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Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem

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Pairing-Based Cryptography – Pairing 2009 (Pairing 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5671))

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Abstract

The Boneh-Boyen signature scheme is a pairing based short signature scheme which is provably secure in the standard model under the q-Strong Diffie-Hellman assumption. In this paper, we prove the converse of this statement, and show that forging Boneh-Boyen signatures is actually equivalent to solving the q-Strong Diffie-Hellman problem. Using this equivalence, we exhibit an algorithm which, on the vast majority of pairing-friendly curves, recovers Boneh-Boyen private keys in \(O(p^{\frac{2}{5}+\varepsilon})\) time, using \(O(p^{\frac{1}{5}+\varepsilon})\) signature queries. We present implementation results comparing the performance of our algorithm and traditional discrete logarithm algorithms such as Pollard’s lambda algorithm and Pollard’s rho algorithm. We also discuss some possible countermeasures and strategies for mitigating the impact of these findings.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    David Jao & Kayo Yoshida

Authors
  1. David Jao
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  2. Kayo Yoshida
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Editors and Affiliations

  1. Department of Computer Science and Engineering, University of California, San Diego, 9500 Gilman Drive, MC 0404, 92093-0404, La Jolla, CA, USA

    Hovav Shacham

  2. University of Texas at Austin Department of Computer Science, 1 University Station C0500 Taylor Hall 2.124, 78712-1188, Austin, TX, USA

    Brent Waters

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Jao, D., Yoshida, K. (2009). Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem. In: Shacham, H., Waters, B. (eds) Pairing-Based Cryptography – Pairing 2009. Pairing 2009. Lecture Notes in Computer Science, vol 5671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03298-1_1

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  • DOI: https://doi.org/10.1007/978-3-642-03298-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03297-4

  • Online ISBN: 978-3-642-03298-1

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