Logical Analysis and Verification of Cryptographic Protocols - Loria

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180 CHAPTER 7. VOTER VERIFIABILITY FOR E-VOTING PROTOCOLS The properties vote-privacy, receipt-freeness, coercion-resistance are called privacy-type properties [97] since they guarantee that the link between the voter and her vote is not revealed by the protocol. They are considered by S. Delaune, S. Kremer and M. Ryan [97]. The properties fairness, inalterability, eligibility are called correctness properties, and some of them have been considered by M. Backes, C. Hritcu and M. Maffei [25]. The properties individual verifiability, universal verifiability are called voter verifiability and some of them have been considered by B. Chevallier-Mames et al. [76], Baskar et al. [30], Talbi et al. [193]. We remark that verifiability properties are related to the correctness properties, but verifiability properties are intuitively stronger than correctness properties. They allow voters and observers to check that the outcome is correct without having to trust the protocol, the administrators or the implementation. In contrast, correctness properties merely assert good behaviour in case the expected protocol was indeed executed by all the participants, i.e. one has to trust the software and the administrators. 7.2 Applied pi calculus The applied pi calculus [11] is a language for describing concurrent systems and their interactions. It is based on the pi calculus [158, 159] which is a process calculus originally developed by R. Millen as a continuation of work on the process calculus CCS (Calculus of Communicating Systems). Th applied pi calculus is intended to be less pure than the pi calculus and therefore more convenient to use. The applied pi calculus is, in some sense, similar to the spi calculus [12]. The key difference between the two formalisms concerns the way the cryptographic primitives are handled. The spi calculus has a fixed set of primitives built-in (symmetric and public-key encryption), while the applied pi calculus allows one to define less usual primitives often used in electronic voting protocols, like zero knowledge proofs, by means of equational theory. The applied pi calculus has been used to study a variety of security protocols, such as a private authentication protocols [114], or a key establishment protocols [8], or electronic voting protocols [97]. In order to represent our properties, we slightly modify the applied pi calculus introduced in [11]. We assume an infinite set of names (which are used to name communication channels or other atomic data), an infinite set of variables and a finite signature Σ which consists of a finite set of function symbols each with an associated arity. A function symbol with arity 0 is a constant symbol. In the case of security protocols, typical function symbols will include enc for encryption, and dec for decryption. Terms are defined as names, variables, and function symbols applied to other terms. A terms is ground if it does not
7.2. APPLIED PI CALCULUS 181 contain variables. Although names, variables, and constant symbols haves similarities, they are kept separate. We let a, b, c, m, n, r, s, t, v . . . range over names and x, y, z, . . . over variables. We use metavariables u, w to range over both names and variables. F, L, M, N, R, T range over arbitrary terms. Terms and function symbols are sorted, and of course function symbol application must respect sorts and arities. We suppose that terms can be of sort Channel or Base type. Function symbols can only be applied to and return terms of base type. As a slight convenient extension, also introduced in [83], we suppose a set of predicates P over terms, each with an arity. In the applied pi calculus, one has plain processes and extended processes. Plain processes are built up in a similar way to processes in the pi calculus, except that messages can contain terms (rather than only names). The grammar for plain processes is shown below where c is supposed to be of channel sort: ψ ::= tests p(M1, . . . , Mn) predicate conjunction ψ1 ∧ ψ2 P, Q, V ::= processes 0 null process P | Q parallel composition ν n.P name restriction c(x).P message input c〈N〉.P message output if ψ then P else Q conditional The null process 0 does nothing; P | Q is the parallel composition of P and Q. the process ν n.P makes a new, private name n then behaves as P . The process c(x).P is ready to input from channel c, then to run P with the actual message replaced for the formal parameter x, while the process c〈N〉.P is ready to output N on channel c, then to run P . In all cases, we omit P when it is 0. Finally, if ψ then P else Q behaves in the standard way. Extended processes add active substitutions and restriction on variables, their grammar is shown below: A, B, C ::= extended processes P plain process A | B parallel composition ν n.A name restriction ν x.A variable restriction {M/x} active substitution We write {M/x} for the substitution that replaces the variable x with the term M. Active substitutions generalise ′ let ′ and the process ν x.({M/x} | P )
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Logical Analysis and Verification o
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Page 214 and 215: 202 BIBLIOGRAPHY [12] M. Abadi and
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Page 220 and 221: 208 BIBLIOGRAPHY [83] H. Comon-Lund
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