diff --git a/bin/ntt.o b/bin/ntt.o
new file mode 100644
index 0000000000000000000000000000000000000000..40679a382429fbc1a6bdbe246ab1e757cb8db3aa
Binary files /dev/null and b/bin/ntt.o differ
diff --git a/bin/seckey.o b/bin/seckey.o
index a4cfdc38f9f44fbab072cae7adc4365fde3b5734..257a327b70529a10066ffeb0315e9c7bb497942d 100644
Binary files a/bin/seckey.o and b/bin/seckey.o differ
diff --git a/comptest.sh b/comptest.sh
index a5908bd2734b83a8a9bc22118474b58a7b90f29a..c72f03683d76e76102f3ec3f05693a8a4e53d1cf 100755
--- a/comptest.sh
+++ b/comptest.sh
@@ -1,4 +1,4 @@
#!/bin/bash
g++ -c -o test.o test.cpp
-g++ -o run test.o ./bin/ciphertext.o ./bin/ckks.o ./bin/encoder.o ./bin/polynomial.o ./bin/pubkey.o ./bin/seckey.o ./bin/evalkey.o
\ No newline at end of file
+g++ -o run test.o ./bin/ciphertext.o ./bin/ckks.o ./bin/encoder.o ./bin/polynomial.o ./bin/pubkey.o ./bin/seckey.o ./bin/evalkey.o ./bin/ntt.o
\ No newline at end of file
diff --git a/run b/run
index 5d77c5dfd8013fe1aa2b97ea64d0029271bd1f2b..f8a7d286a7d0f4d0e133f53be7216f3c2821f13e 100755
Binary files a/run and b/run differ
diff --git a/src/ckks.cpp b/src/ckks.cpp
index 30e7d9d826eae96b9eb38a34047ae6e434d2e191..ec67b53929e96b45d204241282545ff5a06028c1 100644
--- a/src/ckks.cpp
+++ b/src/ckks.cpp
@@ -73,7 +73,7 @@ Ciphertext CKKS::mult(Ciphertext ct1, Ciphertext ct2){
Polynomial d2 = ((ct1.c0 * ct2.c1) + (ct2.c0 * ct1.c1)).modCoeff(ql);
Polynomial d3 = (ct1.c1 * ct2.c1).modCoeff(ql);
- // Relin --> Still weird
+ // Relin
Polynomial d3_0 = (d3 * evk.b).scaleRoundCoeff(1.0/1000.0);
Polynomial d3_1 = (d3 * evk.a).scaleRoundCoeff(1.0/1000.0);
diff --git a/src/compile.sh b/src/compile.sh
index 0bb493acf053a07abd5bd82ac9246398f42d056b..0c7adde5b9bf274114e1632fffa6412ab2463d1a 100755
--- a/src/compile.sh
+++ b/src/compile.sh
@@ -7,3 +7,4 @@ g++ -c -o ../bin/polynomial.o polynomial.cpp
g++ -c -o ../bin/pubkey.o pubkey.cpp
g++ -c -o ../bin/seckey.o seckey.cpp
g++ -c -o ../bin/evalkey.o evalkey.cpp
+g++ -c -o ../bin/ntt.o ntt.cpp
diff --git a/src/ntt.cpp b/src/ntt.cpp
index ea46e39f090b8533c454fb30006697c469a0c780..40be4f1d7c70eeed5024da63d00be543bf5578ce 100644
--- a/src/ntt.cpp
+++ b/src/ntt.cpp
@@ -18,41 +18,138 @@ int NTT::modExp(int base, int power, int mod){
int NTT::modInv(int x, int mod){
int t = 0;
int t1 = 1;
- int r, r1 = mod, x;
+ int r = mod;
+ int r1 = x;
while (r1 != 0){
int quot = (int) (r/r1);
- int temp_t1 = t1;
int temp_t = t;
- int temp_r1 = r1;
int temp_r = r;
- t, t1 = t1, (t - quot * t1);
- r, r1 = r1, (r % r1);
+ t = t1;
+ t1 = (temp_t - quot * t1);
+ r = r1;
+ r1 = (temp_r % r1);
}
-
- if (t<0){
+
+ if (t < 0){
t = t + mod;
}
return t;
}
-void NTT::_ntt(vector<int64_t> &in, bool inverse){
+int NTT::bitLength(int x){
+ int a = x;
+ int len = 0;
+ while (a!=0){
+ a >>= 1;
+ len += 1;
+ }
+ return len;
+}
+
+bool NTT::existSmallerN(int r, int mod, int n){
+ for(int k=2; k<n; k++){
+ if(modExp(r, k, mod) == 1){
+ return true;
+ }
+ }
+ return false;
+}
+
+int64_t NTT::genNthRoot(int mod, int n){
+ int p = mod - 1;
+ int range = mod - 1 + 1;
+ while (true){
+ int64_t a = rand() % range + 1;
+ int64_t b = modExp(a, p/n, mod);
+ if (!existSmallerN(b, mod, n)){
+ return b;
+ }
+ }
+}
+
+void NTT::reverse(vector<int64_t> &in, int bitLen){
+ for (int i=0; i<size(in); i++){
+ int revN = 0;
+ for(int j=0; j<bitLen ; j++){
+ if ((i >> j) & 1){
+ revN |= 1 << (bitLen-1-j);
+ }
+ }
+ int coeff = in[i];
+
+ if (revN > i){
+ coeff ^= in[revN];
+ in[revN] ^= coeff;
+ coeff ^= in[revN];
