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monero/src/ringct/rctOps.cpp
moneromooo-monero d4b62a1e29
rct amount key modified as per luigi1111's recommendations 
This allows the key to be not the same for two outputs sent to
the same address (eg, if you pay yourself, and also get change
back). Also remove the key amounts lists and return parameters
since we don't actually generate random ones, so we don't need
to save them as we can recalculate them when needed if we have
the correct keys.
2016-08-28 21:30:19 +01:00

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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 "misc_log_ex.h"
#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) {
sk = crypto::rand<key>();
sc_reduce32(sk.bytes);
}
//generates a random scalar which can be used as a secret key or mask
key skGen() {
key sk = crypto::rand<key>();
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 C =aG + bH from b, a is given..
void genC(key & C, const key & a, xmr_amount amount) {
key bH = scalarmultH(d2h(amount));
addKeys1(C, a, bH);
}
//generates a <secret , public> / Pedersen commitment to the amount
tuple<ctkey, ctkey> ctskpkGen(xmr_amount amount) {
ctkey sk, pk;
skpkGen(sk.dest, pk.dest);
skpkGen(sk.mask, pk.mask);
key am = d2h(amount);
key bH = scalarmultH(am);
addKeys(pk.mask, pk.mask, bH);
return make_tuple(sk, pk);
}
//generates a <secret , public> / Pedersen commitment but takes bH as input
tuple<ctkey, ctkey> ctskpkGen(key bH) {
ctkey sk, pk;
skpkGen(sk.dest, pk.dest);
skpkGen(sk.mask, pk.mask);
addKeys(pk.mask, pk.mask, bH);
return make_tuple(sk, pk);
}
key zeroCommit(xmr_amount amount) {
key mask = identity();
mask = scalarmultBase(mask);
key am = d2h(amount);
key bH = scalarmultH(am);
addKeys(mask, mask, bH);
return mask;
}
key commit(xmr_amount amount, key mask) {
mask = scalarmultBase(mask);
key am = d2h(amount);
key bH = scalarmultH(am);
addKeys(mask, mask, bH);
return mask;
}
//generates a random uint long long (for testing)
xmr_amount randXmrAmount(xmr_amount upperlimit) {
return h2d(skGen()) % (upperlimit);
}
//Scalar multiplications of curve points
//does a * G where a is a scalar and G is the curve basepoint
void scalarmultBase(key &aG,const key &a) {
ge_p3 point;
sc_reduce32copy(aG.bytes, a.bytes); //do this beforehand!
ge_scalarmult_base(&point, aG.bytes);
ge_p3_tobytes(aG.bytes, &point);
}
//does a * G where a is a scalar and G is the curve basepoint
key scalarmultBase(const key & a) {
ge_p3 point;
key aG;
sc_reduce32copy(aG.bytes, a.bytes); //do this beforehand
ge_scalarmult_base(&point, aG.bytes);
ge_p3_tobytes(aG.bytes, &point);
return aG;
}
//does a * P where a is a scalar and P is an arbitrary point
void scalarmultKey(key & aP, const key &P, const key &a) {
ge_p3 A;
ge_p2 R;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&A, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_scalarmult(&R, a.bytes, &A);
ge_tobytes(aP.bytes, &R);
}
//does a * P where a is a scalar and P is an arbitrary point
key scalarmultKey(const key & P, const key & a) {
ge_p3 A;
ge_p2 R;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&A, P.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_scalarmult(&R, a.bytes, &A);
key aP;
ge_tobytes(aP.bytes, &R);
return aP;
}
//Computes aH where H= toPoint(cn_fast_hash(G)), G the basepoint
key scalarmultH(const key & a) {
ge_p3 A;
ge_p2 R;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&A, H.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_scalarmult(&R, a.bytes, &A);
key aP;
ge_tobytes(aP.bytes, &R);
return aP;
}
//Curve addition / subtractions
//for curve points: AB = A + B
void addKeys(key &AB, const key &A, const key &B) {
ge_p3 B2, A2;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_cached tmp2;
ge_p3_to_cached(&tmp2, &B2);
ge_p1p1 tmp3;
ge_add(&tmp3, &A2, &tmp2);
ge_p1p1_to_p3(&A2, &tmp3);
ge_p3_tobytes(AB.bytes, &A2);
}
//addKeys1
