//we don't have to bother with making sure that gcd(R,M) == 1 since M is odd.
uberzahl modexp_mm(mm_t & mm, uberzahl base, uberzahl exp, uberzahl M){
if(!mm.initialized){
mm.R = next_power(M);
mm.Rbits = mm.R.bitLength();
mm.Mprime = (mm.R-M.inverse(mm.R));
uberzahl z("1");
uberzahl t("2");
mm.Rsq = modexp(mm.R,t,M);
//mm.z_init = mm.R % M;
mm.z_init = montgomery_reduction(mm.Rsq, M, mm.Mprime, mm.Rbits, mm.R);
mm.initialized = true;
}
//convert into Montgomery space
uberzahl z = mm.z_init;
//According to Piazza post we don't even need to calculate the residues with mod
if(base * mm.Rsq < mm.R*M)
base = montgomery_reduction(base * mm.Rsq, M, mm.Mprime, mm.Rbits, mm.R);
else
base = base * mm.R % M;
mediumType i = exp.bitLength() - 1;
while(i >= 0) {
z = montgomery_reduction(z * z, M, mm.Mprime, mm.Rbits, mm.R);
if(exp.bit(i) == 1){
z = montgomery_reduction(z * base , M, mm.Mprime, mm.Rbits, mm.R);
}
if(i == 0)
break;
i -= 1;
}
return montgomery_reduction(z, M, mm.Mprime, mm.Rbits, mm.R);
}
uberzahl originalModExp(uberzahl c, uberzahl a, uberzahl p, uberzahl q){
//a^c mod pq
auto start = chrono::steady_clock::now();
uberzahl z = 1;
uberzahl n = p*q;
unsigned int numBits = c.bitLength();
unsigned int currentBit = 1;
for (unsigned int i = 0; i < numBits; i++){
z = (z*z) % n;
currentBit = c.bit(numBits-i-1);
if (currentBit == 1)
z = (z*a) % n;
}
if(q > 1){
auto current = chrono::steady_clock::now();
auto elapsed = chrono::duration_cast<chrono::duration<double>>(current-start);
double chrono_time = elapsed.count();
cerr << "\tSqMultOrig time: " << chrono_time << "\n";
}
return z;
}
uberzahl modexp_mm_crt(mm_t & mm1, mm_t & mm2, crt_t & crt, uberzahl base, uberzahl exp, uberzahl p, uberzahl q){
if(!crt.initialized){
crt.p_inverse = p.inverse(q);
crt.q_inverse = q.inverse(p);
crt.initialized = true;
}
return ( crt_helper(MONTGOMERY,mm1,base,exp,p,q, crt.q_inverse) + crt_helper(MONTGOMERY, mm2, base, exp, q, p, crt.p_inverse) ) % (p * q);
}
uberzahl modexp_crt(crt_t & crt, uberzahl base, uberzahl exp, uberzahl p, uberzahl q){
mm_t mm;
if(!crt.initialized){
crt.p_inverse = p.inverse(q);
crt.q_inverse = q.inverse(p);
crt.initialized = true;
}
return ( crt_helper(CLASSIC,mm, base,exp,p,q,crt.q_inverse) + crt_helper(CLASSIC, mm, base, exp, q, p, crt.p_inverse) ) % (p * q);
}
inline void ReduceZ(){
// m = (z*NPrime) % R;
m = (z*NPrime) & (( (uberzahl)1 << (R.bitLength()-1) )-(uberzahl)1);
t = (z + m*N) >> (R.bitLength()-1);
if(t >= N)
z = (t-N);
else
z = (t);
}
void encrypt(const uberzahl &m, uberzahl &r, uberzahl &s)
{
//Encrypts m,
//Modifies r, s to the outputs of the encryption
uberzahl low = 2;
uberzahl high = prime - 2;
uberzahl k = random(low, high);
r = generator.expm(k, prime);
s = m * y.expm(k,prime) % prime;
}
uberzahl modexp(uberzahl base, uberzahl exp, uberzahl n){
mediumType i = exp.bitLength() - 1;
uberzahl z((largeType)1);
while(i >= 0){
z = (z * z ) % n;
if(exp.bit(i) == 1)
z = (z * base) % n;
if(i == 0)
break;
i -= 1;
}
return z;
