void BuildSparseIrred(GF2X& f, long n)
{
if (n <= 0) Error("SparseIrred: n <= 0");
if (NTL_OVERFLOW(n, 1, 0))
Error("overflow in BuildSparseIrred");
if (n == 1) {
SetX(f);
return;
}
if (n <= 2048) {
if (GF2X_irred_tab[n][1] == 0) {
clear(f);
SetCoeff(f, n);
SetCoeff(f, GF2X_irred_tab[n][0]);
SetCoeff(f, 0);
}
else {
clear(f);
SetCoeff(f, n);
SetCoeff(f, GF2X_irred_tab[n][0]);
SetCoeff(f, GF2X_irred_tab[n][1]);
SetCoeff(f, GF2X_irred_tab[n][2]);
SetCoeff(f, 0);
}
return;
}
long k3, k2, k1;
k3 = FindTrinom(n);
if (k3) {
clear(f);
SetCoeff(f, n);
SetCoeff(f, k3);
SetCoeff(f, 0);
return;
}
k3 = FindPent(n, k2, k1);
if (k3) {
clear(f);
SetCoeff(f, n);
SetCoeff(f, k3);
SetCoeff(f, k2);
SetCoeff(f, k1);
SetCoeff(f, 0);
return;
}
// the following is probably of only theoretical value...
// it is reasonable to conjecture that for all n >= 2,
// there is either an irreducible trinomial or pentanomial
// of degree n.
BuildIrred(f, n);
}
NTL_CLIENT
int main()
{
ZZ_p::init(conv<ZZ>(17)); // define GF(17)
ZZ_pX P;
BuildIrred(P, 10); // generate an irreducible polynomial P
// of degree 10 over GF(17)
ZZ_pE::init(P); // define GF(17^10)
ZZ_pEX f, g, h; // declare polynomials over GF(17^10)
random(f, 20); // f is a random, monic polynomial of degree 20
SetCoeff(f, 20);
random(h, 20); // h is a random polynomial of degree less than 20
g = MinPolyMod(h, f); // compute the minimum polynomial of h modulo f
if (g == 0) Error("oops (1)"); // check that g != 0
if (CompMod(g, h, f) != 0) // check that g(h) = 0 mod f
Error("oops (2)");
}
NTL_CLIENT
int main()
{
zz_p::init(17);
zz_pX P;
BuildIrred(P, 10);
zz_pE::init(P);
zz_pEX f, g, h;
random(f, 20);
SetCoeff(f, 20);
random(h, 20);
g = MinPolyMod(h, f);
if (deg(g) < 0) Error("bad zz_pEXTest (1)");
if (CompMod(g, h, f) != 0)
Error("bad zz_pEXTest (2)");
vec_pair_zz_pEX_long v;
long i;
for (i = 0; i < 5; i++) {
long n = RandomBnd(20)+1;
cerr << n << " ";
random(f, n);
SetCoeff(f, n);
v = CanZass(f);
g = mul(v);
if (f != g) cerr << "oops1\n";
long i;
for (i = 0; i < v.length(); i++)
if (!DetIrredTest(v[i].a))
Error("bad zz_pEXTest (3)");
}
cerr << "\n";
cerr << "zz_pEXTest OK\n";
}
NTL_CLOSE_NNS
NTL_CLIENT
int main()
{
GF2X p;
BuildIrred(p, 200);
GF2E::init(p);
GF2EX f;
SetCoeff(f, 41);
SetCoeff(f, 1);
SetCoeff(f, 0);
GF2X a;
SetCoeff(a, 117);
SetCoeff(a, 10);
SetCoeff(a, 0);
GF2EX g, h;
SetX(g);
SetCoeff(g, 0, to_GF2E(a));
MinPolyMod(h, g, f);
f = h;
vec_pair_GF2EX_long u;
CanZass(u, f, 1);
cerr << "factorization pattern:";
long i;
for (i = 0; i < u.length(); i++) {
cerr << " ";
long k = u[i].b;
if (k > 1)
cerr << k << "*";
cerr << deg(u[i].a);
}
cerr << "\n\n\n";
GF2EX ff;
mul(ff, u);
if (f != ff || u.length() != 11) {
cerr << "GF2EXTest NOT OK\n";
return 1;
}
{
cerr << "multiplication test...\n";
BuildIrred(p, 512);
GF2E::init(p);
GF2EX A, B, C, C1;
random(A, 512);
random(B, 512);
double t;
long i;
t = GetTime();
for (i = 0; i < 10; i++) PlainMul(C, A, B);
t = GetTime() - t;
cerr << "time for plain mul of degree 511 over GF(2^512): " << (t/10) << "s\n";
