Analytical cryptanalysis upon N = p.sup.2q utilizing Jochemsz-May strategy

This paper presents a cryptanalytic approach on the variants of the RSA which utilizes the modulus N = p.sup.2 q where p and q are balanced large primes. Suppose e[element of]Z+ satisfying gcd(e, [PHI](N)) = 1 where [PHI](N) = p(p - 1)(q - 1) and d < N.sup.[delta] be its multiplicative inverse. From ed - k[PHI](N) = 1, by utilizing the extended strategy of Jochemsz and May, our attack works when the primes share a known amount of Least Significant Bits(LSBs). This is achievable since we obtain the small roots of our specially constructed integer polynomial which leads to the factorization of N. More specifically we show that N can be factored when the bound [delta]119-294+18[gamma]. Our attack enhances the bound of some former attacks upon N = p.sup.2 q.