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Minkowski Sum Based Lattice Construction for Multivariate Simultaneous Coppersmith’s Technique and Applications to RSA

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Information Security and Privacy (ACISP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7959))

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Abstract

We investigate a lattice construction method for the Coppersmith technique for finding small solutions of a modular equation. We consider its variant for simultaneous equations and propose a method to construct a lattice by combining lattices for solving single equations. As applications, we consider a new RSA cryptanalysis. Our algorithm can factor an RSA modulus from ℓ ≥ 2 pairs of RSA public exponents with the common modulus corresponding to secret exponents smaller than N (9ℓ − 5)/(12ℓ + 4), which improves on the previously best known result by Sarkar and Maitra. For partial key exposure situation, we also can factor the modulus if β − δ/2 + 1/4 < (3ℓ − 1)(3ℓ + 1), where β and δ are bit-lengths / logN of the secret exponent and its exposed LSBs, respectively. Due to the spacing limit, some arguments are omitted; see the full-version [1].

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Authors and Affiliations

  1. National Institute of Information and Communications Technology, Japan

    Yoshinori Aono

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  1. Yoshinori Aono
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Editors and Affiliations

  1. Queensland University of Technology, 2434, 4001, Brisbane, QLD, Australia

    Colin Boyd  & Leonie Simpson  & 

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Aono, Y. (2013). Minkowski Sum Based Lattice Construction for Multivariate Simultaneous Coppersmith’s Technique and Applications to RSA. In: Boyd, C., Simpson, L. (eds) Information Security and Privacy. ACISP 2013. Lecture Notes in Computer Science, vol 7959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39059-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-39059-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39058-6

  • Online ISBN: 978-3-642-39059-3

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