Ping-Pong Protocols as Prefix Grammars and Turchin Relation

Abstract

This paper describes how to verify cryptographic protocols by a general-purpose program transformation technique with unfolding. The questions of representation and analysis of the protocols as prefix rewriting grammars are discussed. In these aspects Higman and Turchin embeddings on computational paths are considered, and a refinement of Turchin's relation is presented that allows to algorithmically decide the empty word problem for prefix rewriting grammars.

Verification of Multi-Party Ping-Pong Protocols via Program Transformation

“…The methods presented in [9] can be also applied to the case of Dolev-Yao models with more than two legal parties but the computational complexity of the verification process grows exponentially with the number of parties [5]. In this paper we generalize the results from the paper [9] and show some methods to decrease the complexity of the verification process.…”

“…In particular, the model does not take into account the Church-Rosser property of the ping-pong protocols over the var-operator algebra with the freeness assumption: in the model presented in [9] an application of a single operator string corresponds to a set consisting of numerous rules, most of which are redundant. E.g.…”

“…Let us consider G 2EXP = {a, b, c, A, B, C, e}, R 2EXP , e with the following R 2EXP : R [1] : e → aA R [5] : AA → Λ R [9] : Ba → bB R [2] : Λ → aA R [6] : BB → Λ R [10] : Cb → cC R [3] : Λ → bB R [7] : CC → Λ R [4] : Λ → cC R [8] : c → Λ…”

“…We refine the method described in the paper [9] in such a way that the notion of time indexing becomes unnecessary in the model.…”

“…In our previous work [9] we showed a way to construct Dolev-Yao models of ping-pong protocols via the language of prefix grammars and described how to verify the models by a general purpose program transformation technique with unfolding. The methods presented in [9] can be also applied to the case of Dolev-Yao models with more than two legal parties but the computational complexity of the verification process grows exponentially with the number of parties [5].…”