Re: Help on Semi-prime
- --- In firstname.lastname@example.org,
"kad" <yourskadhir@...> wrote:
> Let N = pq be any semi-prime where factors p and q are unknown.No.
> By knowing 'N' alone is it possible to find a and b such that
> a = b = k(mod p) and a = b = l(mod q) where k != l.
Explanation: by the CRT, the residue of 'a', modulo N, is unique.
Hence 'b' tells us nothing new, since b = a + m*N,
where 'm' is any integer. Knowledge of Mod(a,N) immediately
gives the factorization: N = gcd(N,a-k)*gcd(N,a-1),
so finding 'a' is as difficult as factorizing the semiprime N.