--- In

primenumbers@yahoogroups.com,

"kad" <yourskadhir@...> wrote:

> Let N = pq be any semi-prime where factors p and q are unknown.

> 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.

No.

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.

David