Logical Analysis and Verification of Cryptographic Protocols - Loria

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80 CHAPTER 3. PROTOCOLS WITH VULNERABLE HASH FUNCTIONS 3.5.4 Decidability of ordered Ih-satisfiability problem Following the results obtained in [74], and by Lemmas 13, 14, 15, 16, 17, 18, 19, and 20, we conjecture that we can reduce the ordered Ih satisfiability problem to the ordered Ifree satisfiability problem. And hence, we conjecture that the ordered Ih satisfiability problem is decidable. 3.6 Conclusions We have analysed here the class of cryptographic protocols that use collision vulnerable hash functions. In order to model such hash functions we have introduced new symbols to denote the ability to create messages with the same hash value. This introduction amounts to the skolemisation of the equational property describing the existence of collisions. We believe that this construction can be extended to model the more complex and game-based properties that appear when relating a symbolic and a concrete model of cryptographic primitives. It is well-known that hash functions are widely used in the digital signature schemes which is the topic of the next chapter.
Chapter 4 Analysis of protocols with vulnerable digital signature schemes The idea of digital signature schemes first appeared in W. Diffie and M.E. Hellman’s seminal paper [101]. Digital signatures have many applications in information security, including authentication, data integrity, and non-repudiation. In [117], the authors showed the different flaws of digital signature schemes. Furthermore, the authors defined what is a secure digital signature scheme: a digital signature scheme is considered to be secure if it is existential unforgeable against adaptative chosen message attacks. Unfortunately, while this security notion is adequate to the single-user setting, it is not adequate for the multi-user setting [152]. In this chapter, we are interested by the security of signature schemes in the multi-user setting, and to this end, we consider two properties of digital signature schemes: the constructive exclusive ownership vulnerability property and the destructive exclusive ownership vulnerability property. We show the decidability of the insecurity problem for two classes of cryptographic protocols where the signature schemes employed have respectively these two properties. This result has been published in the proceedings of FSTTCS 2007 conference [66]. Outline. In Section 4.1 we present the signature schemes, in Section 4.2 we define the constructive exclusive ownership vulnerability property (also called duplicate-signature key selection property), and the destructive exclusive ownership vulnerability property is defined in Section 4.3. In Section 4.4, we define the symbolic model of these two perperties (Section 4.4.1 and Section 4.4.2), we prove the decidability of HDSKS and HDEO unifiability problems (Section 4.4.3), and we prove the decidability of IDSKS and IDEO reachability problems (Section 4.4.5). 81
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Logical Analysis and Verification o
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Abstract This thesis is developed i
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x CONTENTS 2.1.7 Unification . . .
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178 CHAPTER 7. VOTER VERIFIABILITY
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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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Logical Analysis and Verification of Cryptographic Protocols - Loria

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