Prime Numbers

2.3 Squares and roots 101
}
x = a (p+3)/8 mod p;
c = x 2 mod p; // Then c ≡±a (mod p).
if(c = a mod p) x = x2 (p−1)/4 mod p;
return x;
2. [Case p ≡ 1(mod8)]
Find a random integer d ∈ [2,p− 1] with
d
p = −1;
// Compute Jacobi symbols via Algorithm 2.3.5.
Represent p − 1=2st, with t odd;
A = at mod p;
D = dt mod p;
m =0; // m will be 2µ of text discussion.
for(0 ≤ i