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ringct: import of Shen Noether's ring confidential transactions

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This commit is contained in:
moneromooo-monero 2016-05-13 20:45:20 +01:00
parent a569b264bc
commit 9b1afe5f2d
No known key found for this signature in database
GPG key ID: 686F07454D6CEFC3
15 changed files with 2410 additions and 13 deletions
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1
src/CMakeLists.txt
View file

@ -91,6 +91,7 @@ endfunction ()
add_subdirectory(common)
add_subdirectory(crypto)
add_subdirectory(ringct)
add_subdirectory(cryptonote_core)
add_subdirectory(blockchain_db)
add_subdirectory(mnemonics)

14
src/crypto/crypto-ops.c
View file

@ -40,17 +40,15 @@ DISABLE_VS_WARNINGS(4146 4244)
static void fe_mul(fe, const fe, const fe);
static void fe_sq(fe, const fe);
static void fe_tobytes(unsigned char *, const fe);
static void ge_madd(ge_p1p1 *, const ge_p3 *, const ge_precomp *);
static void ge_msub(ge_p1p1 *, const ge_p3 *, const ge_precomp *);
static void ge_p2_0(ge_p2 *);
static void ge_p3_dbl(ge_p1p1 *, const ge_p3 *);
static void ge_sub(ge_p1p1 *, const ge_p3 *, const ge_cached *);
static void fe_divpowm1(fe, const fe, const fe);
/* Common functions */
static uint64_t load_3(const unsigned char *in) {
uint64_t load_3(const unsigned char *in) {
uint64_t result;
result = (uint64_t) in[0];
result |= ((uint64_t) in[1]) << 8;
@ -58,7 +56,7 @@ static uint64_t load_3(const unsigned char *in) {
return result;
}
static uint64_t load_4(const unsigned char *in)
uint64_t load_4(const unsigned char *in)
{
uint64_t result;
result = (uint64_t) in[0];
@ -120,7 +118,7 @@ Postconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
static void fe_add(fe h, const fe f, const fe g) {
void fe_add(fe h, const fe f, const fe g) {
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
@ -258,7 +256,7 @@ static void fe_copy(fe h, const fe f) {
/* From fe_invert.c */
static void fe_invert(fe out, const fe z) {
void fe_invert(fe out, const fe z) {
fe t0;
fe t1;
fe t2;
@ -1031,7 +1029,7 @@ Proof:
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
*/
static void fe_tobytes(unsigned char *s, const fe h) {
void fe_tobytes(unsigned char *s, const fe h) {
int32_t h0 = h[0];
int32_t h1 = h[1];
int32_t h2 = h[2];
@ -1591,7 +1589,7 @@ void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) {
r = p - q
*/
static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
fe t0;
fe_add(r->X, p->Y, p->X);
fe_sub(r->Y, p->Y, p->X);

8
src/crypto/crypto-ops.h
View file

@ -143,3 +143,11 @@ void sc_sub(unsigned char *, const unsigned char *, const unsigned char *);
void sc_mulsub(unsigned char *, const unsigned char *, const unsigned char *, const unsigned char *);
int sc_check(const unsigned char *);
int sc_isnonzero(const unsigned char *); /* Doesn't normalize */
// internal
uint64_t load_3(const unsigned char *in);
uint64_t load_4(const unsigned char *in);
void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
void fe_add(fe h, const fe f, const fe g);
void fe_tobytes(unsigned char *, const fe);
void fe_invert(fe out, const fe z);

16
src/crypto/crypto.h
View file

@ -64,6 +64,22 @@ namespace crypto {
friend class crypto_ops;
};
POD_CLASS public_keyV {
std::vector<public_key> keys;
int rows;
};
POD_CLASS secret_keyV {
std::vector<secret_key> keys;
int rows;
};
POD_CLASS public_keyM {
int cols;
int rows;
std::vector<secret_keyV> column_vectors;
};
POD_CLASS key_derivation: ec_point {
friend class crypto_ops;
};

6
src/crypto/keccak.c
View file

@ -73,11 +73,11 @@ void keccakf(uint64_t st[25], int rounds)
// compute a keccak hash (md) of given byte length from "in"
typedef uint64_t state_t[25];
int keccak(const uint8_t *in, int inlen, uint8_t *md, int mdlen)
int keccak(const uint8_t *in, size_t inlen, uint8_t *md, int mdlen)
{
state_t st;
uint8_t temp[144];
int i, rsiz, rsizw;
size_t i, rsiz, rsizw;
rsiz = sizeof(state_t) == mdlen ? HASH_DATA_AREA : 200 - 2 * mdlen;
rsizw = rsiz / 8;
@ -106,7 +106,7 @@ int keccak(const uint8_t *in, int inlen, uint8_t *md, int mdlen)
return 0;
}
void keccak1600(const uint8_t *in, int inlen, uint8_t *md)
void keccak1600(const uint8_t *in, size_t inlen, uint8_t *md)
{
keccak(in, inlen, md, sizeof(state_t));
}

4
src/crypto/keccak.h
View file

@ -16,11 +16,11 @@
#endif
// compute a keccak hash (md) of given byte length from "in"
int keccak(const uint8_t *in, int inlen, uint8_t *md, int mdlen);
int keccak(const uint8_t *in, size_t inlen, uint8_t *md, int mdlen);
// update the state
void keccakf(uint64_t st[25], int norounds);
void keccak1600(const uint8_t *in, int inlen, uint8_t *md);
void keccak1600(const uint8_t *in, size_t inlen, uint8_t *md);
#endif

59
src/ringct/CMakeLists.txt Normal file
View file

@ -0,0 +1,59 @@
# Copyright (c) 2016, The Monero Project
#
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification, are
# permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this list of
# conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice, this list
# of conditions and the following disclaimer in the documentation and/or other
# materials provided with the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its contributors may be
# used to endorse or promote products derived from this software without specific
# prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
# EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
# MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
# THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
# STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
# THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
set(ringct_sources
rctOps.cpp
rctSigs.cpp
rctTypes.cpp
rctCryptoOps.c)
set(ringct_headers)
set(ringct_private_headers
rctOps.h
rctSigs.h
rctTypes.h)
bitmonero_private_headers(ringct
${crypto_private_headers})
bitmonero_add_library(ringct
${ringct_sources}
${ringct_headers}
${ringct_private_headers})
target_link_libraries(ringct
LINK_PUBLIC
common
crypto
${Boost_DATE_TIME_LIBRARY}
${Boost_PROGRAM_OPTIONS_LIBRARY}
${Boost_SERIALIZATION_LIBRARY}
LINK_PRIVATE
${Boost_FILESYSTEM_LIBRARY}
${Boost_SYSTEM_LIBRARY}
${Boost_THREAD_LIBRARY}
${EXTRA_LIBRARIES})

221
src/ringct/rctCryptoOps.c Normal file
View file

@ -0,0 +1,221 @@
// Copyright (c) 2014-2016, The Monero Project
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without modification, are
// permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice, this list of
// conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
// of conditions and the following disclaimer in the documentation and/or other
// materials provided with the distribution.
//
// 3. Neither the name of the copyright holder nor the names of its contributors may be
// used to endorse or promote products derived from this software without specific
// prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers
#include <assert.h>
#include <stdint.h>
#include "crypto/crypto-ops.h"
//DISABLE_VS_WARNINGS(4146 4244)
void sc_reduce32copy(unsigned char * scopy, const unsigned char *s) {
int64_t s0 = 2097151 & load_3(s);
int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
int64_t s8 = 2097151 & load_3(s + 21);
int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
int64_t s11 = (load_4(s + 28) >> 7);
int64_t s12 = 0;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
carry0 = (s0 + (1<<20)) >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 << 21;
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 << 21;
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 << 21;
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 << 21;
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 << 21;
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 << 21;
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 << 21;
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 << 21;
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 << 21;
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 << 21;
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 << 21;
scopy[0] = s0 >> 0;
scopy[1] = s0 >> 8;
scopy[2] = (s0 >> 16) | (s1 << 5);
scopy[3] = s1 >> 3;
scopy[4] = s1 >> 11;
scopy[5] = (s1 >> 19) | (s2 << 2);
scopy[6] = s2 >> 6;
scopy[7] = (s2 >> 14) | (s3 << 7);
scopy[8] = s3 >> 1;
scopy[9] = s3 >> 9;
scopy[10] = (s3 >> 17) | (s4 << 4);
scopy[11] = s4 >> 4;
scopy[12] = s4 >> 12;
scopy[13] = (s4 >> 20) | (s5 << 1);
scopy[14] = s5 >> 7;
scopy[15] = (s5 >> 15) | (s6 << 6);
scopy[16] = s6 >> 2;
scopy[17] = s6 >> 10;
scopy[18] = (s6 >> 18) | (s7 << 3);
scopy[19] = s7 >> 5;
scopy[20] = s7 >> 13;
scopy[21] = s8 >> 0;
scopy[22] = s8 >> 8;
scopy[23] = (s8 >> 16) | (s9 << 5);
scopy[24] = s9 >> 3;
scopy[25] = s9 >> 11;
scopy[26] = (s9 >> 19) | (s10 << 2);
scopy[27] = s10 >> 6;
scopy[28] = (s10 >> 14) | (s11 << 7);
scopy[29] = s11 >> 1;
scopy[30] = s11 >> 9;
scopy[31] = s11 >> 17;
}

37
src/ringct/rctCryptoOps.h Normal file
View file

@ -0,0 +1,37 @@
// Copyright (c) 2014-2016, The Monero Project
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without modification, are
// permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice, this list of
// conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
// of conditions and the following disclaimer in the documentation and/or other
// materials provided with the distribution.
//
// 3. Neither the name of the copyright holder nor the names of its contributors may be
// used to endorse or promote products derived from this software without specific
// prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers
#pragma once
extern "C" {
#include "crypto/crypto-ops.h"
}
void sc_reduce32copy(unsigned char * scopy, const unsigned char *s);

