Block Ciphers And Cryptanalysis by FauzanMirza

By FauzanMirza

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Nevertheless, contrarily to message transducers for which an operational semantics exists and describes their ability to transform sets of messages, term transducers remain only a syntactic notion used in the definition of the TTL logic below. Term transducers w are intended to be interpreted, that is, given a ground substitution σ instantiateing all the free variables occurring in w, we shall denote by wσ the message transducer obtained from w by substituting all free variables according to σ, formally: (t1 , p1 ) · ...

1. Decidability of TTL∃ In the general case the satisfiability problem of a TTL formula is undecidable. It is easy to encode the Post’s correspondence problem as a satisfiability problem in TTL, as we show in [BEL05]. , formulae in TTL∃ ). Since we showed in the previous section given a formula ϕ in TTL∀ and a bounded cryptographic protocol Π, one can compute WLP(Π, ϕ), decidability of the satisfiability of existential formulae yields a decision procedure. Indeed, assume that we are given an existential formula ψ and a property ϕ in TTL∀ , assume also that we are given a bounded cryptographic protocol Π then {ψ}Π{ϕ} is true iff ψ ∧ ¬WLP(Π, ϕ) is not satisfiable.

Bounded number of sessions Let S = (P, act, fresh) be a protocol. In the bounded case, the semantics is defined by the parallel execution of a bounded number of instantiated sessions Sπi . 3 that an instantiated session is fixed by a pair (i, π) and is described by the set of instantiated action sequences. For the sake of uniformity, the set of instantiated actions is represented as a set of guarded commands. The ordering of actions is encoded as guards that bear as program counter. We represent explicitly control points using finite variables pcip , where p ∈ P is a principal parameter and i ∈ is a session identifier.

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