Cryptanalysis of Short Exponent RSA with Primes Sharing Least Significant Bits

Abstract

LSBS-RSA denotes an RSA system with modulus primes, p and q , sharing a large number of least significant bits. In ISC 2007 , Zhao and Qi analyzed the security of short exponent LSBS-RSA. They claimed that short exponent LSBS-RSA is much more vulnerable to the lattice attack than the standard RSA. In this paper, we further raise the security boundary of the Zhao-Qi attack by considering another polynomial. Our improvemet supports the result of analogue Fermat factoring on LSBS-RSA, which claims that p and q cannot share more than $\frac{n}{4}$ least significant bits, where n is the bit-length of pq . In conclusion, it is a trade-off between the number of sharing bits and the security level in LSBS-RSA. One should be more careful when using LSBS-RSA with short exponents.