Let N = pq be the product of two large primes. Consider Chinese remainder theorem-Rivest, Shamir, Adleman (CRT-RSA) with the public encryption exponent e and private decryption exponents dp, dq. It is well known that given any one of dp or dq (or both) one can factorise N in probabilistic poly(log N) time with success probability almost equal to 1. Though this serves all the practical purposes, from theoretical point of view, this is not a deterministic polynomial time algorithm. In this paper, we present a lattice-based deterministic poly(log N) time algorithm that uses both d p, dq (in addition to the public information e, N) to factorise N for certain ranges of dp, dq. We like to stress that proving the equivalence for all the values of dp, d q may be a nontrivial task. © 2012, DESIDOC.