Discrete-Log-Based signatures may not be equivalent to discrete log

  • Authors:
  • Pascal Paillier;Damien Vergnaud

  • Affiliations:
  • Gemplus Card International, Advanced Cryptographic Services, Issy-les-Moulineaux, France;Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, Caen, France

  • Venue:
  • ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
  • Year:
  • 2005

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Abstract

We provide evidence that the unforgeability of several discrete-log based signatures like Schnorr signatures cannot be equivalent to the discrete log problem in the standard model. This contradicts in nature well-known proofs standing in weakened proof methodologies, in particular proofs employing various formulations of the Forking Lemma in the random oracle Model. Our impossibility proofs apply to many discrete-log-based signatures like ElGamal signatures and their extensions, DSA, ECDSA and KCDSA as well as standard generalizations of these, and even RSA-based signatures like GQ. We stress that our work sheds more light on the provable (in)security of popular signature schemes but does not explicitly lead to actual attacks on these.