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International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2003: Advances in Cryptology — EUROCRYPT 2003 pp 401–415Cite as

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A Signature Scheme as Secure as the Diffie-Hellman Problem

A Signature Scheme as Secure as the Diffie-Hellman Problem

  • Eu-Jin Goh5 &
  • Stanisław Jarecki5 
  • Conference paper
  • First Online: 01 January 2003
  • 4411 Accesses

  • 67 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2656)

Abstract

We show a signature scheme whose security is tightly related to the Computational Diffie-Hellman (CDH) assumption in the Random Oracle Model. Existing discrete-log based signature schemes, such as ElGamal, DSS, and Schnorr signatures, either require non-standard assumptions, or their security is only loosely related to the discrete logarithm (DL) assumption using Pointcheval and Stern’s “forking” lemma. Since the hardness of the CDH problem is widely believed to be closely related to the hardness of the DL problem, the signature scheme presented here offers better security guarantees than existing discrete-log based signature schemes. Furthermore, the new scheme has comparable efficiency to existing schemes.

The signature scheme was previously proposed in the cryptographic literature on at least two occasions. However, no security analysis was done, probably because the scheme was viewed as a slight modification of Schnorr signatures. In particular, the scheme’s tight security reduction to CDH has remained unnoticed until now. Interestingly, this discrete-log based signature scheme is similar to the trapdoor permutation based PSS signatures proposed by Bellare and Rogaway, and has a tight reduction for a similar reason.

Keywords

  • Signature Schemes
  • Computational Diffie-Hellman
  • Discrete Logarithm
  • Exact Security
  • Tight Reductions
  • Random Oracle Model

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Author information

Authors and Affiliations

  1. Computer Science Department, Stanford University, Stanford, CA, 94305-9045

    Eu-Jin Goh & Stanisław Jarecki

Authors
  1. Eu-Jin Goh
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  2. Stanisław Jarecki
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technion — Israel Institute of Technology, Haifa, 32000, Israel

    Eli Biham

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© 2003 International Association for Cryptologic Research

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Cite this paper

Goh, EJ., Jarecki, S. (2003). A Signature Scheme as Secure as the Diffie-Hellman Problem. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_25

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  • DOI: https://doi.org/10.1007/3-540-39200-9_25

  • Published: 13 May 2003

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14039-9

  • Online ISBN: 978-3-540-39200-2

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