//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 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 {
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;
}