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