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Reducing Protocol Analysis with XOR to the XOR-free Case in the Horn Theory Based Approach

Ralf Küsters and Tomasz Truderung

In the Horn theory based approach for cryptographic protocol analysis, cryptographic protocols and (Dolev-Yao) intruders are modeled by Horn theories and security analysis boils down to solving the derivation problem for Horn theories. This approach and the tools based on this approach, including ProVerif, have been very successful in the automatic analysis of cryptographic protocols. However, dealing with the algebraic properties of operators, such as the exclusive OR (XOR), which are frequently used in cryptographic protocols has been problematic. In particular, ProVerif cannot deal with XOR. In this paper, we show how to reduce the derivation problem for Horn theories with XOR to the XOR-free case. Our reduction works for an expressive class of Horn theories. A large class of intruder capabilities and protocols that employ the XOR operator can be modeled by these theories. Our reduction allows us to carry out protocol analysis using tools, such as ProVerif, that cannot deal with XOR, but are very efficient in the XOR-free case. We implemented our reduction and, in combination with ProVerif, used it for the fully automatic analysis of several protocols that employ the XOR operator. Among others, our analysis revealed a new attack on an IBM security module.