741
src/ringct/rctOps.cpp Normal file
View file

@ -0,0 +1,741 @@
// 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 "rctOps.h"
using namespace crypto;
using namespace std;
namespace rct {
//Various key initialization functions
//Creates a zero scalar
void zero(key &zero) {
int i = 0;
for (i = 0; i < 32; i++) {
zero[i] = (unsigned char)(0x00);
}
}
//Creates a zero scalar
key zero() {
return{ {0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 , 0x00, 0x00, 0x00,0x00 } };
}
//Creates a zero elliptic curve point
void identity(key &Id) {
int i = 0;
Id[0] = (unsigned char)(0x01);
for (i = 1; i < 32; i++) {
Id[i] = (unsigned char)(0x00);
}
}
//Creates a zero elliptic curve point
key identity() {
key Id;
int i = 0;
Id[0] = (unsigned char)(0x01);
for (i = 1; i < 32; i++) {
Id[i] = (unsigned char)(0x00);
}
return Id;
}
//copies a scalar or point
void copy(key &AA, const key &A) {
int i = 0;
for (i = 0; i < 32; i++) {
AA[i] = A.bytes[i];
}
}
//copies a scalar or point
key copy(const key &A) {
int i = 0;
key AA;
for (i = 0; i < 32; i++) {
AA[i] = A.bytes[i];
}
return AA;
}
//initializes a key matrix;
//first parameter is rows,
//second is columns
keyM keyMInit(int rows, int cols) {
keyM rv(cols);
int i = 0;
for (i = 0 ; i < cols ; i++) {
rv[i] = keyV(rows);
}
return rv;
}
//Various key generation functions
//generates a random scalar which can be used as a secret key or mask
void skGen(key &sk) {
unsigned char tmp[64];
generate_random_bytes(64, tmp);
memcpy(sk.bytes, tmp, 32);
sc_reduce32(sk.bytes);
}
//generates a random scalar which can be used as a secret key or mask
key skGen() {
unsigned char tmp[64];
generate_random_bytes(64, tmp);
key sk;
memcpy(sk.bytes, tmp, 32);
sc_reduce32(sk.bytes);
return sk;
}
//Generates a vector of secret key
//Mainly used in testing
keyV skvGen(int rows ) {
keyV rv(rows);
int 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 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 aH = scalarmultH(am);
addKeys(pk.mask, pk.mask, aH);
return make_tuple(sk, pk);
}
//generates a <secret , public> / Pedersen commitment but takes bH as input
tuple<ctkey, ctkey> ctskpkGen(key bH) {
ctkey sk, pk;
skpkGen(sk.dest, pk.dest);
skpkGen(sk.mask, pk.mask);
//key am = d2h(amount);
//key aH = scalarmultH(am);
addKeys(pk.mask, pk.mask, bH);
return make_tuple(sk, pk);
}
//generates a random uint long long
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;
ge_frombytes_vartime(&A, P.bytes);
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;
ge_frombytes_vartime(&A, P.bytes);
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_p3 A;
ge_p2 R;
key Htmp = { {0x8b, 0x65, 0x59, 0x70, 0x15, 0x37, 0x99, 0xaf, 0x2a, 0xea, 0xdc, 0x9f, 0xf1, 0xad, 0xd0, 0xea, 0x6c, 0x72, 0x51, 0xd5, 0x41, 0x54, 0xcf, 0xa9, 0x2c, 0x17, 0x3a, 0x0d, 0xd3, 0x9c, 0x1f, 0x94} };
ge_frombytes_vartime(&A, Htmp.bytes);
ge_scalarmult(&R, a.bytes, &A);
key aP;
ge_tobytes(aP.bytes, &R);
return aP;
}
//Curve addition / subtractions
//for curve points: AB = A + B
void addKeys(key &AB, const key &A, const key &B) {
ge_p3 B2, A2;
ge_frombytes_vartime(&B2, B.bytes);
ge_frombytes_vartime(&A2, A.bytes);
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);
}
//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;
ge_frombytes_vartime(&B2, B.bytes);
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;
ge_frombytes_vartime(&B2, B.bytes);
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;
ge_frombytes_vartime(&A2, A.bytes);
ge_double_scalarmult_precomp_vartime(&rv, a.bytes, &A2, 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;
ge_frombytes_vartime(&B2, B.bytes);
ge_frombytes_vartime(&A2, A.bytes);
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 as curve points
//without doing curve operations
bool equalKeys(const key & a, const key & b) {
key eqk;
sc_sub(eqk.bytes, cn_fast_hash(a).bytes, cn_fast_hash(b).bytes);
if (sc_isnonzero(eqk.bytes) ) {
//DP("eq bytes");
//DP(eqk);
return false;
}
return true;
}
//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) {
uint8_t md2[32];
int j = 0;
keccak((uint8_t *)data, l, md2, 32);
for (j = 0; j < 32; j++) {
hash[j] = (unsigned char)md2[j];
}
}
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) {
uint8_t md2[32];
int j = 0;
keccak((uint8_t *)in.bytes, 32, md2, 32);
for (j = 0; j < 32; j++) {
hash[j] = (unsigned char)md2[j];
}
}
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) {
uint8_t md2[32];
int j = 0;
key hash;
keccak((uint8_t *)in.bytes, 32, md2, 32);
for (j = 0; j < 32; j++) {
hash[j] = (unsigned char)md2[j];
}
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) {
uint8_t md2[32];
int j = 0;
key hash;
keccak((uint8_t *)in, 128, md2, 32);
for (j = 0; j < 32; j++) {
hash[j] = (unsigned char)md2[j];
}
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(ctkeyV PC) {
key rv = identity();
std::size_t l = (std::size_t)PC.size();
size_t i = 0, j = 0;
vector<char> m(l * 64);
for (i = 0 ; i < l ; i++) {
for (j = 0 ; j < 32 ; j++) {
m[i * 64 + j] = PC[i].dest[j];
m[i * 64 + 32 + j] = PC[i].mask[j];
}
}
cn_fast_hash(rv, &m[0], l);
return rv;
}
key hash_to_scalar(ctkeyV PC) {
key rv = cn_fast_hash(PC);
sc_reduce32(rv.bytes);
return rv;
}
key hashToPointSimple(const key & hh) {
key pointk;
ge_p3 res;
key h = cn_fast_hash(hh);
ge_frombytes_vartime(&res, h.bytes);
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 fe_mul(fe h,const fe f,const fe g)
{
int32_t f0 = f[0];
int32_t f1 = f[1];
int32_t f2 = f[2];
int32_t f3 = f[3];
int32_t f4 = f[4];
int32_t f5 = f[5];
int32_t f6 = f[6];
int32_t f7 = f[7];
int32_t f8 = f[8];
int32_t f9 = f[9];
int32_t g0 = g[0];
int32_t g1 = g[1];
int32_t g2 = g[2];
int32_t g3 = g[3];
int32_t g4 = g[4];
int32_t g5 = g[5];
int32_t g6 = g[6];
int32_t g7 = g[7];
int32_t g8 = g[8];
int32_t g9 = g[9];
int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int32_t g3_19 = 19 * g3;
int32_t g4_19 = 19 * g4;
int32_t g5_19 = 19 * g5;
int32_t g6_19 = 19 * g6;
int32_t g7_19 = 19 * g7;
int32_t g8_19 = 19 * g8;
int32_t g9_19 = 19 * g9;
int32_t f1_2 = 2 * f1;
int32_t f3_2 = 2 * f3;
int32_t f5_2 = 2 * f5;
int32_t f7_2 = 2 * f7;
int32_t f9_2 = 2 * f9;
int64_t f0g0 = f0 * (int64_t) g0;
int64_t f0g1 = f0 * (int64_t) g1;
int64_t f0g2 = f0 * (int64_t) g2;
int64_t f0g3 = f0 * (int64_t) g3;
int64_t f0g4 = f0 * (int64_t) g4;
int64_t f0g5 = f0 * (int64_t) g5;
int64_t f0g6 = f0 * (int64_t) g6;
int64_t f0g7 = f0 * (int64_t) g7;
int64_t f0g8 = f0 * (int64_t) g8;
int64_t f0g9 = f0 * (int64_t) g9;
int64_t f1g0 = f1 * (int64_t) g0;
int64_t f1g1_2 = f1_2 * (int64_t) g1;
int64_t f1g2 = f1 * (int64_t) g2;
int64_t f1g3_2 = f1_2 * (int64_t) g3;
int64_t f1g4 = f1 * (int64_t) g4;
int64_t f1g5_2 = f1_2 * (int64_t) g5;
int64_t f1g6 = f1 * (int64_t) g6;
int64_t f1g7_2 = f1_2 * (int64_t) g7;
int64_t f1g8 = f1 * (int64_t) g8;
int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
int64_t f2g0 = f2 * (int64_t) g0;
int64_t f2g1 = f2 * (int64_t) g1;
int64_t f2g2 = f2 * (int64_t) g2;
int64_t f2g3 = f2 * (int64_t) g3;
int64_t f2g4 = f2 * (int64_t) g4;
int64_t f2g5 = f2 * (int64_t) g5;
int64_t f2g6 = f2 * (int64_t) g6;
int64_t f2g7 = f2 * (int64_t) g7;
int64_t f2g8_19 = f2 * (int64_t) g8_19;
int64_t f2g9_19 = f2 * (int64_t) g9_19;
int64_t f3g0 = f3 * (int64_t) g0;
int64_t f3g1_2 = f3_2 * (int64_t) g1;
int64_t f3g2 = f3 * (int64_t) g2;
int64_t f3g3_2 = f3_2 * (int64_t) g3;
int64_t f3g4 = f3 * (int64_t) g4;
int64_t f3g5_2 = f3_2 * (int64_t) g5;
int64_t f3g6 = f3 * (int64_t) g6;
int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
int64_t f3g8_19 = f3 * (int64_t) g8_19;
int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
int64_t f4g0 = f4 * (int64_t) g0;
int64_t f4g1 = f4 * (int64_t) g1;
int64_t f4g2 = f4 * (int64_t) g2;
int64_t f4g3 = f4 * (int64_t) g3;
int64_t f4g4 = f4 * (int64_t) g4;
int64_t f4g5 = f4 * (int64_t) g5;
int64_t f4g6_19 = f4 * (int64_t) g6_19;
int64_t f4g7_19 = f4 * (int64_t) g7_19;
int64_t f4g8_19 = f4 * (int64_t) g8_19;
int64_t f4g9_19 = f4 * (int64_t) g9_19;
int64_t f5g0 = f5 * (int64_t) g0;
int64_t f5g1_2 = f5_2 * (int64_t) g1;
int64_t f5g2 = f5 * (int64_t) g2;
int64_t f5g3_2 = f5_2 * (int64_t) g3;
int64_t f5g4 = f5 * (int64_t) g4;
int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
int64_t f5g6_19 = f5 * (int64_t) g6_19;
int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
int64_t f5g8_19 = f5 * (int64_t) g8_19;
int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
int64_t f6g0 = f6 * (int64_t) g0;
int64_t f6g1 = f6 * (int64_t) g1;
int64_t f6g2 = f6 * (int64_t) g2;
int64_t f6g3 = f6 * (int64_t) g3;
int64_t f6g4_19 = f6 * (int64_t) g4_19;
int64_t f6g5_19 = f6 * (int64_t) g5_19;
int64_t f6g6_19 = f6 * (int64_t) g6_19;
int64_t f6g7_19 = f6 * (int64_t) g7_19;
int64_t f6g8_19 = f6 * (int64_t) g8_19;
int64_t f6g9_19 = f6 * (int64_t) g9_19;
int64_t f7g0 = f7 * (int64_t) g0;
int64_t f7g1_2 = f7_2 * (int64_t) g1;
int64_t f7g2 = f7 * (int64_t) g2;
int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
int64_t f7g4_19 = f7 * (int64_t) g4_19;
int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
int64_t f7g6_19 = f7 * (int64_t) g6_19;
int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
int64_t f7g8_19 = f7 * (int64_t) g8_19;
int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
int64_t f8g0 = f8 * (int64_t) g0;
int64_t f8g1 = f8 * (int64_t) g1;
int64_t f8g2_19 = f8 * (int64_t) g2_19;
int64_t f8g3_19 = f8 * (int64_t) g3_19;
int64_t f8g4_19 = f8 * (int64_t) g4_19;
int64_t f8g5_19 = f8 * (int64_t) g5_19;
int64_t f8g6_19 = f8 * (int64_t) g6_19;
int64_t f8g7_19 = f8 * (int64_t) g7_19;
int64_t f8g8_19 = f8 * (int64_t) g8_19;
int64_t f8g9_19 = f8 * (int64_t) g9_19;
int64_t f9g0 = f9 * (int64_t) g0;
int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
int64_t f9g2_19 = f9 * (int64_t) g2_19;
int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
int64_t f9g4_19 = f9 * (int64_t) g4_19;
int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
int64_t f9g6_19 = f9 * (int64_t) g6_19;
int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
int64_t f9g8_19 = f9 * (int64_t) g8_19;
int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
/*
|h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
|h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
*/
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = (h1 + (int64_t) (1<<24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry5 = (h5 + (int64_t) (1<<24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
carry2 = (h2 + (int64_t) (1<<25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry6 = (h6 + (int64_t) (1<<25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
carry3 = (h3 + (int64_t) (1<<24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry7 = (h7 + (int64_t) (1<<24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
carry4 = (h4 + (int64_t) (1<<25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry8 = (h8 + (int64_t) (1<<25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
carry9 = (h9 + (int64_t) (1<<24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = (h0 + (int64_t) (1<<25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
h[0] = h0;
h[1] = h1;
h[2] = h2;
h[3] = h3;
h[4] = h4;
h[5] = h5;
h[6] = h6;
h[7] = h7;
h[8] = h8;
h[9] = h9;
}
void ge_tobytes2(unsigned char *s,const ge_p2 *h)
{
fe recip;
fe x;
fe y;
fe_invert(recip,h->Z);
fe_mul(x,h->X,recip);
fe_mul(y,h->Y,recip);
fe_tobytes(s,y);
}
key hashToPoint2(const key & hh) {
key pointk;
ge_p2 point;
key h = cn_fast_hash(hh);
ge_fromfe_frombytes_vartime(&point, h.bytes);
ge_tobytes2(pointk.bytes, &point);
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
void ecdhEncode(ecdhTuple & unmasked, const key & receiverPk) {
key esk;
//compute shared secret
skpkGen(esk, unmasked.senderPk);
key sharedSec1 = hash_to_scalar(scalarmultKey(receiverPk, esk));
key sharedSec2 = hash_to_scalar(sharedSec1);
//encode
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 & receiverSk) {
//compute shared secret
key sharedSec1 = hash_to_scalar(scalarmultKey(masked.senderPk, receiverSk));
key sharedSec2 = hash_to_scalar(sharedSec1);
//encode
sc_sub(masked.mask.bytes, masked.mask.bytes, sharedSec1.bytes);
sc_sub(masked.amount.bytes, masked.amount.bytes, sharedSec2.bytes);
}
}

