A Simple Improvement for Integer Factorizations with Implicit Hints

Abstract

SUMMARY In this paper, we describe an improvement of integer factorization of k RSA moduli N i = p i q i (1 ≤ i ≤ k) with implicit hints, namely all p i share their t least significant bits. May et al. reduced this problem to finding a shortest (or a relatively short) vector in the lattice of dimension k obtained from a given system of k RSA moduli, for which they applied Gaussian reduction or the LLL algorithm. In this paper, we improve their method by increasing the determinant of the lattice obtained from the k RSA moduli. We see that, after our improvement, May et al.'s method works smoothly with higher probability. We further verify the efficiency of our method by computer experiments for various parameters. key words: integer factorization with implicit hints

A new idea for RSA backdoors

“…In the following years many articles improved and extended the results of May and Ritzenhofen [39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]. See also a survey [56] published in 2018.…”