Paper 2008/296

Cryptanalysis of Short Exponent RSA with Primes Sharing Least Significant Bits

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


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.

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Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
mn @ is cs nthu edu tw
2008-07-23: revised
2008-07-04: received
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      author = {Hung-Min Sun and Mu-En Wu and Ron Steinfeld and Jian Guo and Huaxiong Wang},
      title = {Cryptanalysis of Short Exponent RSA with Primes Sharing Least Significant Bits},
      howpublished = {Cryptology ePrint Archive, Paper 2008/296},
      year = {2008},
      note = {\url{}},
      url = {}
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