Computationally sound analysis of protocols using bilinear pairings

  • Authors:
  • Steve Kremer;Laurent Mazaré

  • Affiliations:
  • LSV, ENS Cachan & CNRS & INRIA, Cachan, France. E-mail: kremer@lsv.ens-cachan.fr;LexiFi SAS, Boulogne-Billancourt, France. E-mail: laurent.mazare@polytechnique.org

  • Venue:
  • Journal of Computer Security - 7th International Workshop on Issues in the Theory of Security (WITS'07)
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper, we introduce a symbolic model to analyse protocols that use a bilinear pairing between two cyclic groups. This model consists in an extension of the Abadi-Rogaway logic and we prove that the logic is still computationally sound: symbolic indistinguishability implies computational indistinguishability provided that the Bilinear Decisional Diffie-Hellman assumption holds and that the encryption scheme is IND-CPA secure. We illustrate our results on classical protocols using bilinear pairing like Joux tripartite Diffie-Hellman protocol or the TAK-2 and TAK-3 protocols. We also investigate the security of a newly designed variant of the Burmester-Desmedt protocol using bilinear pairings. More precisely, we show for each of these protocols that the generated key is indistinguishable from a random element.