ringct: import of Shen Noether's ring confidential transactions

1 files changed, 533 insertions, 0 deletions

diff --git a/src/ringct/rctSigs.cpp b/src/ringct/rctSigs.cpp
new file mode 100644
index 000000000..d26678165
--- /dev/null
+++ b/src/ringct/rctSigs.cpp
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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);
+    }
+
+}