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//#define DBG
// 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.
#pragma once
#ifndef RCTOPS_H
#define RCTOPS_H
#include <cstddef>
#include <mutex>
#include <vector>
#include <tuple>
#include "crypto/generic-ops.h"
extern "C" {
#include "crypto/random.h"
#include "crypto/keccak.h"
#include "rctCryptoOps.h"
}
#include "crypto/crypto.h"
#include "rctTypes.h"
//Define this flag when debugging to get additional info on the console
#ifdef DBG
#define DP(x) dp(x)
#else
#define DP(x)
#endif
using namespace std;
using namespace crypto;
namespace rct {
//Various key initialization functions
//Creates a zero scalar
key zero();
void zero(key &z);
//Creates a zero elliptic curve point
key identity();
void identity(key &Id);
//copies a scalar or point
void copy(key &AA, const key &A);
key copy(const key & AA);
//initializes a key matrix;
//first parameter is rows,
//second is columns
keyM keyMInit(int, int);
//Various key generation functions
//generates a random scalar which can be used as a secret key or mask
key skGen();
void skGen(key &);
//generates a vector of secret keys of size "int"
keyV skvGen(int );
//generates a random curve point (for testing)
key pkGen();
//generates a random secret and corresponding public key
void skpkGen(key &sk, key &pk);
tuple<key, key> skpkGen();
//generates a <secret , public> / Pedersen commitment to the amount
tuple<ctkey, ctkey> ctskpkGen(xmr_amount amount);
//this one is mainly for testing, can take arbitrary amounts..
tuple<ctkey, ctkey> ctskpkGen(key bH);
//generates a random uint long long
xmr_amount randXmrAmount(xmr_amount 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);
key scalarmultBase(const key & a);
//does a * P where a is a scalar and P is an arbitrary point
void scalarmultKey(key &aP, const key &P, const key &a);
key scalarmultKey(const key &P, const key &a);
//Computes aH where H= toPoint(cn_fast_hash(G)), G the basepoint
key scalarmultH(const key & a);
//Curve addition / subtractions
//for curve points: AB = A + B
void addKeys(key &AB, const key &A, const key &B);
//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);
//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);
//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);
//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);
//AB = A - B where A, B are curve points
void subKeys(key &AB, const key &A, const key &B);
//checks if A, B are equal as curve points
bool equalKeys(const key & A, const key & B);
//Hashing - cn_fast_hash
//be careful these are also in crypto namespace
//cn_fast_hash for arbitrary l multiples of 32 bytes
void cn_fast_hash(key &hash, const void * data, const size_t l);
void hash_to_scalar(key &hash, const void * data, const size_t l);
//cn_fast_hash for a 32 byte key
void cn_fast_hash(key &hash, const key &in);
void hash_to_scalar(key &hash, const key &in);
//cn_fast_hash for a 32 byte key
key cn_fast_hash(const key &in);
key hash_to_scalar(const key &in);
//for mg sigs
key cn_fast_hash128(const void * in);
key hash_to_scalar128(const void * in);
key cn_fast_hash(ctkeyV PC);
key hash_to_scalar(ctkeyV PC);
//returns hashToPoint as described in https://github.com/ShenNoether/ge_fromfe_writeup
key hashToPointSimple(const key &in);
key hashToPoint(const key &in);
key hashToPoint2(const key &in);
void hashToPoint(key &out, const key &in);
//sums a vector of curve points (for scalars use sc_add)
void sumKeys(key & Csum, const key &Cis);
//Elliptic Curve Diffie Helman: encodes and decodes the amount b and mask a
// where C= aG + bH
void ecdhEncode(ecdhTuple & unmasked, const key & receiverPk);
void ecdhDecode(ecdhTuple & masked, const key & receiverSk);
}
#endif /* RCTOPS_H */

