Logical relation for encryption

  • Authors:

  • Eijiro Sumii;Benjamin C. Pierce

  • Affiliations:

  • Department of Computer Science, Graduate School of Information Science and Technology, University of Tokyo, Rigaku-bu 7-gokan, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;Department of Computer and Information Science, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA

  • Venue:
  • Journal of Computer Security - Special issue on CSFW14
  • Year:
  • 2003

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Abstract

The theory of relational parametricity and its logical relations proof technique are powerful tools for reasoning about information hiding in the polymorphic λ-calculus. We investigate the application of these tools in the security domain by defining a cryptographic λ-calculus - an extension of the standard simply typed λ-calculus with primitives for encryption, decryption, and key generation - and introducing syntactic logical relations (in the style of Pitts and Birkedal-Harper) for this calculus that can be used to prove behavioral equivalences between programs that use encryption.We illustrate the framework by encoding some simple security protocols, including the Needham-Schroeder public-key protocol. We give a natural account of the well-known attack on the original protocol and a straightforward proof that the improved variant of the protocol is secure.