Paper 2007/199

A Framework for Game-Based Security Proofs

David Nowak


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: 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: 7 Nov 2007: added more explanations following comments by anonymous reviewers

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Published elsewhere. A short version of this paper will appear in the proceedings of ICICS 2007
sequence of gamesproof assistantformal verificationmonadprobability
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david nowak @ aist go jp
2007-11-07: last of 3 revisions
2007-05-31: received
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      author = {David Nowak},
      title = {A Framework for Game-Based Security Proofs},
      howpublished = {Cryptology ePrint Archive, Paper 2007/199},
      year = {2007},
      note = {\url{}},
      url = {}
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