Logical Analysis and Verification of Cryptographic Protocols - Loria

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16 CHAPTER 1. INTRODUCTION the ordered satisfiability problem for the intruder exploiting the collision vulnerability property of hash functions can be reduced to the ordered satisfiability problem for an intruder operating on words, that is with an associative symbol of concatenation. We show the decidability of the last problem, which is interesting in its own as it is the first decidability result that we are aware of for an intruder system for which unification is infinitary. Furthermore, it permits one to consider in other contexts an associative concatenation of messages instead of their pairing. Chapter 4: Analysis of protocols with vulnerable digital signature schemes. In chapter 4, we study two classes of cryptographic protocols: the class of protocols using digital signature schemes vulnerable to constructive exclusive ownership property, and the class of protocols using digital signature schemes vulnerable to destructive exclusive ownership property. The constructive exclusive ownership vulnerability property for a digital signature schemes permits the intruder, given a public verification key and a signed message, to compute a new pair of signature and verification keys such that the message appears to be signed with the new signature key; and the destructive exclusive ownership vulnerability property for a digital signature schemes permits the intruder, given a public verification key and a signed message, to compute a new pair of signature and verification keys, and a new message, such that the given signature appears to be the signature of the new computed message with the new signature key. We show the decidability of the insecurity problem for these two classes of cryptographic protocols, and that by reducing the insecurity problem to the reachability problem for our intruder deduction systems. Chapter 5: Decidability results for saturated deduction systems. In chapter 5, we generalise the results obtained in Chapter 4. We consider the class of cryptographic protocols where the cryptographic primitives are represented by equational theories generated by convergent rewrite systems having the finite variant property. This property has been introduced in [86], and means that one can compute all possible normal forms of the instances of a term t. First, we show the decidability of the ground reachability problem for our class of deduction systems. This decidability result is obtained by (1) reducing the reachability problem modulo an equational theory to the reachability problem modulo the empty theory, (2) computing a transitive closure of the possible deductions (using a saturation procedure), and (3) showing that the termination of this computation implies the decidability of the ground reachability problem. Next, we give a new criterion, based on counting the number of variables in a reachability problem before and after a deduction is guessed, that permits
1.5. CONTRIBUTIONS AND PLAN OF THIS THESIS 17 us to reduce the general reachability problem to the ground reachability problem. This criterion is a generalisation of the one employed for the specific cases in Chapter 4, and we give an example showing that such additional criterion is needed, that is the decidability of the ground reachability problem without this criterion does not imply the decidability of the general reachability problem. Another contribution of this chapter is a decidability result of the ground reachability problem for the theory of blind signature [136], and a decidability result of the general reachability problem for a class of subterm convergent equational theories. Other decidability results have been obtained for the theory of blind signature in [9, 91] but they are different from our. Similarly, a more general decidability result for the subterm convergent theory was given in [31], but our proofs are simpler and can be easily generalised to other classes. 1.5.2 Chapter 6: Decidability result for the ground entailment problem in the first order logic Deduction systems representing the intruder’s deductive capabilities can be viewed as sets of Horn clauses with one unary predicate. We generalise in Chapter 6 the saturation procedure employed in Chapter 5 in order to study the ground entailment problem for a new set of first order clauses. It is wellknown that the satisfiability and the ground entailment problem are undecidable for both clauses and Horn clauses sets, but several decidability results have been obtained for several fragments of first order logic [150, 28, 84, 180, 205]. In this chapter, we introduce a new fragment of first order logic and we prove the decidability of its ground entailment problem. This decidability result relies on the use of the selected resolution (widely studied in the literature [134, 133, 137, 146, 164]) and on the use of an atom ordering compatible with a complete simplification term ordering. We remark that when the complete term ordering is arbitrary, a saturated set of clauses does not necessarily have a decidable ground entailment problem. We also show how to use this result in order to decide the insecurity problem for cryptographic protocols in the case of bounded number of sessions. While in this chapter the application of Horn clauses on security protocols is limited to the search of attacks, the analysis of cryptographic protocols using Horn clauses may go beyond that: actually one can use Horn clauses to prove the correctness of such protocols, and that by including the clauses describing the protocol in the saturation process.
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178 CHAPTER 7. VOTER VERIFIABILITY
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198 CHAPTER 8. CONCLUSION AND PERSP
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202 BIBLIOGRAPHY [12] M. Abadi and
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204 BIBLIOGRAPHY [36] M. Bellare, A
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206 BIBLIOGRAPHY [60] U. Hustadt Ch
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208 BIBLIOGRAPHY [83] H. Comon-Lund
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210 BIBLIOGRAPHY [108] B. Donovan,
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212 BIBLIOGRAPHY [132] T. Kohno, A.
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214 BIBLIOGRAPHY [160] J. C. Mitche
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216 BIBLIOGRAPHY [187] H. Seidl and
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