A Framework for Game-Based Security Proofs

David Nowak

Paper 2007/199

A Framework for Game-Based Security Proofs

David Nowak

Abstract

Information security is nowadays an important issue. Its essential ingredient is cryptography. A common way to present security proofs is to structure them as sequences of games. The main contribution of this paper is a framework which refines this approach. We make explicit important theorems used implicitly by cryptographers but never explicitly stated. Our aim is to have a framework in which proofs are precise enough to be mechanically checked, and readable enough to be humanly checked. We illustrate the use of our framework by proving in a systematic way the so-called semantic security of the encryption scheme ElGamal and its hashed version. All proofs have been mechanically checked in the proof assistant Coq.

Note: The source code is available at: http://staff.aist.go.jp/david.nowak/ICICS2007/ 28 May 2007: first public version 22 Jun 2007: added application to the hashed version of the encryption scheme ElGamal 1 Oct 2007: short version accepted at ICICS 2007: http://www.icics2007.org.cn/ 7 Nov 2007: added more explanations following comments by anonymous reviewers

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. A short version of this paper will appear in the proceedings of ICICS 2007
Keywords: sequence of games proof assistant formal verification monad probability
Contact author(s): david nowak @ aist go jp
History: 2007-11-07: last of 3 revisions; 2007-05-31: received; See all versions
Short URL: https://ia.cr/2007/199
License: CC BY

BibTeX

@misc{cryptoeprint:2007/199,
      author = {David Nowak},
      title = {A Framework for Game-Based Security Proofs},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/199},
      year = {2007},
      url = {https://eprint.iacr.org/2007/199}
}