Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem

  • David Jao
  • Kayo Yoshida
Conference paper

DOI: 10.1007/978-3-642-03298-1_1

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5671)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • David Jao
    • 1
  • Kayo Yoshida
    • 1
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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