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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 "rctSigs.h"
using namespace crypto;
using namespace std;
namespace rct {
//Schnorr Non-linkable
//Gen Gives a signature (L1, s1, s2) proving that the sender knows "x" such that xG = one of P1 or P2
//Ver Verifies that signer knows an "x" such that xG = one of P1 or P2
//These are called in the below ASNL sig generation
void GenSchnorrNonLinkable(key & L1, key & s1, key & s2, const key & x, const key & P1, const key & P2, int index) {
key c1, c2, L2;
key a = skGen();
if (index == 0) {
scalarmultBase(L1, a);
hash_to_scalar(c2, L1);
skGen(s2);
addKeys2(L2, s2, c2, P2);
hash_to_scalar(c1, L2);
sc_mulsub(s1.bytes, x.bytes, c1.bytes, a.bytes);
}
if (index == 1) {
scalarmultBase(L2, a);
skGen(s1);
hash_to_scalar(c1, L2);
addKeys2(L1, s1, c1, P1);
hash_to_scalar(c2, L1);
sc_mulsub(s2.bytes, x.bytes, c2.bytes, a.bytes);
}
}
//Schnorr Non-linkable
//Gen Gives a signature (L1, s1, s2) proving that the sender knows "x" such that xG = one of P1 or P2
//Ver Verifies that signer knows an "x" such that xG = one of P1 or P2
//These are called in the below ASNL sig generation
bool VerSchnorrNonLinkable(const key & P1, const key & P2, const key & L1, const key & s1, const key & s2) {
key c2, L2, c1, L1p;
hash_to_scalar(c2, L1);
addKeys2(L2, s2, c2, P2);
hash_to_scalar(c1, L2);
addKeys2(L1p, s1, c1, P1);
return equalKeys(L1, L1p);
}
//Aggregate Schnorr Non-linkable Ring Signature (ASNL)
// c.f. http://eprint.iacr.org/2015/1098 section 5.
// These are used in range proofs (alternatively Borromean could be used)
// Gen gives a signature which proves the signer knows, for each i,
// an x[i] such that x[i]G = one of P1[i] or P2[i]
// Ver Verifies the signer knows a key for one of P1[i], P2[i] at each i
asnlSig GenASNL(key64 x, key64 P1, key64 P2, bits indices) {
DP("Generating Aggregate Schnorr Non-linkable Ring Signature\n");
key64 s1;
int j = 0;
asnlSig rv;
rv.s = zero();
for (j = 0; j < ATOMS; j++) {
//void GenSchnorrNonLinkable(Bytes L1, Bytes s1, Bytes s2, const Bytes x, const Bytes P1,const Bytes P2, int index) {
GenSchnorrNonLinkable(rv.L1[j], s1[j], rv.s2[j], x[j], P1[j], P2[j], (int)indices[j]);
sc_add(rv.s.bytes, rv.s.bytes, s1[j].bytes);
}
return rv;
}
//Aggregate Schnorr Non-linkable Ring Signature (ASNL)
// c.f. http://eprint.iacr.org/2015/1098 section 5.
// These are used in range proofs (alternatively Borromean could be used)
// Gen gives a signature which proves the signer knows, for each i,
// an x[i] such that x[i]G = one of P1[i] or P2[i]
// Ver Verifies the signer knows a key for one of P1[i], P2[i] at each i
bool VerASNL(key64 P1, key64 P2, asnlSig &as) {
DP("Verifying Aggregate Schnorr Non-linkable Ring Signature\n");
key LHS = identity();
key RHS = scalarmultBase(as.s);
key c2, L2, c1;
int j = 0;
for (j = 0; j < ATOMS; j++) {
hash_to_scalar(c2, as.L1[j]);
addKeys2(L2, as.s2[j], c2, P2[j]);
addKeys(LHS, LHS, as.L1[j]);
hash_to_scalar(c1, L2);
addKeys(RHS, RHS, scalarmultKey(P1[j], c1));
}
key cc;
sc_sub(cc.bytes, LHS.bytes, RHS.bytes);
DP(cc);
return sc_isnonzero(cc.bytes) == 0;
}
//Multilayered Spontaneous Anonymous Group Signatures (MLSAG signatures)
//These are aka MG signatutes in earlier drafts of the ring ct paper
// c.f. http://eprint.iacr.org/2015/1098 section 2.
// keyImageV just does I[i] = xx[i] * Hash(xx[i] * G) for each i
// Gen creates a signature which proves that for some column in the keymatrix "pk"
// the signer knows a secret key for each row in that column
// Ver verifies that the MG sig was created correctly
keyV keyImageV(const keyV &xx) {
keyV II(xx.size());
size_t i = 0;
for (i = 0; i < xx.size(); i++) {
II[i] = scalarmultKey(hashToPoint(scalarmultBase(xx[i])), xx[i]);
}
return II;
}
//Multilayered Spontaneous Anonymous Group Signatures (MLSAG signatures)
//This is a just slghtly more efficient version than the ones described below
//(will be explained in more detail in Ring Multisig paper
//These are aka MG signatutes in earlier drafts of the ring ct paper
// c.f. http://eprint.iacr.org/2015/1098 section 2.
// keyImageV just does I[i] = xx[i] * Hash(xx[i] * G) for each i
// Gen creates a signature which proves that for some column in the keymatrix "pk"
// the signer knows a secret key for each row in that column
// Ver verifies that the MG sig was created correctly
mgSig MLSAG_Gen(key message, const keyM & pk, const keyV & xx, const int index) {
mgSig rv;
int rows = pk[0].size();
int cols = pk.size();
if (cols < 2) {
printf("Error! What is c if cols = 1!");
}
int i = 0, j = 0;
key c, c_old, L, R, Hi;
sc_0(c_old.bytes);
vector<geDsmp> Ip(rows);
rv.II = keyV(rows);
rv.ss = keyM(cols, rv.II);
keyV alpha(rows);
keyV aG(rows);
keyV aHP(rows);
key m2hash;
unsigned char m2[128];
memcpy(m2, message.bytes, 32);
DP("here1");
for (i = 0; i < rows; i++) {
skpkGen(alpha[i], aG[i]); //need to save alphas for later..
Hi = hashToPoint(pk[index][i]);
aHP[i] = scalarmultKey(Hi, alpha[i]);
memcpy(m2+32, pk[index][i].bytes, 32);
memcpy(m2 + 64, aG[i].bytes, 32);
memcpy(m2 + 96, aHP[i].bytes, 32);
rv.II[i] = scalarmultKey(Hi, xx[i]);
precomp(Ip[i].k, rv.II[i]);
m2hash = hash_to_scalar128(m2);
sc_add(c_old.bytes, c_old.bytes, m2hash.bytes);
}
i = (index + 1) % cols;
if (i == 0) {
copy(rv.cc, c_old);
}
while (i != index) {
rv.ss[i] = skvGen(rows);
sc_0(c.bytes);
for (j = 0; j < rows; j++) {
addKeys2(L, rv.ss[i][j], c_old, pk[i][j]);
hashToPoint(Hi, pk[i][j]);
addKeys3(R, rv.ss[i][j], Hi, c_old, Ip[j].k);
memcpy(m2+32, pk[i][j].bytes, 32);
memcpy(m2 + 64, L.bytes, 32);
memcpy(m2 + 96, R.bytes, 32);
m2hash = hash_to_scalar128(m2);
sc_add(c.bytes, c.bytes, m2hash.bytes);
}
copy(c_old, c);
i = (i + 1) % cols;
if (i == 0) {
copy(rv.cc, c_old);
}
}
for (j = 0; j < rows; j++) {
sc_mulsub(rv.ss[index][j].bytes, c.bytes, xx[j].bytes, alpha[j].bytes);
}
return rv;
}
//Multilayered Spontaneous Anonymous Group Signatures (MLSAG signatures)
//This is a just slghtly more efficient version than the ones described below
//(will be explained in more detail in Ring Multisig paper
//These are aka MG signatutes in earlier drafts of the ring ct paper
// c.f. http://eprint.iacr.org/2015/1098 section 2.
// keyImageV just does I[i] = xx[i] * Hash(xx[i] * G) for each i
// Gen creates a signature which proves that for some column in the keymatrix "pk"
// the signer knows a secret key for each row in that column
// Ver verifies that the MG sig was created correctly
bool MLSAG_Ver(key message, keyM & pk, mgSig & rv) {
int rows = pk[0].size();
int cols = pk.size();
if (cols < 2) {
printf("Error! What is c if cols = 1!");
}
int i = 0, j = 0;
key c, L, R, Hi;
key c_old = copy(rv.cc);
vector<geDsmp> Ip(rows);
for (i= 0 ; i< rows ; i++) {
precomp(Ip[i].k, rv.II[i]);
}
unsigned char m2[128];
memcpy(m2, message.bytes, 32);
key m2hash;
i = 0;
while (i < cols) {
sc_0(c.bytes);
for (j = 0; j < rows; j++) {
addKeys2(L, rv.ss[i][j], c_old, pk[i][j]);
hashToPoint(Hi, pk[i][j]);
addKeys3(R, rv.ss[i][j], Hi, c_old, Ip[j].k);
memcpy(m2 + 32, pk[i][j].bytes, 32);
memcpy(m2 + 64, L.bytes, 32);
memcpy(m2 + 96, R.bytes, 32);
m2hash = hash_to_scalar128(m2);
sc_add(c.bytes, c.bytes, m2hash.bytes);
}
copy(c_old, c);
i = (i + 1);
}
DP("c0");
DP(rv.cc);
DP("c_old");
DP(c_old);
sc_sub(c.bytes, c_old.bytes, rv.cc.bytes);
return sc_isnonzero(c.bytes) == 0;
}
//proveRange and verRange
//proveRange gives C, and mask such that \sumCi = C
// c.f. http://eprint.iacr.org/2015/1098 section 5.1
// and Ci is a commitment to either 0 or 2^i, i=0,...,63
// thus this proves that "amount" is in [0, 2^64]
// mask is a such that C = aG + bH, and b = amount
//verRange verifies that \sum Ci = C and that each Ci is a commitment to 0 or 2^i
rangeSig proveRange(key & C, key & mask, const xmr_amount & amount) {
sc_0(mask.bytes);
identity(C);
bits b;
d2b(b, amount);
rangeSig sig;
key64 ai;
key64 CiH;
int i = 0;
for (i = 0; i < ATOMS; i++) {
sc_0(ai[i].bytes);
if (b[i] == 0) {
scalarmultBase(sig.Ci[i], ai[i]);
}
if (b[i] == 1) {
addKeys1(sig.Ci[i], ai[i], H2[i]);
}
subKeys(CiH[i], sig.Ci[i], H2[i]);
sc_add(mask.bytes, mask.bytes, ai[i].bytes);
addKeys(C, C, sig.Ci[i]);
}
sig.asig = GenASNL(ai, sig.Ci, CiH, b);
return sig;
}
//proveRange and verRange
//proveRange gives C, and mask such that \sumCi = C
// c.f. http://eprint.iacr.org/2015/1098 section 5.1
// and Ci is a commitment to either 0 or 2^i, i=0,...,63
// thus this proves that "amount" is in [0, 2^64]
// mask is a such that C = aG + bH, and b = amount
//verRange verifies that \sum Ci = C and that each Ci is a commitment to 0 or 2^i
bool verRange(key & C, rangeSig & as) {
key64 CiH;
int i = 0;
key Ctmp = identity();
for (i = 0; i < 64; i++) {
subKeys(CiH[i], as.Ci[i], H2[i]);
addKeys(Ctmp, Ctmp, as.Ci[i]);
}
bool reb = equalKeys(C, Ctmp);
DP("is sum Ci = C:");
DP(reb);
bool rab = VerASNL(as.Ci, CiH, as.asig);
DP("Is in range?");
DP(rab);
return (reb && rab);
}
//Ring-ct MG sigs
//Prove:
// c.f. http://eprint.iacr.org/2015/1098 section 4. definition 10.
// This does the MG sig on the "dest" part of the given key matrix, and
// the last row is the sum of input commitments from that column - sum output commitments
// this shows that sum inputs = sum outputs
//Ver:
// verifies the above sig is created corretly
mgSig proveRctMG(const ctkeyM & pubs, const ctkeyV & inSk, const ctkeyV &outSk, const ctkeyV & outPk, int index) {
mgSig mg;
//setup vars
int rows = pubs[0].size();
int cols = pubs.size();
keyV sk(rows + 1);
keyV tmp(rows + 1);
int i = 0, j = 0;
for (i = 0; i < rows + 1; i++) {
sc_0(sk[i].bytes);
identity(tmp[i]);
}
keyM M(cols, tmp);
//create the matrix to mg sig
for (i = 0; i < cols; i++) {
M[i][rows] = identity();
for (j = 0; j < rows; j++) {
M[i][j] = pubs[i][j].dest;
addKeys(M[i][rows], M[i][rows], pubs[i][j].mask);
}
}
sc_0(sk[rows].bytes);
for (j = 0; j < rows; j++) {
sk[j] = copy(inSk[j].dest);
sc_add(sk[rows].bytes, sk[rows].bytes, inSk[j].mask.bytes);
}
for (i = 0; i < cols; i++) {
for (size_t j = 0; j < outPk.size(); j++) {
subKeys(M[i][rows], M[i][rows], outPk[j].mask);
}
}
for (size_t j = 0; j < outPk.size(); j++) {
sc_sub(sk[rows].bytes, sk[rows].bytes, outSk[j].mask.bytes);
}
key message = cn_fast_hash(outPk);
return MLSAG_Gen(message, M, sk, index);
}
//Ring-ct MG sigs
//Prove:
// c.f. http://eprint.iacr.org/2015/1098 section 4. definition 10.
// This does the MG sig on the "dest" part of the given key matrix, and
// the last row is the sum of input commitments from that column - sum output commitments
// this shows that sum inputs = sum outputs
//Ver:
// verifies the above sig is created corretly
bool verRctMG(mgSig mg, ctkeyM & pubs, ctkeyV & outPk) {
//setup vars
int rows = pubs[0].size();
int cols = pubs.size();
keyV tmp(rows + 1);
int i = 0, j = 0;
for (i = 0; i < rows + 1; i++) {
identity(tmp[i]);
}
keyM M(cols, tmp);
//create the matrix to mg sig
for (j = 0; j < rows; j++) {
for (i = 0; i < cols; i++) {
M[i][j] = pubs[i][j].dest;
addKeys(M[i][rows], M[i][rows], pubs[i][j].mask);
}
}
for (size_t j = 0; j < outPk.size(); j++) {
for (i = 0; i < cols; i++) {
subKeys(M[i][rows], M[i][rows], outPk[j].mask);
}
}
key message = cn_fast_hash(outPk);
DP("message:");
DP(message);
return MLSAG_Ver(message, M, mg);
}
//These functions get keys from blockchain
//replace these when connecting blockchain
//getKeyFromBlockchain grabs a key from the blockchain at "reference_index" to mix with
//populateFromBlockchain creates a keymatrix with "mixin" columns and one of the columns is inPk
// the return value are the key matrix, and the index where inPk was put (random).
void getKeyFromBlockchain(ctkey & a, size_t reference_index) {
a.mask = pkGen();
a.dest = pkGen();
}
//These functions get keys from blockchain
//replace these when connecting blockchain
//getKeyFromBlockchain grabs a key from the blockchain at "reference_index" to mix with
//populateFromBlockchain creates a keymatrix with "mixin" columns and one of the columns is inPk
// the return value are the key matrix, and the index where inPk was put (random).
tuple<ctkeyM, xmr_amount> populateFromBlockchain(ctkeyV inPk, int mixin) {
int rows = inPk.size();
ctkeyM rv(mixin, inPk);
int index = randXmrAmount(mixin);
int i = 0, j = 0;
for (i = 0; i < mixin; i++) {
if (i != index) {
for (j = 0; j < rows; j++) {
getKeyFromBlockchain(rv[i][j], (size_t)randXmrAmount);
}
}
}
return make_tuple(rv, index);
}
//RingCT protocol
//genRct:
// creates an rctSig with all data necessary to verify the rangeProofs and that the signer owns one of the
// columns that are claimed as inputs, and that the sum of inputs = sum of outputs.
// Also contains masked "amount" and "mask" so the receiver can see how much they received
//verRct:
// verifies that all signatures (rangeProogs, MG sig, sum inputs = outputs) are correct
//decodeRct: (c.f. http://eprint.iacr.org/2015/1098 section 5.1.1)
// uses the attached ecdh info to find the amounts represented by each output commitment
// must know the destination private key to find the correct amount, else will return a random number
rctSig genRct(ctkeyV & inSk, ctkeyV & inPk, const keyV & destinations, const vector<xmr_amount> amounts, const int mixin) {
rctSig rv;
rv.outPk.resize(destinations.size());
rv.rangeSigs.resize(destinations.size());
rv.ecdhInfo.resize(destinations.size());
size_t i = 0;
keyV masks(destinations.size()); //sk mask..
ctkeyV outSk(destinations.size());
for (i = 0; i < destinations.size(); i++) {
//add destination to sig
rv.outPk[i].dest = copy(destinations[i]);
//compute range proof
rv.rangeSigs[i] = proveRange(rv.outPk[i].mask, outSk[i].mask, amounts[i]);
#ifdef DBG
verRange(rv.outPk[i].mask, rv.rangeSigs[i]);
#endif
//mask amount and mask
rv.ecdhInfo[i].mask = copy(outSk[i].mask);
rv.ecdhInfo[i].amount = d2h(amounts[i]);
ecdhEncode(rv.ecdhInfo[i], destinations[i]);
}
int index;
tie(rv.mixRing, index) = populateFromBlockchain(inPk, mixin);
rv.MG = proveRctMG(rv.mixRing, inSk, outSk, rv.outPk, index);
return rv;
}
//RingCT protocol
//genRct:
// creates an rctSig with all data necessary to verify the rangeProofs and that the signer owns one of the
// columns that are claimed as inputs, and that the sum of inputs = sum of outputs.
// Also contains masked "amount" and "mask" so the receiver can see how much they received
//verRct:
// verifies that all signatures (rangeProogs, MG sig, sum inputs = outputs) are correct
//decodeRct: (c.f. http://eprint.iacr.org/2015/1098 section 5.1.1)
// uses the attached ecdh info to find the amounts represented by each output commitment
// must know the destination private key to find the correct amount, else will return a random number
bool verRct(rctSig & rv) {
size_t i = 0;
bool rvb = true;
bool tmp;
DP("range proofs verified?");
for (i = 0; i < rv.outPk.size(); i++) {
tmp = verRange(rv.outPk[i].mask, rv.rangeSigs[i]);
DP(tmp);
rvb = (rvb && tmp);
}
bool mgVerd = verRctMG(rv.MG, rv.mixRing, rv.outPk);
DP("mg sig verified?");
DP(mgVerd);
return (rvb && mgVerd);
}
//RingCT protocol
//genRct:
// creates an rctSig with all data necessary to verify the rangeProofs and that the signer owns one of the
// columns that are claimed as inputs, and that the sum of inputs = sum of outputs.
// Also contains masked "amount" and "mask" so the receiver can see how much they received
//verRct:
// verifies that all signatures (rangeProogs, MG sig, sum inputs = outputs) are correct
//decodeRct: (c.f. http://eprint.iacr.org/2015/1098 section 5.1.1)
// uses the attached ecdh info to find the amounts represented by each output commitment
// must know the destination private key to find the correct amount, else will return a random number
xmr_amount decodeRct(rctSig & rv, key & sk, int i) {
//mask amount and mask
ecdhDecode(rv.ecdhInfo[i], sk);
key mask = rv.ecdhInfo[i].mask;
key amount = rv.ecdhInfo[i].amount;
key C = rv.outPk[i].mask;
DP("C");
DP(C);
key Ctmp;
addKeys2(Ctmp, mask, amount, H);
DP("Ctmp");
DP(Ctmp);
if (equalKeys(C, Ctmp) == false) {
printf("warning, amount decoded incorrectly, will be unable to spend");
}
return h2d(amount);
}
}