t = GetTime();
for (i = 0; i < 10; i++) mul(C1, A, B);
t = GetTime() - t;
cerr << "time for karatsuba mul of degree 511 over GF(2^512): " << (t/10) << "s\n";
if (C != C1) {
cerr << "GF2EXTest NOT OK\n";
return 1;
}
}
{
cerr << "multiplication test...\n";
BuildIrred(p, 16);
GF2E::init(p);
GF2EX A, B, C, C1;
random(A, 512);
random(B, 512);
double t;
t = GetTime();
for (i = 0; i < 10; i++) PlainMul(C, A, B);
t = GetTime() - t;
cerr << "time for plain mul of degree 511 over GF(2^16): " << (t/10) << "s\n";
t = GetTime();
for (i = 0; i < 10; i++) mul(C1, A, B);
t = GetTime() - t;
cerr << "time for karatsuba mul of degree 511 over GF(2^16): " << (t/10) << "s\n";
if (C != C1) {
cerr << "GF2EXTest NOT OK\n";
return 1;
}
}
cerr << "GF2EXTest OK\n";
return 0;
}
int main()
{
/*initiation*/
int m = 16; int t = 9; int delta = 3;
int n= int(pow(double(2),double(m)));
GF2X gf2e_mod;
//BuildIrred(gf2e_mod,m); // randomly generate an irreducible polynomial over GF(2^m)
// fix the field polynomial to be f = x**16 + x**5 + x**3 + x**2 + 1
SetCoeff(gf2e_mod,16,1);
SetCoeff(gf2e_mod,5,1);
SetCoeff(gf2e_mod,3,1);
SetCoeff(gf2e_mod,2,1);
SetCoeff(gf2e_mod,0,1);
//cout << "GF_2m field_poly: " << gf2e_mod << endl;
GF2E::init(gf2e_mod);// construct GF(2^m)
GF2EX g;
BuildIrred(g,t); //generate goppa polynomial with t degree
GF2X g0, g1, g2, g3, g4, g5, g6, g7, g8, g9;
//g0=[0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1]
SetCoeff(g0,1,1);
SetCoeff(g0,2,1);
SetCoeff(g0,4,1);
SetCoeff(g0,6,1);
SetCoeff(g0,8,1);
SetCoeff(g0,9,1);
SetCoeff(g0,11,1);
SetCoeff(g0,12,1);
SetCoeff(g0,14,1);
SetCoeff(g0,15,1);
//g1=[0 1 1 1 0 0 1 1 1 1 0 0 1 0 1]
SetCoeff(g1,1,1);
SetCoeff(g1,2,1);
SetCoeff(g1,3,1);
SetCoeff(g1,6,1);
SetCoeff(g1,7,1);
SetCoeff(g1,8,1);
SetCoeff(g1,9,1);
SetCoeff(g1,12,1);
SetCoeff(g1,14,1);
//g2=[1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 1]
SetCoeff(g2,0,1);
SetCoeff(g2,1,1);
SetCoeff(g2,4,1);
SetCoeff(g2,5,1);
SetCoeff(g2,6,1);
SetCoeff(g2,8,1);
SetCoeff(g2,10,1);
SetCoeff(g2,11,1);
SetCoeff(g2,12,1);
SetCoeff(g2,13,1);
SetCoeff(g2,15,1);
//g3=[0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]
SetCoeff(g3,3,1);
SetCoeff(g3,4,1);
SetCoeff(g3,5,1);
SetCoeff(g3,6,1);
SetCoeff(g3,7,1);
SetCoeff(g3,8,1);
SetCoeff(g3,9,1);
SetCoeff(g3,10,1);
SetCoeff(g3,11,1);
SetCoeff(g3,12,1);
SetCoeff(g3,13,1);
SetCoeff(g3,14,1);
//g4=[1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1]
SetCoeff(g4,0,1);
SetCoeff(g4,1,1);
SetCoeff(g4,2,1);
SetCoeff(g4,3,1);
SetCoeff(g4,4,1);
SetCoeff(g4,6,1);
SetCoeff(g4,9,1);
SetCoeff(g4,11,1);
SetCoeff(g4,14,1);
SetCoeff(g4,15,1);
//g5=[1 1 0 0 1 0 1 0 1 1 1 0 1 1]
SetCoeff(g5,0,1);
SetCoeff(g5,1,1);
SetCoeff(g5,4,1);
SetCoeff(g5,6,1);
SetCoeff(g5,8,1);
SetCoeff(g5,9,1);
SetCoeff(g5,10,1);
SetCoeff(g5,12,1);
SetCoeff(g5,13,1);
//g6=[1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1]
SetCoeff(g6,0,1);
SetCoeff(g6,2,1);
SetCoeff(g6,3,1);
SetCoeff(g6,8,1);
SetCoeff(g6,10,1);
