Logical Analysis and Verification of Cryptographic Protocols - Loria

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198 CHAPTER 8. CONCLUSION AND PERSPECTIVES these two properties. We first reduced the insecurity problem of our two classes of protocols to the reachability problem for our respective intruder deduction systems. We then provided a decision procedure, based on the saturation of intruder deduction systems, for the reachability problem. This decision procedure was then extended in Chapter 5 in order to capture a general class of cryptographic protocols: the class of protocols using cryptographic primitives represented by convergent equational theories with finite variant property. A simple generalisation of the decision procedure given in Chapter 4 allowed us to prove the decidability of the ground reachability problem for our class of deduction systems. Actually, we slightly modified the saturation algorithm introduced in Chapter 4, and showed that the termination of its application on our class of intruder deduction systems implies the decidability of the ground reachability problem. We also showed that this termination is not sufficient to prove the decidability of the general reachability problem. We then gave an additional syntactic condition on the deduction systems that allowed us to prove the decidability of the general reachability problem. As an application of our result, we gave an alternative proof for the decidability of the ground reachability problem for the blind signature theory. This decidability result has been initially proved in [9]. We also gave an alternative proof for the decidability of the general reachability problem for the subterm convergent theory, which is already proved in [31]. We note that in Chapter 5, we have only considered the class of convergent equational theories with finite variant property. We plan to extend the results of Chapter 5 to the class of AC-convergent equational theories with finite variant property. As showed in [86], such extention may include several theories such as the theory of exclusive or and the theory of abelian groups. We also plan to weaken the syntactic condition we assume on the deduction systems in order to prove the decidability of the general reachability problem. In Chapter 6, we showed the decidability of the ground entailment problem for a new class of clauses. This decidability result is obtained by generalising the saturation procedure given in Chapter 5, and it relies on the use of selected resolution and on some syntactic conditions on the atom and term orderings. We also showed how to use this result in order to decide the insecurity problem of cryptographic protocols in the case of bounded number of sessions. In future works, we plan to: 1. implement the decision procedure: with respect to the result of D. Basin and H. Ganzinger [28], we remark that for ground entailment problem, it suffices to consider inferences by selected resolution in which one of the atoms is ground. Thus we do not need to construct the set of ground atoms before solving an entailment problem. 2. extend this result to the case where the clauses are considered modulo an
equational theory, i.e. we reason modulo an equational theory on atoms and terms. 199 3. extend the application on cryptographic protocols from search of proofs to proof of correctness, and that by including the clauses describing the protocol to the set of clauses. 4. extend the application on cryptographic protocols to the unperfect cryptography hypothesis, and that by including the clauses describing the algebraic properties of primitives and the clauses representing the congruence relation to the set of clauses. In Chapter 7, we studied a new class of cryptographic protocols: the electronic-voting protocols, and in particular the voter verifiability property, which includes the individual verifiability and the universal verifiability properties. We formally defined these two properties using the applied pi calculus, and we applied our definition to the e-voting protocol due to Fujioka, Okamoto & Ohta [115] and the e-voting protocol due to Lee et al. [141]. In future works, we plan to: 1. extend the scope of e-voting protocols on which we apply our definition in order to capture more relevant protocols such as the protocol due to Okamoto [165], and the protocol due to D. Sandler et al. [182]. 2. extend the decidability results obtained on the saturated systems in order to prove the voter verifiability property. 3. analyse the e-voting protocols by taking into consideration algebraic properties of cryptographic primitives.
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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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Logical Analysis and Verification of Cryptographic Protocols - Loria

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