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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.
#pragma once
//#define DBG
#ifndef RCTSIGS_H
#define RCTSIGS_H
#include <cstddef>
#include <mutex>
#include <vector>
#include <tuple>
#include "crypto/generic-ops.h"
extern "C" {
#include "crypto/random.h"
#include "crypto/keccak.h"
}
#include "crypto/crypto.h"
#include "rctTypes.h"
#include "rctOps.h"
//Define this flag when debugging to get additional info on the console
#ifdef DBG
#define DP(x) dp(x)
#else
#define DP(x)
#endif
using namespace std;
using namespace crypto;
namespace rct {
//Schnorr Non-linkable
//Gen Gives a signature (L1, s1, s2) proving that the sender knows "x" such that xG = one of P1 or P2
//Ver Verifies that signer knows an "x" such that xG = one of P1 or P2
//These are called in the below ASNL sig generation
void GenSchnorrNonLinkable(key & L1, key & s1, key & s2, const key & x, const key & P1, const key & P2, int index);
bool VerSchnorrNonLinkable(const key & P1, const key & P2, const key & L1, const key & s1, const key & s2);
//Aggregate Schnorr Non-linkable Ring Signature (ASNL)
// c.f. http://eprint.iacr.org/2015/1098 section 5.
// These are used in range proofs (alternatively Borromean could be used)
// Gen gives a signature which proves the signer knows, for each i,
// an x[i] such that x[i]G = one of P1[i] or P2[i]
// Ver Verifies the signer knows a key for one of P1[i], P2[i] at each i
asnlSig GenASNL(key64 x, key64 P1, key64 P2, bits indices);
bool VerASNL(key64 P1, key64 P2, asnlSig &as);
//Multilayered Spontaneous Anonymous Group Signatures (MLSAG signatures)
//These are aka MG signatutes in earlier drafts of the ring ct paper
// c.f. http://eprint.iacr.org/2015/1098 section 2.
// keyImageV just does I[i] = xx[i] * HashToPoint(xx[i] * G) for each i
// Gen creates a signature which proves that for some column in the keymatrix "pk"
// the signer knows a secret key for each row in that column
// Ver verifies that the MG sig was created correctly
keyV keyImageV(const keyV &xx);
mgSig MLSAG_Gen(key message, const keyM & pk, const keyV & xx, const int index);
bool MLSAG_Ver(key message, keyM &pk, mgSig &sig);
//mgSig MLSAG_Gen_Old(const keyM & pk, const keyV & xx, const int index);
//proveRange and verRange
//proveRange gives C, and mask such that \sumCi = C
// c.f. http://eprint.iacr.org/2015/1098 section 5.1
// and Ci is a commitment to either 0 or 2^i, i=0,...,63
// thus this proves that "amount" is in [0, 2^64]
// mask is a such that C = aG + bH, and b = amount
//verRange verifies that \sum Ci = C and that each Ci is a commitment to 0 or 2^i
rangeSig proveRange(key & C, key & mask, const xmr_amount & amount);
bool verRange(key & C, rangeSig & as);
//Ring-ct MG sigs
//Prove:
// c.f. http://eprint.iacr.org/2015/1098 section 4. definition 10.
// This does the MG sig on the "dest" part of the given key matrix, and
// the last row is the sum of input commitments from that column - sum output commitments
// this shows that sum inputs = sum outputs
//Ver:
// verifies the above sig is created corretly
mgSig proveRctMG(const ctkeyM & pubs, const ctkeyV & inSk, const keyV &outMasks, const ctkeyV & outPk, int index);
bool verRctMG(mgSig mg, ctkeyM & pubs, ctkeyV & outPk);
//These functions get keys from blockchain
//replace these when connecting blockchain
//getKeyFromBlockchain grabs a key from the blockchain at "reference_index" to mix with
//populateFromBlockchain creates a keymatrix with "mixin" columns and one of the columns is inPk
// the return value are the key matrix, and the index where inPk was put (random).
void getKeyFromBlockchain(ctkey & a, size_t reference_index);
tuple<ctkeyM, xmr_amount> populateFromBlockchain(ctkeyV inPk, int mixin);
//RingCT protocol
//genRct:
// creates an rctSig with all data necessary to verify the rangeProofs and that the signer owns one of the
// columns that are claimed as inputs, and that the sum of inputs = sum of outputs.
// Also contains masked "amount" and "mask" so the receiver can see how much they received
//verRct:
// verifies that all signatures (rangeProogs, MG sig, sum inputs = outputs) are correct
//decodeRct: (c.f. http://eprint.iacr.org/2015/1098 section 5.1.1)
// uses the attached ecdh info to find the amounts represented by each output commitment
// must know the destination private key to find the correct amount, else will return a random number
rctSig genRct(ctkeyV & inSk, ctkeyV & inPk, const keyV & destinations, const vector<xmr_amount> amounts, const int mixin);
bool verRct(rctSig & rv);
xmr_amount decodeRct(rctSig & rv, key & sk, int i);
}
#endif /* RCTSIGS_H */

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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 "rctTypes.h"
using namespace crypto;
using namespace std;
namespace rct {
//dp
//Debug printing for the above types
//Actually use DP(value) and #define DBG
void dp(key a) {
int j = 0;
printf("\"");
for (j = 0; j < 32; j++) {
printf("%02x", (unsigned char)a.bytes[j]);
}
printf("\"");
printf("\n");
}
void dp(bool a) {
printf(" ... %s ... ", a ? "true" : "false");
printf("\n");
}
void dp(const char * a, int l) {
int j = 0;
printf("\"");
for (j = 0; j < l; j++) {
printf("%02x", (unsigned char)a[j]);
}
printf("\"");
printf("\n");
}
void dp(keyV a) {
size_t j = 0;
printf("[");
for (j = 0; j < a.size(); j++) {
dp(a[j]);
if (j < a.size() - 1) {
printf(",");
}
}
printf("]");
printf("\n");
}
void dp(keyM a) {
size_t j = 0;
printf("[");
for (j = 0; j < a.size(); j++) {
dp(a[j]);
if (j < a.size() - 1) {
printf(",");
}
}
printf("]");
printf("\n");
}
void dp(xmr_amount vali) {
printf("x: ");
std::cout << vali;
printf("\n\n");
}
void dp(int vali) {
printf("x: %d\n", vali);
printf("\n");
}
void dp(bits amountb) {
for (int i = 0; i < 64; i++) {
printf("%d", amountb[i]);
}
printf("\n");
}
void dp(const char * st) {
printf("%s\n", st);
}
//Various Conversions
//uint long long to 32 byte key
void d2h(key & amounth, const xmr_amount in) {
sc_0(amounth.bytes);
xmr_amount val = in;
int i = 0;
while (val != 0) {
amounth[i] = (unsigned char)(val & 0xFF);
i++;
val /= (xmr_amount)256;
}
}
//uint long long to 32 byte key
key d2h(const xmr_amount in) {
key amounth;
sc_0(amounth.bytes);
xmr_amount val = in;
int i = 0;
while (val != 0) {
amounth[i] = (unsigned char)(val & 0xFF);
i++;
val /= (xmr_amount)256;
}
return amounth;
}
//uint long long to int[64]
void d2b(bits amountb, xmr_amount val) {
int i = 0;
while (val != 0) {
amountb[i] = val & 1;
i++;
val >>= 1;
}
while (i < 64) {
amountb[i] = 0;
i++;
}
}
//32 byte key to uint long long
// if the key holds a value > 2^64
// then the value in the first 8 bytes is returned
xmr_amount h2d(const key & test) {
xmr_amount vali = 0;
int j = 0;
for (j = 7; j >= 0; j--) {
vali = (xmr_amount)(vali * 256 + (unsigned char)test.bytes[j]);
}
return vali;
}
//32 byte key to int[64]
void h2b(bits amountb2, const key & test) {
int val = 0, i = 0, j = 0;
for (j = 0; j < 8; j++) {
val = (unsigned char)test.bytes[j];
i = 8 * j;
while (val != 0) {
amountb2[i] = val & 1;
i++;
val >>= 1;
}
while (i < 8 * (j + 1)) {
amountb2[i] = 0;
}
}
}
//int[64] to 32 byte key
void b2h(key & amountdh, const bits amountb2) {
int byte, i, j;
for (j = 0; j < 8; j++) {
byte = 0;
//val = (unsigned char) test[j];
i = 8 * j;
for (i = 7; i > -1; i--) {
byte = byte * 2 + amountb2[8 * j + i];
}
amountdh[j] = (unsigned char)byte;
}
for (j = 8; j < 32; j++) {
amountdh[j] = (unsigned char)(0x00);
}
}
//int[64] to uint long long
xmr_amount b2d(bits amountb) {
xmr_amount vali = 0;
int j = 0;
for (j = 63; j >= 0; j--) {
vali = (xmr_amount)(vali * 2 + amountb[j]);
}
return vali;
}
}