//aGB = aG + B where a is a scalar, G is the basepoint, and B is a point
void addKeys1(key &aGB, const key &a, const key & B) {
key aG = scalarmultBase(a);
addKeys(aGB, aG, B);
}
//addKeys2
//aGbB = aG + bB where a, b are scalars, G is the basepoint and B is a point
void addKeys2(key &aGbB, const key &a, const key &b, const key & B) {
ge_p2 rv;
ge_p3 B2;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_double_scalarmult_base_vartime(&rv, b.bytes, &B2, a.bytes);
ge_tobytes(aGbB.bytes, &rv);
}
//Does some precomputation to make addKeys3 more efficient
// input B a curve point and output a ge_dsmp which has precomputation applied
void precomp(ge_dsmp rv, const key & B) {
ge_p3 B2;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_dsm_precomp(rv, &B2);
}
//addKeys3
//aAbB = a*A + b*B where a, b are scalars, A, B are curve points
//B must be input after applying "precomp"
void addKeys3(key &aAbB, const key &a, const key &A, const key &b, const ge_dsmp B) {
ge_p2 rv;
ge_p3 A2;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_double_scalarmult_precomp_vartime(&rv, a.bytes, &A2, b.bytes, B);
ge_tobytes(aAbB.bytes, &rv);
}
//subtract Keys (subtracts curve points)
//AB = A - B where A, B are curve points
void subKeys(key & AB, const key &A, const key &B) {
ge_p3 B2, A2;
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&B2, B.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&A2, A.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_cached tmp2;
ge_p3_to_cached(&tmp2, &B2);
ge_p1p1 tmp3;
ge_sub(&tmp3, &A2, &tmp2);
ge_p1p1_to_p3(&A2, &tmp3);
ge_p3_tobytes(AB.bytes, &A2);
}
//checks if A, B are equal as curve points
//without doing curve operations
bool equalKeys(const key & a, const key & b) {
bool rv = true;
for (int i = 0; i < 32; ++i) {
if (a.bytes[i] != b.bytes[i]) {
rv = false;
}
}
return rv;
}
//Hashing - cn_fast_hash
//be careful these are also in crypto namespace
//cn_fast_hash for arbitrary multiples of 32 bytes
void cn_fast_hash(key &hash, const void * data, const std::size_t l) {
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], 64*l);
return rv;
}
key hash_to_scalar(ctkeyV PC) {
key rv = cn_fast_hash(PC);
sc_reduce32(rv.bytes);
return rv;
}
//cn_fast_hash for a key-vector of arbitrary length
//this is useful since you take a number of keys
//put them in the key vector and it concatenates them
//and then hashes them
key cn_fast_hash(const keyV &keys) {
size_t l = keys.size();
vector<unsigned char> m(l * 32);
size_t i, j;
for (i = 0 ; i < l ; i++) {
for (j = 0 ; j < 32 ; j++) {
m[i * 32 + j] = keys[i][j];
}
}
key rv;
cn_fast_hash(rv, &m[0], 32 * l);
//dp(rv);
return rv;
}
key hash_to_scalar(const keyV &keys) {
key rv = cn_fast_hash(keys);
sc_reduce32(rv.bytes);
return rv;
}
key hashToPointSimple(const key & hh) {
key pointk;
ge_p1p1 point2;
ge_p2 point;
ge_p3 res;
key h = cn_fast_hash(hh);
CHECK_AND_ASSERT_THROW_MES(ge_frombytes_vartime(&res, h.bytes) == 0, "ge_frombytes_vartime failed at "+boost::lexical_cast<std::string>(__LINE__));
ge_p3_to_p2(&point, &res);
ge_mul8(&point2, &point);
ge_p1p1_to_p3(&res, &point2);
ge_p3_tobytes(pointk.bytes, &res);
return pointk;
}
key hashToPoint(const key & hh) {
key pointk;
ge_p2 point;
ge_p1p1 point2;
ge_p3 res;
key h = cn_fast_hash(hh);
ge_fromfe_frombytes_vartime(&point, h.bytes);
ge_mul8(&point2, &point);
ge_p1p1_to_p3(&res, &point2);
ge_p3_tobytes(pointk.bytes, &res);
return pointk;
}
void 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 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 & sharedSec) {
key sharedSec1 = hash_to_scalar(sharedSec);
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 & sharedSec) {
key sharedSec1 = hash_to_scalar(sharedSec);
key sharedSec2 = hash_to_scalar(sharedSec1);
//decode
sc_sub(masked.mask.bytes, masked.mask.bytes, sharedSec1.bytes);
sc_sub(masked.amount.bytes, masked.amount.bytes, sharedSec2.bytes);
}
}
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