monero/src/ringct/rctOps.cpp

// Copyright (c) 2016, Monero Research Labs
//
// Author: Shen Noether <shen.noether@gmx.com>
//
// All rights reserved.
//
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// permitted provided that the following conditions are met:
//
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//    conditions and the following disclaimer.
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#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) {
        memset(&zero, 0, 32);
    }

    //Creates a zero scalar
    key zero() {
        static const key z = { {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  } };
        return z;
    }

    //Creates a zero elliptic curve point
    void identity(key &Id) {
        Id[0] = (unsigned char)(0x01);
        memset(Id.bytes+1, 0, 31);
    }

    //Creates a zero elliptic curve point
    key identity() {
        key Id;
        Id[0] = (unsigned char)(0x01);
        memset(Id.bytes+1, 0, 31);
        return Id;
    }

    //copies a scalar or point
    void copy(key &AA, const key &A) {
        memcpy(&AA, &A, 32);
    }

    //copies a scalar or point
    key copy(const key &A) {
        key AA;
        memcpy(&AA, &A, 32);
        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) {
        keccak((uint8_t *)data, l, hash.bytes, 32);
    }
    
    void hash_to_scalar(key &hash, const void * data, const std::size_t l) {
        cn_fast_hash(hash, data, l);
        sc_reduce32(hash.bytes);
    }

    //cn_fast_hash for a 32 byte key
    void cn_fast_hash(key & hash, const key & in) {
        keccak((uint8_t *)in.bytes, 32, hash.bytes, 32);
    }
    
    void hash_to_scalar(key & hash, const key & in) {
        cn_fast_hash(hash, in);
        sc_reduce32(hash.bytes);
    }

    //cn_fast_hash for a 32 byte key
    key cn_fast_hash(const key & in) {
        key hash;
        keccak((uint8_t *)in.bytes, 32, hash.bytes, 32);
        return hash;
    }
    
     key hash_to_scalar(const key & in) {
        key hash = cn_fast_hash(in);
        sc_reduce32(hash.bytes);
        return hash;
     }
    
    //cn_fast_hash for a 128 byte unsigned char
    key cn_fast_hash128(const void * in) {
        key hash;
        keccak((uint8_t *)in, 128, hash.bytes, 32);
        return hash;
    }
    
    key hash_to_scalar128(const void * in) {
        key hash = cn_fast_hash128(in);
        sc_reduce32(hash.bytes);
        return hash;
    }
    
    //cn_fast_hash for multisig purpose
    //This takes the outputs and commitments
    //and hashes them into a 32 byte sized key
    key cn_fast_hash(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++) {
            memcpy(&m[i * 64], &PC[i].dest, 32);
            memcpy(&m[i * 64 + 32], &PC[i].mask, 32);
        }
        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;
       for (i = 0 ; i < l ; i++) {
           memcpy(&m[i * 32], keys[i].bytes, 32);
       }
       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 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);
    }
}