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A New Partial Key Exposure Attack on Multi-power RSA

  • Muhammed F. EsginEmail author
  • Mehmet S. Kiraz
  • Osmanbey Uzunkol
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9270)

Abstract

An important attack on multi-power RSA (\(N=p^rq\)) was introduced by Sarkar in 2014, by extending the small private exponent attack of Boneh and Durfee on classical RSA. In particular, he showed that N can be factored efficiently for \(r=2\) with private exponent d satisfying \(d<N^{0.395}\). In this paper, we generalize this work by introducing a new partial key exposure attack for finding small roots of polynomials using Coppersmith’s algorithm and Gröbner basis computation. Our attack works for all multi-power RSA exponents e (resp. d) when the exponent d (resp. e) has full size bit length. The attack requires prior knowledge of least significant bits (LSBs), and has the property that the required known part of LSB becomes smaller in the size of e. For practical validation of our attack, we demonstrate several computer algebra experiments.

Keywords

Multi-power RSA Integer factorization Partial key exposure Coppersmith’s method Small roots of polynomials 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Muhammed F. Esgin
    • 1
    • 2
    Email author
  • Mehmet S. Kiraz
    • 1
  • Osmanbey Uzunkol
    • 1
  1. 1.TÜBİTAK BİLGEM UEKAEKocaeliTurkey
  2. 2.Graduate School of Natural and Applied Sciencesİstanbul Şehir UniversityIstanbulTurkey

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