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International Conference on Information and Communications Security

ICICS 2012: Information and Communications Security pp 33–44Cite as

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Cryptanalysis of Multi-Prime RSA with Small Prime Difference

Cryptanalysis of Multi-Prime RSA with Small Prime Difference

  • Hatem M. Bahig18,
  • Ashraf Bhery18 &
  • Dieaa I. Nassr18 
  • Conference paper
  • 2082 Accesses

  • 9 Citations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7618)

Abstract

We show that the attack of de Weger on RSA using continued fractions extends to Multi-Prime RSA. Let (n,e) be a Multi-Prime RSA public-key with private key d, where n = p 1 p 2 ⋯ p r is a product of r distinct balanced (roughly of the same bit size) primes, and p 1 < p 2 < … < p r . We show that if p r  − p 1 = n α, 0 < α ≤ 1/r, r ≥ 3 and \(2d^2+1<\frac{n^{2/r - \alpha}}{6r},\) then Multi-Prime RSA is insecure.

Keywords

  • continued fractions
  • RSA
  • Multi-Prime RSA
  • Wiener’s attack
  • de Weger’s attack

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Author information

Authors and Affiliations

  1. Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, 11566, Egypt

    Hatem M. Bahig, Ashraf Bhery & Dieaa I. Nassr

Authors
  1. Hatem M. Bahig
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  2. Ashraf Bhery
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  3. Dieaa I. Nassr
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Hong Kong, Room 519, 5/F, Haking Building, Pokfulam Road, 852, Hong Kong, China

    Tat Wing Chim

  2. Department of Computer Science, The University of Hong Kong, Room 519, 5/F, Haking Wong Building, Pokfulam Road, 852, Hong Kong, China

    Tsz Hon Yuen

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© 2012 Springer-Verlag Berlin Heidelberg

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Bahig, H.M., Bhery, A., Nassr, D.I. (2012). Cryptanalysis of Multi-Prime RSA with Small Prime Difference. In: Chim, T.W., Yuen, T.H. (eds) Information and Communications Security. ICICS 2012. Lecture Notes in Computer Science, vol 7618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34129-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-34129-8_4

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