Cryptology ePrint Archive: Report 2006/323

Computational Soundness of Formal Indistinguishability and Static Equivalence

Gergei Bana and Payman Mohassel and Till Stegers

Abstract: In the research of the relationship between the formal and the computational view of cryptography, a recent approach uses static equivalence from cryptographic pi calculi as a notion of formal indistinguishability. Previous work has shown that this yields the soundness of natural interpretations of some interesting equational theories, such as certain cryptographic operations and a theory of XOR. In this paper however, we argue that static equivalence is too coarse for sound interpretations of equational theories in general. We show some explicit examples how static equivalence fails to work in interesting cases. To fix this problem, we propose a notion of formal indistinguishability that is more flexible than static equivalence. We provide a general framework along with general theorems, and then discuss how this new notion works for the explicit examples where static equivalence failed to ensure soundness. We also improve the treatment by using ordered sorts in the formal view, and by allowing arbitrary probability distributions of the interpretations.

Category / Keywords: foundations / formal method, computational method, soundness

Publication Info: A shorter version was presented at ASIAN 2006.

Date: received 25 Sep 2006, last revised 9 Jan 2007

Contact author: bana at math upenn edu

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Version: 20070109:232923 (All versions of this report)

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