}
uberzahl increment (uberzahl x) {
// Extract and "increment" least significant 32 bits from x
uberzahl leastSigBits = betterExtract(x, 0, 31) + 1;
uberzahl modulo = 4294967296;
leastSigBits = leastSigBits % modulo;
// Set least significant bits in x
for (int i = 0; i < 32; ++i) {
if(leastSigBits.bit(i) == 0) {
x.clearBit(i);
}
else {
x.setBit(i);
}
}
return x;
}
uberzahl decrypt(const uberzahl &r, const uberzahl &s, uberzahl &m)
{
//Takes in r, s and decrypts them
//modifies m to the decrypted ciphertext value
uberzahl rx = r.expm(x, prime);
m = s * rx.inverse(prime) % prime;
return m;
}
uberzahl chineseModExp2(uberzahl c, uberzahl a, uberzahl p, uberzahl q){
//a^c mod pq
auto start = chrono::steady_clock::now();
uberzahl dp = c % (p-1);
uberzahl dq = c % (q-1);
uberzahl T = q.inverse(p);
uberzahl S = p.inverse(q);
uberzahl m1 = originalModExp(dp,a,p,1);
uberzahl m2 = originalModExp(dq,a,q,1);
uberzahl m = (m1*q*T + m2*p*S) % (p*q);
auto current = chrono::steady_clock::now();
auto elapsed = chrono::duration_cast<chrono::duration<double>>(current-start);
double chrono_time = elapsed.count();
cerr << "\tSqMult_CRT time: " << chrono_time << "\n";
return m;
}
vector<uberzahl> Speck::generateKeys(){
vector<uberzahl> keySeed;
uberzahl lowerBound = two.exp(n - 1) - one;
uberzahl upperBound = two.exp(n + 1) - one;
for(int i = 0; i < m; i++){
keySeed.push_back(random(lowerBound, upperBound) & modulus);
}
keyExpansion(keySeed);
return keySeed;
}
uberzahl multiply (uberzahl x, uberzahl y) {
uberzahl z, v = y, r = "299076299051606071403356588563077529600";
for (int i = 127; i >= 0; --i) {
// Set z block
if (x.bit(i) == 0) {
z = z;
}
else {
z = z ^ v;
}
// Set v block
if (v.bit(0) == 0) {
v = v >> 1;
}
else {
elGamal()
{
//Initializes all of the required values using a 128-bit prime
srand(time(NULL));
uberzahl temp = 2;
minPrime = temp.exp(126);
temp = 2;
maxPrime = temp.exp(127);
prime = getPrime(minPrime, maxPrime);
uberzahl low = 2;
uberzahl high = prime - 2;
x = random(low, high);
generator = gen(prime);
y = generator.expm(x, prime);
}
int main(int argc, char **argv){
srand(time(0));
//uberzahl new_key = generate();
vector<uberzahl> k;
vector<uberzahl> plaintext_vector;
vector<uberzahl> ciphertext_vector;
uberzahl ciphertext;
uberzahl plaintext;
uberzahl zero = "0";
if(strcmp(argv[1],"encrypt") == 0)
{
key = argv[2];
if(key.bitLength() > 256)
{
cout << "key bit length is more than 256 bit, please see README file." << endl;
return 0;
}
plaintext = argv[3];
//For test the result
// k.push_back(0x1f1e1d1c1b1a1918);
// k.push_back(0x1716151413121110);
// k.push_back(0x0f0e0d0c0b0a0908);
// k.push_back(0x0706050403020100);
// key = (k[0] << (3*n)) | (k[1] << (2*n)) | (k[2] << (n)) | k[3];
// plaintext = 0x74206e69206d6f6f;
// plaintext = (plaintext << n) | 0x6d69732061207369;
int num_block = 0;
uberzahl result;
uberzahl temp;
while(plaintext != zero)
{
temp = plaintext & take_128_bit;
plaintext = plaintext >> (2*n);
result = encrypt(temp, key);
