International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Cryptanalysis of Short Exponent RSA with Primes Sharing Least Significant Bits

Hung-Min Sun
Mu-En Wu
Ron Steinfeld
Jian Guo
Huaxiong Wang
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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.
  title={Cryptanalysis of Short Exponent RSA with Primes Sharing Least Significant Bits},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / cryptanalysis},
  note={ 14083 received 3 Jul 2008, last revised 22 Jul 2008},
  author={Hung-Min Sun and Mu-En Wu and Ron Steinfeld and Jian Guo and Huaxiong Wang},