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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.
#pragma once
#ifndef RCT_TYPES_H
#define RCT_TYPES_H
#include <cstddef>
#include <mutex>
#include <vector>
#include <tuple>
#include <iostream>
#include <cinttypes>
extern "C" {
#include "crypto/generic-ops.h"
#include "crypto/crypto-ops.h"
#include "crypto/random.h"
#include "crypto/keccak.h"
}
#include "crypto/crypto.h"
//Define this flag when debugging to get additional info on the console
#ifdef DBG
#define DP(x) dp(x)
#else
#define DP(x)
#endif
//atomic units of moneros
#define ATOMS 64
//for printing large ints
using namespace std;
using namespace crypto;
//Namespace specifically for ring ct code
namespace rct {
//basic ops containers
typedef unsigned char * Bytes;
// Can contain a secret or public key
// similar to secret_key / public_key of crypto-ops,
// but uses unsigned chars,
// also includes an operator for accessing the i'th byte.
struct key {
unsigned char & operator[](int i) {
return bytes[i];
}
unsigned char bytes[32];
};
typedef vector<key> keyV; //vector of keys
typedef vector<keyV> keyM; //matrix of keys (indexed by column first)
//containers For CT operations
//if it's representing a private ctkey then "dest" contains the secret key of the address
// while "mask" contains a where C = aG + bH is CT pedersen commitment and b is the amount
// (store b, the amount, separately
//if it's representing a public ctkey, then "dest" = P the address, mask = C the commitment
struct ctkey {
key dest;
key mask; //C here if public
};
typedef vector<ctkey> ctkeyV;
typedef vector<ctkeyV> ctkeyM;
//data for passing the amount to the receiver secretly
// If the pedersen commitment to an amount is C = aG + bH,
// "mask" contains a 32 byte key a
// "amount" contains a hex representation (in 32 bytes) of a 64 bit number
// "senderPk" is not the senders actual public key, but a one-time public key generated for
// the purpose of the ECDH exchange
struct ecdhTuple {
key mask;
key amount;
key senderPk;
};
//containers for representing amounts
typedef uint64_t xmr_amount;
typedef unsigned int bits[ATOMS];
typedef key key64[64];
//just contains the necessary keys to represent asnlSigs
//c.f. http://eprint.iacr.org/2015/1098
struct asnlSig {
key64 L1;
key64 s2;
key s;
};
//Container for precomp
struct geDsmp {
ge_dsmp k;
};
//just contains the necessary keys to represent MLSAG sigs
//c.f. http://eprint.iacr.org/2015/1098
struct mgSig {
keyM ss;
key cc;
keyV II;
};
//contains the data for an asnl sig
// also contains the "Ci" values such that
// \sum Ci = C
// and the signature proves that each Ci is either
// a Pedersen commitment to 0 or to 2^i
//thus proving that C is in the range of [0, 2^64]
struct rangeSig {
asnlSig asig;
key64 Ci;
};
//A container to hold all signatures necessary for RingCT
// rangeSigs holds all the rangeproof data of a transaction
// MG holds the MLSAG signature of a transaction
// mixRing holds all the public keypairs (P, C) for a transaction
// ecdhInfo holds an encoded mask / amount to be passed to each receiver
// outPk contains public keypairs which are destinations (P, C),
// P = address, C = commitment to amount
struct rctSig {
vector<rangeSig> rangeSigs;
mgSig MG;
ctkeyM mixRing; //the set of all pubkeys / copy
//pairs that you mix with
vector<ecdhTuple> ecdhInfo;
ctkeyV outPk;
};
struct rmsSig {
vector<rangeSig> rangeSigs;
mgSig MG;
ctkeyM mixRing;
vector<ecdhTuple> destinationEcdhInfo;
vector<ecdhTuple> participantEcdhInfo;
ctkeyV outPk;
};
//other basepoint H = toPoint(cn_fast_hash(G)), G the basepoint
static const key H = { {0x8b, 0x65, 0x59, 0x70, 0x15, 0x37, 0x99, 0xaf, 0x2a, 0xea, 0xdc, 0x9f, 0xf1, 0xad, 0xd0, 0xea, 0x6c, 0x72, 0x51, 0xd5, 0x41, 0x54, 0xcf, 0xa9, 0x2c, 0x17, 0x3a, 0x0d, 0xd3, 0x9c, 0x1f, 0x94} };
//H2 contains 2^i H in each index, i.e. H, 2H, 4H, 8H, ...
//This is used for the range proofG
static const key64 H2 = { {0x8b, 0x65, 0x59, 0x70, 0x15, 0x37, 0x99, 0xaf, 0x2a, 0xea, 0xdc, 0x9f, 0xf1, 0xad, 0xd0, 0xea, 0x6c, 0x72, 0x51, 0xd5, 0x41, 0x54, 0xcf, 0xa9, 0x2c, 0x17, 0x3a, 0x0d, 0xd3, 0x9c, 0x1f, 0x94},
{0x8f, 0xaa, 0x44, 0x8a, 0xe4, 0xb3, 0xe2, 0xbb, 0x3d, 0x4d, 0x13, 0x09, 0x09, 0xf5, 0x5f, 0xcd, 0x79, 0x71, 0x1c, 0x1c, 0x83, 0xcd, 0xbc, 0xca, 0xdd, 0x42, 0xcb, 0xe1, 0x51, 0x5e, 0x87, 0x12},
{0x12, 0xa7, 0xd6, 0x2c, 0x77, 0x91, 0x65, 0x4a, 0x57, 0xf3, 0xe6, 0x76, 0x94, 0xed, 0x50, 0xb4, 0x9a, 0x7d, 0x9e, 0x3f, 0xc1, 0xe4, 0xc7, 0xa0, 0xbd, 0xe2, 0x9d, 0x18, 0x7e, 0x9c, 0xc7, 0x1d},
{0x78, 0x9a, 0xb9, 0x93, 0x4b, 0x49, 0xc4, 0xf9, 0xe6, 0x78, 0x5c, 0x6d, 0x57, 0xa4, 0x98, 0xb3, 0xea, 0xd4, 0x43, 0xf0, 0x4f, 0x13, 0xdf, 0x11, 0x0c, 0x54, 0x27, 0xb4, 0xf2, 0x14, 0xc7, 0x39},
{0x77, 0x1e, 0x92, 0x99, 0xd9, 0x4f, 0x02, 0xac, 0x72, 0xe3, 0x8e, 0x44, 0xde, 0x56, 0x8a, 0xc1, 0xdc, 0xb2, 0xed, 0xc6, 0xed, 0xb6, 0x1f, 0x83, 0xca, 0x41, 0x8e, 0x10, 0x77, 0xce, 0x3d, 0xe8},
{0x73, 0xb9, 0x6d, 0xb4, 0x30, 0x39, 0x81, 0x9b, 0xda, 0xf5, 0x68, 0x0e, 0x5c, 0x32, 0xd7, 0x41, 0x48, 0x88, 0x84, 0xd1, 0x8d, 0x93, 0x86, 0x6d, 0x40, 0x74, 0xa8, 0x49, 0x18, 0x2a, 0x8a, 0x64},
{0x8d, 0x45, 0x8e, 0x1c, 0x2f, 0x68, 0xeb, 0xeb, 0xcc, 0xd2, 0xfd, 0x5d, 0x37, 0x9f, 0x5e, 0x58, 0xf8, 0x13, 0x4d, 0xf3, 0xe0, 0xe8, 0x8c, 0xad, 0x3d, 0x46, 0x70, 0x10, 0x63, 0xa8, 0xd4, 0x12},
{0x09, 0x55, 0x1e, 0xdb, 0xe4, 0x94, 0x41, 0x8e, 0x81, 0x28, 0x44, 0x55, 0xd6, 0x4b, 0x35, 0xee, 0x8a, 0xc0, 0x93, 0x06, 0x8a, 0x5f, 0x16, 0x1f, 0xa6, 0x63, 0x75, 0x59, 0x17, 0x7e, 0xf4, 0x04},
{0xd0, 0x5a, 0x88, 0x66, 0xf4, 0xdf, 0x8c, 0xee, 0x1e, 0x26, 0x8b, 0x1d, 0x23, 0xa4, 0xc5, 0x8c, 0x92, 0xe7, 0x60, 0x30, 0x97, 0x86, 0xcd, 0xac, 0x0f, 0xed, 0xa1, 0xd2, 0x47, 0xa9, 0xc9, 0xa7},
