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monero/src/ringct/rctOps.cpp
moneromooo-monero 9b70856ccb
rct: make the amount key derivable by a third party with the tx key 
Scheme design from luigi1114.
2016-08-28 21:29:46 +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 ecdhEncodeFromSharedSecret(ecdhTuple & unmasked, const key & sharedSec1) {
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 ecdhEncode(ecdhTuple & unmasked, const key & receiverPk) {
key esk;
//compute shared secret
skpkGen(esk, unmasked.senderPk);
key sharedSec1 = hash_to_scalar(scalarmultKey(receiverPk, esk));
ecdhEncodeFromSharedSecret(unmasked, sharedSec1);
}
void ecdhDecodeFromSharedSecret(ecdhTuple & masked, const key & sharedSec1) {
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);
}
void ecdhDecode(ecdhTuple & masked, const key & receiverSk) {
//compute shared secret
key sharedSec1 = hash_to_scalar(scalarmultKey(masked.senderPk, receiverSk));
ecdhDecodeFromSharedSecret(masked, sharedSec1);
}
}
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