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Partial Key Exposure on RSA with Private Exponents Larger Than N

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Information Security Practice and Experience (ISPEC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7232))

Abstract

In 1998, Boneh, Durfee and Frankel described several attacks against RSA enabling an attacker given a fraction of the bits of the private exponent d to recover all of d. These attacks were later improved and extended in various ways. They however always consider that the private exponent d is smaller than the RSA modulus N. When it comes to implementation, d can be enlarged to a value larger than N so as to improve the performance (by lowering its Hamming weight) or to increase the security (by preventing certain side-channel attacks). This paper studies this extended setting and quantifies the number of bits of d required to mount practical partial key exposure attacks. Both the cases of known most significant bits (MSBs) and least significant bits (LSBs) are analyzed. Our results are based on Coppersmith’s heuristic methods and validated by practical experiments run through the SAGE computer-algebra system.

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Author information

Authors and Affiliations

  1. Technicolor, Security & Content Protection Labs, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné Cedex, France

    Marc Joye

  2. CryptoExperts, 41 boulevard des Capucines, 75002, Paris, France

    Tancrède Lepoint

  3. Laboratoire d’Informatique de l’École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Tancrède Lepoint

Authors
  1. Marc Joye
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  2. Tancrède Lepoint
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Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, UK

    Mark D. Ryan

  2. Toshiba Corporation, 1, Komukai-Toshiba–Cho, 212-8582, Saiwai-ku, Kawasaki, Japan

    Ben Smyth

  3. School of Computer Science & Software Engineering, University of Wollongong, Northfields Avenue, 2522, Wollongong, NSW, Australia

    Guilin Wang

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Joye, M., Lepoint, T. (2012). Partial Key Exposure on RSA with Private Exponents Larger Than N . In: Ryan, M.D., Smyth, B., Wang, G. (eds) Information Security Practice and Experience. ISPEC 2012. Lecture Notes in Computer Science, vol 7232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29101-2_25

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  • DOI: https://doi.org/10.1007/978-3-642-29101-2_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29100-5

  • Online ISBN: 978-3-642-29101-2

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