{0x55, 0xcd, 0xaa, 0xd5, 0x18, 0xbd, 0x87, 0x1d, 0xd1, 0xeb, 0x7b, 0xc7, 0x02, 0x3e, 0x1d, 0xc0, 0xfd, 0xf3, 0x33, 0x98, 0x64, 0xf8, 0x8f, 0xdd, 0x2d, 0xe2, 0x69, 0xfe, 0x9e, 0xe1, 0x83, 0x2d},
{0xe7, 0x69, 0x7e, 0x95, 0x1a, 0x98, 0xcf, 0xd5, 0x71, 0x2b, 0x84, 0xbb, 0xe5, 0xf3, 0x4e, 0xd7, 0x33, 0xe9, 0x47, 0x3f, 0xcb, 0x68, 0xed, 0xa6, 0x6e, 0x37, 0x88, 0xdf, 0x19, 0x58, 0xc3, 0x06},
{0xf9, 0x2a, 0x97, 0x0b, 0xae, 0x72, 0x78, 0x29, 0x89, 0xbf, 0xc8, 0x3a, 0xdf, 0xaa, 0x92, 0xa4, 0xf4, 0x9c, 0x7e, 0x95, 0x91, 0x8b, 0x3b, 0xba, 0x3c, 0xdc, 0x7f, 0xe8, 0x8a, 0xcc, 0x8d, 0x47},
{0x1f, 0x66, 0xc2, 0xd4, 0x91, 0xd7, 0x5a, 0xf9, 0x15, 0xc8, 0xdb, 0x6a, 0x6d, 0x1c, 0xb0, 0xcd, 0x4f, 0x7d, 0xdc, 0xd5, 0xe6, 0x3d, 0x3b, 0xa9, 0xb8, 0x3c, 0x86, 0x6c, 0x39, 0xef, 0x3a, 0x2b},
{0x3e, 0xec, 0x98, 0x84, 0xb4, 0x3f, 0x58, 0xe9, 0x3e, 0xf8, 0xde, 0xea, 0x26, 0x00, 0x04, 0xef, 0xea, 0x2a, 0x46, 0x34, 0x4f, 0xc5, 0x96, 0x5b, 0x1a, 0x7d, 0xd5, 0xd1, 0x89, 0x97, 0xef, 0xa7},
{0xb2, 0x9f, 0x8f, 0x0c, 0xcb, 0x96, 0x97, 0x7f, 0xe7, 0x77, 0xd4, 0x89, 0xd6, 0xbe, 0x9e, 0x7e, 0xbc, 0x19, 0xc4, 0x09, 0xb5, 0x10, 0x35, 0x68, 0xf2, 0x77, 0x61, 0x1d, 0x7e, 0xa8, 0x48, 0x94},
{0x56, 0xb1, 0xf5, 0x12, 0x65, 0xb9, 0x55, 0x98, 0x76, 0xd5, 0x8d, 0x24, 0x9d, 0x0c, 0x14, 0x6d, 0x69, 0xa1, 0x03, 0x63, 0x66, 0x99, 0x87, 0x4d, 0x3f, 0x90, 0x47, 0x35, 0x50, 0xfe, 0x3f, 0x2c},
{0x1d, 0x7a, 0x36, 0x57, 0x5e, 0x22, 0xf5, 0xd1, 0x39, 0xff, 0x9c, 0xc5, 0x10, 0xfa, 0x13, 0x85, 0x05, 0x57, 0x6b, 0x63, 0x81, 0x5a, 0x94, 0xe4, 0xb0, 0x12, 0xbf, 0xd4, 0x57, 0xca, 0xaa, 0xda},
{0xd0, 0xac, 0x50, 0x7a, 0x86, 0x4e, 0xcd, 0x05, 0x93, 0xfa, 0x67, 0xbe, 0x7d, 0x23, 0x13, 0x43, 0x92, 0xd0, 0x0e, 0x40, 0x07, 0xe2, 0x53, 0x48, 0x78, 0xd9, 0xb2, 0x42, 0xe1, 0x0d, 0x76, 0x20},
{0xf6, 0xc6, 0x84, 0x0b, 0x9c, 0xf1, 0x45, 0xbb, 0x2d, 0xcc, 0xf8, 0x6e, 0x94, 0x0b, 0xe0, 0xfc, 0x09, 0x8e, 0x32, 0xe3, 0x10, 0x99, 0xd5, 0x6f, 0x7f, 0xe0, 0x87, 0xbd, 0x5d, 0xeb, 0x50, 0x94},
{0x28, 0x83, 0x1a, 0x33, 0x40, 0x07, 0x0e, 0xb1, 0xdb, 0x87, 0xc1, 0x2e, 0x05, 0x98, 0x0d, 0x5f, 0x33, 0xe9, 0xef, 0x90, 0xf8, 0x3a, 0x48, 0x17, 0xc9, 0xf4, 0xa0, 0xa3, 0x32, 0x27, 0xe1, 0x97},
{0x87, 0x63, 0x22, 0x73, 0xd6, 0x29, 0xcc, 0xb7, 0xe1, 0xed, 0x1a, 0x76, 0x8f, 0xa2, 0xeb, 0xd5, 0x17, 0x60, 0xf3, 0x2e, 0x1c, 0x0b, 0x86, 0x7a, 0x5d, 0x36, 0x8d, 0x52, 0x71, 0x05, 0x5c, 0x6e},
{0x5c, 0x7b, 0x29, 0x42, 0x43, 0x47, 0x96, 0x4d, 0x04, 0x27, 0x55, 0x17, 0xc5, 0xae, 0x14, 0xb6, 0xb5, 0xea, 0x27, 0x98, 0xb5, 0x73, 0xfc, 0x94, 0xe6, 0xe4, 0x4a, 0x53, 0x21, 0x60, 0x0c, 0xfb},
{0xe6, 0x94, 0x50, 0x42, 0xd7, 0x8b, 0xc2, 0xc3, 0xbd, 0x6e, 0xc5, 0x8c, 0x51, 0x1a, 0x9f, 0xe8, 0x59, 0xc0, 0xad, 0x63, 0xfd, 0xe4, 0x94, 0xf5, 0x03, 0x9e, 0x0e, 0x82, 0x32, 0x61, 0x2b, 0xd5},
{0x36, 0xd5, 0x69, 0x07, 0xe2, 0xec, 0x74, 0x5d, 0xb6, 0xe5, 0x4f, 0x0b, 0x2e, 0x1b, 0x23, 0x00, 0xab, 0xcb, 0x42, 0x2e, 0x71, 0x2d, 0xa5, 0x88, 0xa4, 0x0d, 0x3f, 0x1e, 0xbb, 0xbe, 0x02, 0xf6},
{0x34, 0xdb, 0x6e, 0xe4, 0xd0, 0x60, 0x8e, 0x5f, 0x78, 0x36, 0x50, 0x49, 0x5a, 0x3b, 0x2f, 0x52, 0x73, 0xc5, 0x13, 0x4e, 0x52, 0x84, 0xe4, 0xfd, 0xf9, 0x66, 0x27, 0xbb, 0x16, 0xe3, 0x1e, 0x6b},
{0x8e, 0x76, 0x59, 0xfb, 0x45, 0xa3, 0x78, 0x7d, 0x67, 0x4a, 0xe8, 0x67, 0x31, 0xfa, 0xa2, 0x53, 0x8e, 0xc0, 0xfd, 0xf4, 0x42, 0xab, 0x26, 0xe9, 0xc7, 0x91, 0xfa, 0xda, 0x08, 0x94, 0x67, 0xe9},
{0x30, 0x06, 0xcf, 0x19, 0x8b, 0x24, 0xf3, 0x1b, 0xb4, 0xc7, 0xe6, 0x34, 0x60, 0x00, 0xab, 0xc7, 0x01, 0xe8, 0x27, 0xcf, 0xbb, 0x5d, 0xf5, 0x2d, 0xcf, 0xa4, 0x2e, 0x9c, 0xa9, 0xff, 0x08, 0x02},
{0xf5, 0xfd, 0x40, 0x3c, 0xb6, 0xe8, 0xbe, 0x21, 0x47, 0x2e, 0x37, 0x7f, 0xfd, 0x80, 0x5a, 0x8c, 0x60, 0x83, 0xea, 0x48, 0x03, 0xb8, 0x48, 0x53, 0x89, 0xcc, 0x3e, 0xbc, 0x21, 0x5f, 0x00, 0x2a},
{0x37, 0x31, 0xb2, 0x60, 0xeb, 0x3f, 0x94, 0x82, 0xe4, 0x5f, 0x1c, 0x3f, 0x3b, 0x9d, 0xcf, 0x83, 0x4b, 0x75, 0xe6, 0xee, 0xf8, 0xc4, 0x0f, 0x46, 0x1e, 0xa2, 0x7e, 0x8b, 0x6e, 0xd9, 0x47, 0x3d},
{0x9f, 0x9d, 0xab, 0x09, 0xc3, 0xf5, 0xe4, 0x28, 0x55, 0xc2, 0xde, 0x97, 0x1b, 0x65, 0x93, 0x28, 0xa2, 0xdb, 0xc4, 0x54, 0x84, 0x5f, 0x39, 0x6f, 0xfc, 0x05, 0x3f, 0x0b, 0xb1, 0x92, 0xf8, 0xc3},
{0x5e, 0x05, 0x5d, 0x25, 0xf8, 0x5f, 0xdb, 0x98, 0xf2, 0x73, 0xe4, 0xaf, 0xe0, 0x84, 0x64, 0xc0, 0x03, 0xb7, 0x0f, 0x1e, 0xf0, 0x67, 0x7b, 0xb5, 0xe2, 0x57, 0x06, 0x40, 0x0b, 0xe6, 0x20, 0xa5},
{0x86, 0x8b, 0xcf, 0x36, 0x79, 0xcb, 0x6b, 0x50, 0x0b, 0x94, 0x41, 0x8c, 0x0b, 0x89, 0x25, 0xf9, 0x86, 0x55, 0x30, 0x30, 0x3a, 0xe4, 0xe4, 0xb2, 0x62, 0x59, 0x18, 0x65, 0x66, 0x6a, 0x45, 0x90},
{0xb3, 0xdb, 0x6b, 0xd3, 0x89, 0x7a, 0xfb, 0xd1, 0xdf, 0x3f, 0x96, 0x44, 0xab, 0x21, 0xc8, 0x05, 0x0e, 0x1f, 0x00, 0x38, 0xa5, 0x2f, 0x7c, 0xa9, 0x5a, 0xc0, 0xc3, 0xde, 0x75, 0x58, 0xcb, 0x7a},
{0x81, 0x19, 0xb3, 0xa0, 0x59, 0xff, 0x2c, 0xac, 0x48, 0x3e, 0x69, 0xbc, 0xd4, 0x1d, 0x6d, 0x27, 0x14, 0x94, 0x47, 0x91, 0x42, 0x88, 0xbb, 0xea, 0xee, 0x34, 0x13, 0xe6, 0xdc, 0xc6, 0xd1, 0xeb},
{0x10, 0xfc, 0x58, 0xf3, 0x5f, 0xc7, 0xfe, 0x7a, 0xe8, 0x75, 0x52, 0x4b, 0xb5, 0x85, 0x00, 0x03, 0x00, 0x5b, 0x7f, 0x97, 0x8c, 0x0c, 0x65, 0xe2, 0xa9, 0x65, 0x46, 0x4b, 0x6d, 0x00, 0x81, 0x9c},
{0x5a, 0xcd, 0x94, 0xeb, 0x3c, 0x57, 0x83, 0x79, 0xc1, 0xea, 0x58, 0xa3, 0x43, 0xec, 0x4f, 0xcf, 0xf9, 0x62, 0x77, 0x6f, 0xe3, 0x55, 0x21, 0xe4, 0x75, 0xa0, 0xe0, 0x6d, 0x88, 0x7b, 0x2d, 0xb9},
{0x33, 0xda, 0xf3, 0xa2, 0x14, 0xd6, 0xe0, 0xd4, 0x2d, 0x23, 0x00, 0xa7, 0xb4, 0x4b, 0x39, 0x29, 0x0d, 0xb8, 0x98, 0x9b, 0x42, 0x79, 0x74, 0xcd, 0x86, 0x5d, 0xb0, 0x11, 0x05, 0x5a, 0x29, 0x01},
{0xcf, 0xc6, 0x57, 0x2f, 0x29, 0xaf, 0xd1, 0x64, 0xa4, 0x94, 0xe6, 0x4e, 0x6f, 0x1a, 0xeb, 0x82, 0x0c, 0x3e, 0x7d, 0xa3, 0x55, 0x14, 0x4e, 0x51, 0x24, 0xa3, 0x91, 0xd0, 0x6e, 0x9f, 0x95, 0xea},