SetCoeff(g6,11,1);
SetCoeff(g6,12,1);
SetCoeff(g6,13,1);
SetCoeff(g6,15,1);
//g7=[0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1]
SetCoeff(g7,1,1);
SetCoeff(g7,3,1);
SetCoeff(g7,4,1);
SetCoeff(g7,5,1);
SetCoeff(g7,7,1);
SetCoeff(g7,8,1);
SetCoeff(g7,10,1);
SetCoeff(g7,12,1);
SetCoeff(g7,14,1);
SetCoeff(g7,15,1);
//g8=[0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1]
SetCoeff(g8,1,1);
SetCoeff(g8,4,1);
SetCoeff(g8,5,1);
SetCoeff(g8,10,1);
SetCoeff(g8,11,1);
SetCoeff(g8,12,1);
SetCoeff(g8,14,1);
SetCoeff(g8,15,1);
//g9=[1]
SetCoeff(g9,0,1);
SetCoeff(g,0,conv<GF2E>(g0));
SetCoeff(g,1,conv<GF2E>(g1));
SetCoeff(g,2,conv<GF2E>(g2));
SetCoeff(g,3,conv<GF2E>(g3));
SetCoeff(g,4,conv<GF2E>(g4));
SetCoeff(g,5,conv<GF2E>(g5));
SetCoeff(g,6,conv<GF2E>(g6));
SetCoeff(g,7,conv<GF2E>(g7));
SetCoeff(g,8,conv<GF2E>(g8));
SetCoeff(g,9,conv<GF2E>(g9));
cout << "goppa_poly: " << g << endl;
GF2EX g_square = g;
if (OPTION == "GoppaCode"){
GoppaCode goppacode(n,m,g_square);
GF2EX g = goppacode.GetGoppaPolynomial();
/*Timer starts*/
long beginTime = clock();
mat_GF2 message = GetRandomMessage(n-m*t);
//cout << "random message: " << message << endl;
mat_GF2 codeword = goppacode.Encode(message);
//cout << "codeword: " << codeword << endl;
mat_GF2 error = GetRandomMessageWithWeight(n,t);
//cout << "error: " << error << endl;
mat_GF2 ciphertext = codeword + error;
//cout << "ciphertext: " << ciphertext << endl;
/*Timer ends*/
long endTime = clock();
cout << "Encryption Time Elpased: " << double(endTime-beginTime)/CLOCKS_PER_SEC << endl;
//Decrypt the ciphertext using algebraic syndrome decoding algorihtm
/*Timer starts*/
beginTime = clock();
mat_GF2 recoveredtext1 = goppacode.Decode(ciphertext, "Euclidean");
//cout << "recovered message1: " << recoveredtext1 << endl;
/*Timer ends*/
endTime = clock();
cout << "Decryption Time Elpased(seconds): " << double(endTime-beginTime)/CLOCKS_PER_SEC << endl;
if (recoveredtext1 == codeword)
cout << "It works!" << endl;
else
cout << "Something wrong!" << endl;
//output the parity check matrix to the file
const char *path="/home/david/Dropbox/GoppaCode/Code_Based_Cryptography_Cplusplus/src/Data/ParityCheckMatrix.txt";
ofstream ParityCheckMatrix;
ParityCheckMatrix.open(path);
if (ParityCheckMatrix.is_open()){
ParityCheckMatrix << "Row: " << goppacode.GetGeneratorMatrix().NumRows()
<< "\t" << "Col: " << goppacode.GetGeneratorMatrix().NumCols() << endl;
/*for(int i = 0; i < t; i++){
for(int j = 0; j < n; j++){
ParityCheckMatrix << goppacode.GetParityCheckMatrixPoly()[i][j]<<"\t";
}
ParityCheckMatrix << endl;
}*/
ParityCheckMatrix << goppacode.GetParityCheckMatrixPoly();
ParityCheckMatrix.close();
}
else {
cout << "file not saved." << endl;
}
}
else if (OPTION == "McElieceCryptosystem"){
McElieceCryptosystem McEliece(n,m,g);
int k = McEliece.GetGoppaCode().GetGeneratorMatrix().NumRows();
mat_GF2 message = GetRandomMessage(k);
cout << "random message: " << endl;
mat_GF2 ciphertext = McEliece.Encrypt(message);
