Logical Analysis and Verification of Cryptographic Protocols - Loria

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12 CHAPTER 1. INTRODUCTION Figure 1.2 Security problem of cryptographic protocols Input: a protocol P, and a security property A. Output: SECURE if and only if the P satisfies A. the intruder and that all messages received by the honest agents are always sent by the intruder. Besides the control of the network, the intruder has some specific rules to deduce new messages. In this document, we follow the symbolic approach in order to analyse cryptographic protocols. 1.4.2 Symbolic analysis of cryptographic protocols Cryptographic protocols are difficult to verify for several reasons: the unbounded complexity of the exchanged messages, the unbounded number of the new generated data, the unbounded number of participants, and the unbounded number of sessions. The “security problem” of cryptographic protocols which is stated in Figure 1.2 is undecidable in general [111]. In [110], the authors showed that the problem remains undecidable even if data constructors, message depth, message width, number of distinct roles, role length, and depth of encryption are bounded by constants. Another restrictions consist in bounding the number of fresh values (nonces) used during the attack. However several undecidable problems like PCP may be encoded in that case [89]. In order to decide the security problem of cryptographic protocols, we need to add more restrictions. We describe below a few methods used to symbolically analyse cryptographic protocols, then we give some obtained (un)decidability results. Search for logical attacks. A first attempt was to search for logical attacks in the case of bounded number of sessions. In [192], the authors showed that, in this method, it is sufficient to consider a unique intruder. The first tools were based on model-checking. Such tools represent the protocols as finite-state machines and security properties as formula in temporal logic. Examples of such tools are FDR [108], Murφ [160], or Brutus [79]. They discovered several interesting attacks assuming a bounded number of sessions and messages of bounded size. The most famous attack discovered using these tools is the attack on the Needham-Schroeder public key protocol [145]. A. Huima [122] was the first to suggest that bounding the size of messages is not necessary, and to analyse cryptographic protocols in that case, proposed the use of symbolic constraints. The use of symbolic constraints to analyse
1.4. ANALYSIS OF CRYPTOGRAPHIC PROTOCOLS 13 cryptographic protocols has been studied later by [15, 156, 53], and then by [68, 95, 73, 70, 69, 54] who considered cryptographic protocols with algebraic primitives such as modular exponentiation, exclusive or, etc. Constraint solving has become the standard model to analyse cryptographic protocols in the case of bounded number of sessions. In this approach, other works have been done in order to capture other security properties such as the resistance to the dictionary attacks [96], equivalencebased properties [109], and the properties related to contract-signing protocols [135]. Search for proofs. The drawback of this approach is that, assuming a bounded number of sessions, it does not prove the correctness of the protocol. We show here another approach, the “search for proofs”, which does not assume a bounded number of sessions. One of its inconvenient is that it may introduce false attacks, that is it may reject protocols that do not have logical attacks. We give below some of the methods elaborated in this approach: • Methods that use theorem provers such as the inductive approach of L. Paulson [168] which uses Isabelle to prove security properties, and the approach of Bolignano [52]. • Methods based on process algebra such as pi-calculus, spi-calculus and applied pi-calculus [12, 11]. • Methods based on logics such as BAN logic [57] which is due to M. Burrows and M. Abadi and R. M. Needham. • NRL protocol analyser [151] which is known to be the first tool that does not impose any restriction. • Methods that use tree automata [161, 118, 85]. • Methods based on Horn clauses [46, 180, 84, 205]. Several automatic tools have been developed to symbolically verify cryptographic protocols such as “Proverif” [46, 50], “AVISS” [17], or “AVISPA” [19]. The symbolic methods have been used to analyse a wide class of cryptographic protocols such as key exchange and authentication protocols, voting protocols [136, 97], contract-signing protocols [128], recursive protocols [138], Web Services [41, 72], and others. (Un)Decidability results The security problem of cryptographic protocols, stated in Figure 1.2 is undecidable in general [111], but under some restrictions several decidability results
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112 CHAPTER 5. SATURATED DEDUCTION
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148 CHAPTER 6. ON THE GROUND ENTAIL
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178 CHAPTER 7. VOTER VERIFIABILITY
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198 CHAPTER 8. CONCLUSION AND PERSP
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200 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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214 BIBLIOGRAPHY [160] J. C. Mitche
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216 BIBLIOGRAPHY [187] H. Seidl and
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