_hash(hash, data, l);
538  sc_reduce32(hash.bytes);
539  }
540 
541  //cn_fast_hash for a 32 byte key
542  void cn_fast_hash(key & hash, const key & in) {
543  keccak((const uint8_t *)in.bytes, 32, hash.bytes, 32);
544  }
545 
546  void hash_to_scalar(key & hash, const key & in) {
547  cn_fast_hash(hash, in);
548  sc_reduce32(hash.bytes);
549  }
550 
551  //cn_fast_hash for a 32 byte key
552  key cn_fast_hash(const key & in) {
553  key hash;
554  keccak((const uint8_t *)in.bytes, 32, hash.bytes, 32);
555  return hash;
556  }
557 
558  key hash_to_scalar(const key & in) {
559  key hash = cn_fast_hash(in);
560  sc_reduce32(hash.bytes);
561  return hash;
562  }
563 
564  //cn_fast_hash for a 128 byte unsigned char
565  key cn_fast_hash128(const void * in) {
566  key hash;
567  keccak((const uint8_t *)in, 128, hash.bytes, 32);
568  return hash;
569  }
570 
571  key hash_to_scalar128(const void * in) {
572  key hash = cn_fast_hash128(in);
573  sc_reduce32(hash.bytes);
574  return hash;
575  }
576 
577  //cn_fast_hash for multisig purpose
578  //This takes the outputs and commitments
579  //and hashes them into a 32 byte sized key
580  key cn_fast_hash(const ctkeyV &PC) {
581  if (PC.empty()) return rct::hash2rct(crypto::cn_fast_hash("", 0));
582  key rv;
583  cn_fast_hash(rv, &PC[0], 64*PC.size());
584  return rv;
585  }
586 
587  key hash_to_scalar(const ctkeyV &PC) {
588  key rv = cn_fast_hash(PC);
589  sc_reduce32(rv.bytes);
590  return rv;
591  }
592 
593  //cn_fast_hash for a key-vector of arbitrary length
594  //this is useful since you take a number of keys
595  //put them in the key vector and it concatenates them
596  //and then hashes them
597  key cn_fast_hash(const keyV &keys) {
598  if (keys.empty()) return rct::hash2rct(crypto::cn_fast_hash("", 0));
599  key rv;
600  cn_fast_hash(rv, &keys[0], keys.size() * sizeof(keys[0]));
601  //dp(rv);
602  return rv;
603  }
604 
605  key hash_to_scalar(const keyV &keys) {
606  key rv = cn_fast_hash(keys);
607  sc_reduce32(rv.bytes);
608  return rv;
609  }
610 
611  key cn_fast_hash(const key64 keys) {
612  key rv;
613  cn_fast_hash(rv, &keys[0], 64 * sizeof(keys[0]));
614  //dp(rv);
615  return rv;
616  }
617 
618  key hash_to_scalar(const key64 keys) {
619  key rv = cn_fast_hash(keys);
620  sc_reduce32(rv.bytes);
621  return rv;
622  }
623 
624  key hashToPointSimple(const key & hh) {
625  key pointk;
626  ge_p1p1 point2;
627  ge_p2 point;
628  ge_p3 res;
629  key h = cn_fast_hash(hh);
630  CHECK_AND_ASSERT_THROW_MES_L1(ge_frombytes_vartime(&res, h.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
631  ge_p3_to_p2(&point, &res);
632  ge_mul8(&point2, &point);
633  ge_p1p1_to_p3(&res, &point2);
634  ge_p3_tobytes(pointk.bytes, &res);
635  return pointk;
636  }
637 
638  key hashToPoint(const key & hh) {
639  key pointk;
640  ge_p2 point;
641  ge_p1p1 point2;
642  ge_p3 res;
643  key h = cn_fast_hash(hh);
645  ge_mul8(&point2, &point);
646  ge_p1p1_to_p3(&res, &point2);
647  ge_p3_tobytes(pointk.bytes, &res);
648  return pointk;
649  }
650 
651  void hashToPoint(key & pointk, const key & hh) {
652  ge_p2 point;
653  ge_p1p1 point2;
654  ge_p3 res;
655  key h = cn_fast_hash(hh);
657  ge_mul8(&point2, &point);
658  ge_p1p1_to_p3(&res, &point2);
659  ge_p3_tobytes(pointk.bytes, &res);
660  }
661 
662  //sums a vector of curve points (for scalars use sc_add)
663  void sumKeys(key & Csum, const keyV & Cis) {
664  identity(Csum);
665  size_t i = 0;
666  for (i = 0; i < Cis.size(); i++) {
667  addKeys(Csum, Csum, Cis[i]);
668  }
669  }
670 
671  //Elliptic Curve Diffie Helman: encodes and decodes the amount b and mask a
672  // where C= aG + bH
673  static key ecdhHash(const key &k)
674  {
675  char data[38];
676  rct::key hash;
677  memcpy(data, "amount", 6);
678  memcpy(data + 6, &k, sizeof(k));
679  cn_fast_hash(hash, data, sizeof(data));
680  return hash;
681  }
682  static void xor8(key &v, const key &k)
683  {
684  for (int i = 0; i < 8; ++i)
685  v.bytes[i] ^= k.bytes[i];
686  }
688  {
689  char data[15 + sizeof(key)];
690  memcpy(data, "commitment_mask", 15);
691  memcpy(data + 15, &sk, sizeof(sk));
692  key scalar;
693  hash_to_scalar(scalar, data, sizeof(data));
694  return scalar;
695  }
696 
697  void ecdhEncode(ecdhTuple & unmasked, const key & sharedSec, bool v2) {
698  //encode
699  if (v2)
700  {
701  unmasked.mask = zero();
702  xor8(unmasked.amount, ecdhHash(sharedSec));
703  }
704  else
705  {
706  key sharedSec1 = hash_to_scalar(sharedSec);
707  key sharedSec2 = hash_to_scalar(sharedSec1);
708  sc_add(unmasked.mask.bytes, unmasked.mask.bytes, sharedSec1.bytes);
709  sc_add(unmasked.amount.bytes, unmasked.amount.bytes, sharedSec2.bytes);
710  }
711  }
712  void ecdhDecode(ecdhTuple & masked, const key & sharedSec, bool v2) {
713  //decode
714  if (v2)
715  {
716  masked.mask = genCommitmentMask(sharedSec);
717  xor8(masked.amount, ecdhHash(sharedSec));
718  }
719  else
720  {
721  key sharedSec1 = hash_to_scalar(sharedSec);
722  key sharedSec2 = hash_to_scalar(sharedSec1);
723  sc_sub(masked.mask.bytes, masked.mask.bytes, sharedSec1.bytes);
724  sc_sub(masked.amount.bytes, masked.amount.bytes, sharedSec2.bytes);
725  }
726  }
727 }
const char * res
Definition: hmac_keccak.cpp:41
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Definition: rctOps.cpp:663
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Definition: hmac_keccak.cpp:39
crypto namespace.
Definition: crypto.cpp:58
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Definition: rctOps.cpp:571
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Definition: crypto.h:339
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Definition: stdint.h:124
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Definition: rctOps.cpp:697
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Definition: rctOps.cpp:377
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Definition: rctTypes.h:97
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Definition: gtest-tuple.h:675
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Definition: rctOps.cpp:389
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Definition: rctOps.cpp:343
const GenericPointer< typename T::ValueType > T2 T::AllocatorType & a
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Definition: rctTypes.h:89
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