cout << "ciphertext: " << endl;
mat_GF2 recoveredtext1 = McEliece.Decrypt(ciphertext);
cout << "recovered message1: " << recoveredtext1 << endl;
if (recoveredtext1 == message)
cout << "It works!" << endl;
else
cout << "Something wrong!" << endl;
}
else if (OPTION == "NiederreiterCryptosystem"){
NiederreiterCryptosystem Niederreiter(n,m,g_square,delta);
//output the parity check matrix to the file
const char *path="/home/david/Dropbox/GoppaCode/Code_Based_Cryptography_Cplusplus/src/Data/NiederreiterPublicKey.txt";
//const char *path= "/Users/David/Dropbox/GoppaCode/Code_Based_Cryptography_Cplusplus/src/Data/NiederreiterPublicKey.txt";
ofstream PublicKeyMatrix;
PublicKeyMatrix.open(path);
/*mat_GF2 message = GetRandomMessageWithWeight(n,deg(g_square)/1);
getchar();
cout << "random message: " << message << endl;
vector<int> message_index;
for (int i = 0; i < message.NumCols(); i++)
if (message[0][i] == 1)
message_index.push_back(i);
if (PublicKeyMatrix.is_open()){
PublicKeyMatrix << "message_weight: " << message_index.size() << endl;
PublicKeyMatrix << "message_index: " << endl;
for (int i = 0; i < message_index.size(); i++)
PublicKeyMatrix << message_index[i] << "\t";
PublicKeyMatrix << endl;
//PublicKeyMatrix << message << endl;
PublicKeyMatrix << "ParityCheckMatrix Transposed: " << endl;
PublicKeyMatrix << transpose(Niederreiter.GetGoppaCode().GetParityCheckMatrix()) << endl;
PublicKeyMatrix.close();
}
else {
cout << "file not saved." << endl;
}
mat_GF2 ciphertext = Niederreiter.Encrypt(message);
cout << "ciphertext: " << ciphertext << endl;
getchar();
mat_GF2 recoveredtext1 = Niederreiter.Decrypt(ciphertext,"Patterson");
//cout << "recovered message1: " << recoveredtext1 << endl;
if (recoveredtext1 == message)
cout << "It works!" << endl;
else
cout << "Something wrong!" << endl;
getchar();
*/
//mat_GF2 message_hash = GetRandomMessage(m*deg(g_square));//length:m*t
mat_GF2 message_hash = GetRandomMessageWithWeight(n,10)*transpose(Niederreiter.GetGoppaCode().GetParityCheckMatrix());
cout << "hashed message: " << message_hash << endl;
if(PublicKeyMatrix.is_open()){
PublicKeyMatrix << "hashed message:" << endl;
PublicKeyMatrix << message_hash << endl;
}
PublicKeyMatrix.close();
getchar();
/*Timer starts*/
long beginTime = clock();
mat_GF2 signature = Niederreiter.Signature(message_hash,"random");
cout << "signature: " << signature << endl;
vector<int> signature_index;
for (int i = 0; i < signature.NumCols(); i++)
if (signature[0][i] == 1)
signature_index.push_back(i);
PublicKeyMatrix.open(path,ios::app);
PublicKeyMatrix << "signature index: " << signature_index.size() << endl;
for (int i = 0; i < signature_index.size(); i++)
PublicKeyMatrix << signature_index[i] << endl;
bool verification = Niederreiter.Verify(signature, message_hash);
cout << "Signature: " << verification << endl;
/*Timer ends*/
long endTime = clock();
PublicKeyMatrix.close();
cout << "Decryption Time Elpased(seconds): " << double(endTime-beginTime)/CLOCKS_PER_SEC << endl;
}
return 0;
}
