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);
}
//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 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;
}