ciphertext = ciphertext | (result << num_block*(2*n));
num_block++;
}
cout << "The ciphertext is: " << endl;
cout << ciphertext << endl;
}
//x is a random number 0 < x < q - private key
void pqgGen(uberzahl & p, uberzahl & q, uberzahl & g) {
//find a L-bit long p prime
/* uberzahl rand;
p = 2;
rand.random(L);
string p_string = rand.convert_to_string();
mpz_class p_mpz(p_string, 10);
while(p.bitLength() != L) {
mpz_nextprime(p_mpz.get_mpz_t(), p_mpz.get_mpz_t());
p_string = p_mpz.get_str(10);
p = p_string.c_str();
}
cout<<p<<endl;
*/
//find an N bit q such that p-1 divides q
//method 1
/* rand.random(N);
string q_string = rand.convert_to_string();
mpz_class q_mpz(q_string, 10);
while(q.bitLength() != N || (((p-1)%q) != zero)) {
mpz_nextprime(q_mpz.get_mpz_t(), q_mpz.get_mpz_t());
q_string = q_mpz.get_str(10);
q = q_string.c_str();
cout<<1<<endl;
}
cout<<q<<endl;
*/
//method2
/* uberzahl two = 2;
uberzahl lower_bound = two.exp(N-1);
q = lower_bound;
mpz_class q_mpz(q.convert_to_string(), 10);
string q_string;
while(((p-1) % q) != zero) {
mpz_nextprime(q_mpz.get_mpz_t(), q_mpz.get_mpz_t());
q_string = q_mpz.get_str(10);
q = q_string.c_str();
if (q.bitLength() != N) {
cout<<"no such q exists"<<endl;
exit(1);
}
cout<<1<<endl;
}
cout<<q<<endl;
cout<<2<<endl;
*/
string p_string, q_string;
mpz_class p_mpz;
uberzahl rand;
bool none = 0;
while(1) {
//find random N bit prime q
do {
rand.random(N);
q = nextprime(rand, 10);
q_string = q.convert_to_string();
q = q_string.c_str();
}
while (q.bitLength() != N);
mpz_class q_mpz(q_string, 10);
mpz_class mult_mpz = 3;
while (1) {
mpz_class product_mpz = mult_mpz * q_mpz;
//if product is odd -> no way product+1 is prime
if ((product_mpz % 2) == one) {
mult_mpz = mult_mpz + 1;
continue;
}
//this number should be p-1
mpz_class product_1_mpz = product_mpz + 1;
//check if p is a prime
uberzahl product = (product_mpz.get_str(10)).c_str();
uberzahl product_1 = (product_1_mpz.get_str(10)).c_str();
//missing 1 bit
if (product.bitLength() == L-1) {
mult_mpz = mult_mpz * 2;
}
//increment mult if mult not big enough
if (product.bitLength() < L) {
double diff = L - product.bitLength();
mult_mpz = mult_mpz * diff;
}
//increment multi if mult is not big enough
//mult too high? find other q
if (product.bitLength() > L) {
none = 1;
break;
}
//if it is of bitlength N --> check product if it is a prime
if (mpz_probab_prime_p(product_1_mpz.get_mpz_t(), 10) > 0) {
//found a right p
p_string = product_1_mpz.get_str(10);
p = p_string.c_str();
break;
}
else {
mult_mpz = mult_mpz + 1;
}
}
if (none) {
none = 0;
continue;
}
else
break;
}
// while (q.bitLength() != N || ((p-1) % q) != zero ) {
// rand.random(N);
// uberzahl rand = random(lower_bound, upper_bound);
// q = nextprime(rand, 20); // this is gonna EVEN slower
// }
//find g with multiplicative order modulo p = q
uberzahl h = 20;
g = 1;
while (g == 1) {
uberzahl c = ((p-1)/q);
g = h.expm(c, p);
h = h + 1;
if (h == (p-1)) {
cout<<"no such generator g"<<endl;
exit(1);
}
}
}