+ in[i] = coeff;
+ }
+ }
+}
+
+void NTT::_ntt(vector<int64_t> &in, int64_t w){
+ int N = size(in);
+ int nBit = bitLength(N) - 1;
+ reverse(in, nBit);
+
+ vector<int> points(N, 0);
+ for(int i=0; i<nBit; i++){
+ vector<int64_t> p1;
+ vector<int64_t> p2;
+ for(int j=0; j<N/2; j++){
+ int shift = nBit - i - 1;
+ int P = (j >> shift) << shift;
+ int wP = modExp(w, P, M);
+ int64_t odd = in[2*j+1] * wP;
+ int64_t even = in[2*j];
+ p1.push_back((even + odd) % M);
+ p2.push_back((even - odd) % M);
+ }
+
+ for(int k=0; k<N/2; k++){
+ points[k] = p1[k];
+ points[k+N/2] = p2[k];
+ }
+
+ if(1!=nBit){
+ for(int k=0; k<N; k++){
+ in[k] = points[k];
+ }
+ }
+ }
+ for(int k=0; k<N; k++){
+ in[k] = points[k];
+ if(in[k] < 0){
+ in[k] += M;
+ }
+ }
}
-vector<int64_t> NTT::ntt(Polynomial in){
- vector<int64_t> out(in.degree,0);
- _ntt(out, true);
+vector<int64_t> NTT::ntt(Polynomial in, int degree, int64_t w){
+ vector<int64_t> out(degree,0);
+ for(int i=0; i<degree; i++){
+ out[i] = (int64_t) in.coeffs[i];
+ }
+ _ntt(out, w);
return out;
}
-Polynomial NTT::intt(vector<int64_t> in){
- vector<int64_t> out(size(in),0);
- Polynomial pOut(size(out));
- int n_inv = modInv(size(out), M);
+Polynomial NTT::intt(vector<int64_t> &in, int w){
+ int N = size(in);
+ Polynomial pOut(N);
+ double coeff[N];
+
+ int wInv = modInv(w, M);
+ int nInv = modInv(N, M);
- _ntt(out,false);
+ _ntt(in, wInv);
+
+ for(int i=0; i<size(in); i++){
+ coeff[i] = (in[i] * nInv) % M;
+ }
+ pOut.setCoeffs(coeff);
return pOut;
}
\ No newline at end of file
diff --git a/src/ntt.h b/src/ntt.h
index 5f3646928ed19ba18c7fd9b0a0e3fb3805d3443c..74a6110ac3c456c214e46a32ceb1afea44bd1751 100644
--- a/src/ntt.h
+++ b/src/ntt.h
@@ -12,12 +12,16 @@ using namespace std;
class NTT{
public:
int g = 3;
- int M = 998244353;
+ int M = 2013265921;
int modExp(int base, int power, int mod);
int modInv(int x, int mod);
- void _ntt(vector<int64_t> &in, bool inverse);
- vector<int64_t> ntt(Polynomial in);
- Polynomial intt(vector<int64_t> in);
+ int bitLength(int x);
+ void reverse(vector<int64_t> &in, int bitLen);
+ bool existSmallerN(int r, int mod, int n);
+ int64_t genNthRoot(int mod, int n);
+ void _ntt(vector<int64_t> &in, int64_t w);
+ vector<int64_t> ntt(Polynomial in, int degree, int64_t w);
+ Polynomial intt(vector<int64_t> &in, int w);
};
diff --git a/src/polynomial.h b/src/polynomial.h
index 04e8de8d713e73e38ee069131d91cbcf4cdfd1ca..e1322333c7fc0c48318b7f977c04217ac7fb36c6 100644
--- a/src/polynomial.h
+++ b/src/polynomial.h
@@ -1,3 +1,4 @@
+#include<iostream>
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
diff --git a/test.cpp b/test.cpp
index bab3c670b54c25ccdf1a266938e22f2bf6f41ad3..ce8fe33fb82f8ad660557f307523923d57e547e6 100644
--- a/test.cpp
+++ b/test.cpp
@@ -2,6 +2,8 @@
#include "src/encoder.h"
#include "src/polynomial.h"
#include "src/ckks.h"
+#include "src/ntt.h"
+#include <vector>
#include <string>
@@ -57,5 +59,22 @@ int main(){
}
cout << endl;
+ cout << "NTT test" << endl;
+ NTT ntt;
+ int64_t w = 1728404513;
+ double coeff[] = {2, 1, 0, 0};
+ Polynomial n(4, coeff);
+
+ vector<int64_t> test = ntt.ntt(n, 4, w);
+ cout <<"test"<<endl;
+ for(int i=0;i<4;i++){
+ cout << test[i] << " ";
+ }
+ cout << endl;
+
+ cout <<"test"<<endl;
+ Polynomial testOut = ntt.intt(test, w);
+ testOut.printPol();
+
return 0;
}
\ No newline at end of file
diff --git a/test.o b/test.o
index 1fd77b778c7af00a5f6a8ead0a26b90c439a17f1..4a9916dc459ad9e40041cc478df7c8e32c0585b8 100644
Binary files a/test.o and b/test.o differ