Analytical cryptanalysis upon N = p2q utilizing Jochemsz-May strategy

This paper presents a cryptanalytic approach on the variants of the RSA which utilizes the modulus N = p 2 q where p and q are balanced large primes. Supposee ∈ Z +satisfying gcd( e , ϕ ( N )) = 1 where ϕ ( N ) = p ( p − 1)( q − 1) and d < N δ be its multiplicative inverse. From ed − kϕ ( 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 boundδ < 11 9 − 2 94 + 18 γ. Our attack enhances the bound of some former attacks upon N = p 2 q .