**Cryptanalysis of Short Exponent RSA with Primes Sharing Least Significant Bits**

*Hung-Min Sun, Mu-En Wu, Ron Steinfeld, Jian Guo, and Huaxiong Wang*

**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 point out that there exist some errors in the calculation of Zhao & Qi's attack. After re-calculating, the result shows that their attack is unable for attacking RSA with primes sharing bits. Consequently, we give a revised version to make their attack feasible. We also propose a new method to further extend the security boundary, compared with the revised version. The proposed attack also supports the result of analogue Fermat factoring on LSBS-RSA, which claims that p and q cannot share more than (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.

**Category / Keywords: **public-key cryptography / cryptanalysis

**Date: **received 3 Jul 2008, last revised 22 Jul 2008

**Contact author: **mn at is cs nthu edu tw

**Available format(s): **PDF | BibTeX Citation

**Version: **20080723:014411 (All versions of this report)

**Short URL: **ia.cr/2008/296

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