Logical Analysis and Verification of Cryptographic Protocols - Loria

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xii CONTENTS 5.8 Decidability of reachability problems for subterm convergent theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.8.1 Decidability result . . . . . . . . . . . . . . . . . . . . . . . 142 5.9 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 5.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6 On the ground entailment problems 147 6.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.1.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.1.2 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.1.3 Orderings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 6.2 Decidable fragments of first order logic . . . . . . . . . . . . . . . 153 6.2.1 McAllester’s work . . . . . . . . . . . . . . . . . . . . . . . 154 6.2.2 Basin and Ganzinger work . . . . . . . . . . . . . . . . . . 154 6.3 From cryptographic protocols to logic of clauses . . . . . . . . . . 155 6.3.1 Comon-Lundh and Cortier work . . . . . . . . . . . . . . . 155 6.3.2 Zalinescu’s work . . . . . . . . . . . . . . . . . . . . . . . . 156 6.3.3 Delaune, Lin and Lynch work . . . . . . . . . . . . . . . . . 157 6.4 Our contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6.4.1 Model for cryptographic protocols . . . . . . . . . . . . . . 158 6.5 A decidability result . . . . . . . . . . . . . . . . . . . . . . . . . . 163 6.5.1 Selected resolution . . . . . . . . . . . . . . . . . . . . . . . 163 6.5.2 A decidability result . . . . . . . . . . . . . . . . . . . . . . 168 6.6 Discussions and conclusions . . . . . . . . . . . . . . . . . . . . . . 175 7 Voter verifiability for e-voting protocols 177 7.1 Electronic voting protocols . . . . . . . . . . . . . . . . . . . . . . . 178 7.1.1 Properties of electronic voting protocols . . . . . . . . . . . 179 7.2 Applied pi calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 7.3 Formalising electronic voting protocols . . . . . . . . . . . . . . . 184 7.4 Formalising voter verifiability property . . . . . . . . . . . . . . . 185 7.5 Cases studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 7.5.1 Postal ballot voting protocol . . . . . . . . . . . . . . . . . . 187 7.5.2 Traditional ballot box voting example . . . . . . . . . . . . 188 7.5.3 Protocol due to Fujioka, Okamoto & Ohta . . . . . . . . . . 188 7.5.4 Protocol due to Lee et al. . . . . . . . . . . . . . . . . . . . . 190 7.6 Relates works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 8 Conclusion and Perspectives 197 Bibliography 199
Chapter 1 Introduction In our society, the use of electronic applications such as ecommunication, e-voting, e-banking, e-commerce, etc is increasing. Among several important requirements, security figures as one crucial aspect. To guarantee security, such applications use cryptographic protocols. These are small concurrent programs executed by several distant agents through a network. Messages, or part of the messages, are produced using cryptographic functions (encryption, signature, hashing, etc). Cryptography has been used for thousands of years to safeguard military and diplomatic communications. For example, the famous Roman emperor Julius Caesar used encryption to securely communicate with his troops. Unfortunately, the usage of cryptographic primitives in a protocol is not sufficient to ensure its security and several attacks were found on established protocols [78]. The most stating example is the bug (a so-called man-in-the-middle attack) of the Needham-Schroeder protocol found by G. Lowe [144] 17 years after the publication of the protocol. This situation leads to, and shows the importance of, the development of tools and decision procedures for the formal verification of security protocols. 1.1 Cryptographic protocols 1.1.1 Communication via exchanges of messages A communication protocol, or simply protocol can be described by exchanges of messages between many participants. These exchanges are usually described by a scenario, sequence of rules each one specifying the sender, the receiver, and the exchanged message. The scenario describes a normal (also said correct) run of the protocol, that is how the execution of the protocol should proceed in the 1
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202 BIBLIOGRAPHY [12] M. Abadi and
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214 BIBLIOGRAPHY [160] J. C. Mitche
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216 BIBLIOGRAPHY [187] H. Seidl and
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