{0xd5, 0x31, 0x2a, 0x4b, 0x0e, 0xf6, 0x15, 0xa3, 0x31, 0xf6, 0x35, 0x2c, 0x2e, 0xd2, 0x1d, 0xac, 0x9e, 0x7c, 0x36, 0x39, 0x8b, 0x93, 0x9a, 0xec, 0x90, 0x1c, 0x25, 0x7f, 0x6c, 0xbc, 0x9e, 0x8e},
{0x55, 0x1d, 0x67, 0xfe, 0xfc, 0x7b, 0x5b, 0x9f, 0x9f, 0xdb, 0xf6, 0xaf, 0x57, 0xc9, 0x6c, 0x8a, 0x74, 0xd7, 0xe4, 0x5a, 0x00, 0x20, 0x78, 0xa7, 0xb5, 0xba, 0x45, 0xc6, 0xfd, 0xe9, 0x3e, 0x33},
{0xd5, 0x0a, 0xc7, 0xbd, 0x5c, 0xa5, 0x93, 0xc6, 0x56, 0x92, 0x8f, 0x38, 0x42, 0x80, 0x17, 0xfc, 0x7b, 0xa5, 0x02, 0x85, 0x4c, 0x43, 0xd8, 0x41, 0x49, 0x50, 0xe9, 0x6e, 0xcb, 0x40, 0x5d, 0xc3},
{0x07, 0x73, 0xe1, 0x8e, 0xa1, 0xbe, 0x44, 0xfe, 0x1a, 0x97, 0xe2, 0x39, 0x57, 0x3c, 0xfa, 0xe3, 0xe4, 0xe9, 0x5e, 0xf9, 0xaa, 0x9f, 0xaa, 0xbe, 0xac, 0x12, 0x74, 0xd3, 0xad, 0x26, 0x16, 0x04},
{0xe9, 0xaf, 0x0e, 0x7c, 0xa8, 0x93, 0x30, 0xd2, 0xb8, 0x61, 0x5d, 0x1b, 0x41, 0x37, 0xca, 0x61, 0x7e, 0x21, 0x29, 0x7f, 0x2f, 0x0d, 0xed, 0x8e, 0x31, 0xb7, 0xd2, 0xea, 0xd8, 0x71, 0x46, 0x60},
{0x7b, 0x12, 0x45, 0x83, 0x09, 0x7f, 0x10, 0x29, 0xa0, 0xc7, 0x41, 0x91, 0xfe, 0x73, 0x78, 0xc9, 0x10, 0x5a, 0xcc, 0x70, 0x66, 0x95, 0xed, 0x14, 0x93, 0xbb, 0x76, 0x03, 0x42, 0x26, 0xa5, 0x7b},
{0xec, 0x40, 0x05, 0x7b, 0x99, 0x54, 0x76, 0x65, 0x0b, 0x3d, 0xb9, 0x8e, 0x9d, 0xb7, 0x57, 0x38, 0xa8, 0xcd, 0x2f, 0x94, 0xd8, 0x63, 0xb9, 0x06, 0x15, 0x0c, 0x56, 0xaa, 0xc1, 0x9c, 0xaa, 0x6b},
{0x01, 0xd9, 0xff, 0x72, 0x9e, 0xfd, 0x39, 0xd8, 0x37, 0x84, 0xc0, 0xfe, 0x59, 0xc4, 0xae, 0x81, 0xa6, 0x70, 0x34, 0xcb, 0x53, 0xc9, 0x43, 0xfb, 0x81, 0x8b, 0x9d, 0x8a, 0xe7, 0xfc, 0x33, 0xe5},
{0x00, 0xdf, 0xb3, 0xc6, 0x96, 0x32, 0x8c, 0x76, 0x42, 0x45, 0x19, 0xa7, 0xbe, 0xfe, 0x8e, 0x0f, 0x6c, 0x76, 0xf9, 0x47, 0xb5, 0x27, 0x67, 0x91, 0x6d, 0x24, 0x82, 0x3f, 0x73, 0x5b, 0xaf, 0x2e},
{0x46, 0x1b, 0x79, 0x9b, 0x4d, 0x9c, 0xee, 0xa8, 0xd5, 0x80, 0xdc, 0xb7, 0x6d, 0x11, 0x15, 0x0d, 0x53, 0x5e, 0x16, 0x39, 0xd1, 0x60, 0x03, 0xc3, 0xfb, 0x7e, 0x9d, 0x1f, 0xd1, 0x30, 0x83, 0xa8},
{0xee, 0x03, 0x03, 0x94, 0x79, 0xe5, 0x22, 0x8f, 0xdc, 0x55, 0x1c, 0xbd, 0xe7, 0x07, 0x9d, 0x34, 0x12, 0xea, 0x18, 0x6a, 0x51, 0x7c, 0xcc, 0x63, 0xe4, 0x6e, 0x9f, 0xcc, 0xe4, 0xfe, 0x3a, 0x6c},
{0xa8, 0xcf, 0xb5, 0x43, 0x52, 0x4e, 0x7f, 0x02, 0xb9, 0xf0, 0x45, 0xac, 0xd5, 0x43, 0xc2, 0x1c, 0x37, 0x3b, 0x4c, 0x9b, 0x98, 0xac, 0x20, 0xce, 0xc4, 0x17, 0xa6, 0xdd, 0xb5, 0x74, 0x4e, 0x94},
{0x93, 0x2b, 0x79, 0x4b, 0xf8, 0x9c, 0x6e, 0xda, 0xf5, 0xd0, 0x65, 0x0c, 0x7c, 0x4b, 0xad, 0x92, 0x42, 0xb2, 0x56, 0x26, 0xe3, 0x7e, 0xad, 0x5a, 0xa7, 0x5e, 0xc8, 0xc6, 0x4e, 0x09, 0xdd, 0x4f},
{0x16, 0xb1, 0x0c, 0x77, 0x9c, 0xe5, 0xcf, 0xef, 0x59, 0xc7, 0x71, 0x0d, 0x2e, 0x68, 0x44, 0x1e, 0xa6, 0xfa, 0xcb, 0x68, 0xe9, 0xb5, 0xf7, 0xd5, 0x33, 0xae, 0x0b, 0xb7, 0x8e, 0x28, 0xbf, 0x57},
{0x0f, 0x77, 0xc7, 0x67, 0x43, 0xe7, 0x39, 0x6f, 0x99, 0x10, 0x13, 0x9f, 0x49, 0x37, 0xd8, 0x37, 0xae, 0x54, 0xe2, 0x10, 0x38, 0xac, 0x5c, 0x0b, 0x3f, 0xd6, 0xef, 0x17, 0x1a, 0x28, 0xa7, 0xe4},
{0xd7, 0xe5, 0x74, 0xb7, 0xb9, 0x52, 0xf2, 0x93, 0xe8, 0x0d, 0xde, 0x90, 0x5e, 0xb5, 0x09, 0x37, 0x3f, 0x3f, 0x6c, 0xd1, 0x09, 0xa0, 0x22, 0x08, 0xb3, 0xc1, 0xe9, 0x24, 0x08, 0x0a, 0x20, 0xca},
{0x45, 0x66, 0x6f, 0x8c, 0x38, 0x1e, 0x3d, 0xa6, 0x75, 0x56, 0x3f, 0xf8, 0xba, 0x23, 0xf8, 0x3b, 0xfa, 0xc3, 0x0c, 0x34, 0xab, 0xdd, 0xe6, 0xe5, 0xc0, 0x97, 0x5e, 0xf9, 0xfd, 0x70, 0x0c, 0xb9},
{0xb2, 0x46, 0x12, 0xe4, 0x54, 0x60, 0x7e, 0xb1, 0xab, 0xa4, 0x47, 0xf8, 0x16, 0xd1, 0xa4, 0x55, 0x1e, 0xf9, 0x5f, 0xa7, 0x24, 0x7f, 0xb7, 0xc1, 0xf5, 0x03, 0x02, 0x0a, 0x71, 0x77, 0xf0, 0xdd},
{0x7e, 0x20, 0x88, 0x61, 0x85, 0x6d, 0xa4, 0x2c, 0x8b, 0xb4, 0x6a, 0x75, 0x67, 0xf8, 0x12, 0x13, 0x62, 0xd9, 0xfb, 0x24, 0x96, 0xf1, 0x31, 0xa4, 0xaa, 0x90, 0x17, 0xcf, 0x36, 0x6c, 0xdf, 0xce},
{0x5b, 0x64, 0x6b, 0xff, 0x6a, 0xd1, 0x10, 0x01, 0x65, 0x03, 0x7a, 0x05, 0x56, 0x01, 0xea, 0x02, 0x35, 0x8c, 0x0f, 0x41, 0x05, 0x0f, 0x9d, 0xfe, 0x3c, 0x95, 0xdc, 0xcb, 0xd3, 0x08, 0x7b, 0xe0},
{0x74, 0x6d, 0x1d, 0xcc, 0xfe, 0xd2, 0xf0, 0xff, 0x1e, 0x13, 0xc5, 0x1e, 0x2d, 0x50, 0xd5, 0x32, 0x43, 0x75, 0xfb, 0xd5, 0xbf, 0x7c, 0xa8, 0x2a, 0x89, 0x31, 0x82, 0x8d, 0x80, 0x1d, 0x43, 0xab},
{0xcb, 0x98, 0x11, 0x0d, 0x4a, 0x6b, 0xb9, 0x7d, 0x22, 0xfe, 0xad, 0xbc, 0x6c, 0x0d, 0x89, 0x30, 0xc5, 0xf8, 0xfc, 0x50, 0x8b, 0x2f, 0xc5, 0xb3, 0x53, 0x28, 0xd2, 0x6b, 0x88, 0xdb, 0x19, 0xae},
{0x60, 0xb6, 0x26, 0xa0, 0x33, 0xb5, 0x5f, 0x27, 0xd7, 0x67, 0x6c, 0x40, 0x95, 0xea, 0xba, 0xbc, 0x7a, 0x2c, 0x7e, 0xde, 0x26, 0x24, 0xb4, 0x72, 0xe9, 0x7f, 0x64, 0xf9, 0x6b, 0x8c, 0xfc, 0x0e},
{0xe5, 0xb5, 0x2b, 0xc9, 0x27, 0x46, 0x8d, 0xf7, 0x18, 0x93, 0xeb, 0x81, 0x97, 0xef, 0x82, 0x0c, 0xf7, 0x6c, 0xb0, 0xaa, 0xf6, 0xe8, 0xe4, 0xfe, 0x93, 0xad, 0x62, 0xd8, 0x03, 0x98, 0x31, 0x04},
{0x05, 0x65, 0x41, 0xae, 0x5d, 0xa9, 0x96, 0x1b, 0xe2, 0xb0, 0xa5, 0xe8, 0x95, 0xe5, 0xc5, 0xba, 0x15, 0x3c, 0xbb, 0x62, 0xdd, 0x56, 0x1a, 0x42, 0x7b, 0xad, 0x0f, 0xfd, 0x41, 0x92, 0x31, 0x99} };
//Debug printing for the above types
//Actually use DP(value) and #define DBG
void dp(key a);
void dp(bool a);
void dp(const char * a, int l);
void dp(keyV a);
void dp(keyM a);
void dp(xmr_amount vali);
void dp(int vali);
void dp(bits amountb);
void dp(const char * st);
//various conversions
//uint long long to 32 byte key
void d2h(key & amounth, xmr_amount val);
key d2h(xmr_amount val);
//uint long long to int[64]
void d2b(bits amountb, xmr_amount val);
//32 byte key to uint long long
// if the key holds a value > 2^64
// then the value in the first 8 bytes is returned
xmr_amount h2d(const key &test);
//32 byte key to int[64]
void h2b(bits amountb2, key & test);
//int[64] to 32 byte key
void b2h(key & amountdh, bits amountb2);
//int[64] to uint long long
xmr_amount b2d(bits amountb);
}
#endif /* RCTTYPES_H */