Abstract. In the research of the relationship between the formal and the computational view of cryptography, a recent approach, first proposed in [9] , uses static equivalence from cryptographic pi calculi as a notion of formal indistinguishability. Previous work [9, 1] 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.
In REF , Bana et al. argue that the notion of static equivalence is too coarse and not sound for many interesting equational theories.
Computational Soundness of Formal Indistinguishability and Static Equivalence
IN PROC. 11TH ASIAN COMPUTING SCIENCE CONFERENCE (ASIAN’06), LNCS
Mathematics Computer Science