Logical Analysis and Verification of Cryptographic Protocols - Loria

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10 CHAPTER 1. INTRODUCTION intercepted all messages between a and b. I can then later trick b into using the key Kab as follows: first I replays the message enc s (〈Kab, a〉, Kbs) to b I ⇒ b : enc s (〈Kab, a〉, Kbs) Assuming that a has initiated a new conversation, b replies to a b ⇒ I(a) : enc s (n ′ b, Kab) I intercepts the message, deciphers it, and impersonates a ′ s response: I(a) ⇒ b : enc s (n ′ b − 1, Kab) Thereafter, I can send false messages to b that appear to be from a. This attack, called a replay attack is the most famous attack on the Needham- Schroeder symmetric key protocol. 1.4 Analysis of cryptographic protocols 1.4.1 Overview Cryptographic protocols are programs designed to ensure secure electronic communications between participants using an insecure network. They use cryptographic primitives such as encryption schemes, signature schemes, hash functions, and others to construct exchanged messages. These cryptographic primitives are based on mathematical notions such as modular exponentiation and elliptic curves and on algorithmically hard problems such as factorisation into prime numbers, extracting the modular logarithm, and others. Unfortunately, the existence of cryptographic primitives is not sufficient to ensure security and several attacks were found on established protocols [78, 2]. The most relevant example is the bug of the Needham-Schroeder public key protocol [163] found by Lowe [144] using a model-checking tool. It took 17 years since the protocol was published to find the attack, a man-in-the-middle one. This situation shows that the design of a cryptographic protocol is tricky, and that it is easy to have it wrong. Thus, one needs formal verification. In the literature, we find two distinct worlds for the verification of cryptographic protocols: the computational world and the symbolic world. Let us now review briefly these two approaches: The “computational” world In the computational models, also called probabilistic, or cryptographic, or concrete models, messages are bit strings, and the intruder is an arbitrary probabilistic polynomial-time Turing machine. These models are closer to the reality than
1.4. ANALYSIS OF CRYPTOGRAPHIC PROTOCOLS 11 the symbolic ones, and hence results obtained in these models yield stronger security guarantees, but the validation proofs are essentially manual [38, 142, 49]. Recently, I. Tsahhirov and P. Laud [194] have developed an automatic tool to verify cryptographic protocols in the computational models, and B. Blanchet [48] has developed another automatic tool “CryptoVerif” which is more developed than the tool in [194]. Many results have been obtained in the computational models [13, 33, 26, 56, 203, 155]. For instance, in [26], M. Backes and B. Pfitzmann proved that the Needham-Schroeder-Lowe protocol is secure under real, and active cryptographic attacks including concurrent protocol runs. Still, another computationally sound proof of security for the Needham-Schroeder- Lowe protocol has been given in [203], where B. Warinschi has proved that the protocol is secure if it is implemented with an encryption scheme that satisfies indistinguishability under chosen-ciphertext attack. In [155], D. Micciancio and B. Warinschi showed that, in the case of assymetric encryption, the perfect encryption hypothesis is a sound abstraction for encryption schemes satisfying the IND-CCA2 property. In [13], M. Abadi and Ph. Rogaway showed that if two messages are formally indistinguishable then they are computationally indistinguishable, and that in the case where the symmetric encryption is the unique encryption scheme in addition of some technical restrictions. This result has been extended by M. Baudet, V. Cortier and S. Kremer [33] to take into consideration cryptographic primitives represented by a wide class of equational theories including exclusive or, and by E. Bresson, Y. Lakhnech, L. Mazaré and B. Warinschi [56] who take into consideration the modular exponentiation. The “symbolic” world The first symbolic models for the verification of cryptographic protocols are attributed to R. Needham and M. Schroeder [163], and to D. Dolev and A. Yao [107]. These models represent an abstraction of the real world, and hence allow simpler reasoning and an automatic analysis of security protocols. In the symbolic world, the cryptographic primitives are represented by function symbols, messages by elements in a signature (a set of function symbols representing the cryptographic primitives), and the intruder by a set of deduction rules. Such approaches adopt the so-called Dolev-Yao intruder model [107] represented as follows: The intruder has a complete control over the communication medium (network), he listens to the communication and can obtain any message passing through the network, he can intercept, block, and/or redirect all messages sent by honest agents. He also can masquerade his identity and take part in the protocol under the identity of an honest agent. His control of the network is modelled by assuming that all messages sent by honest agents are sent directly to
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112 CHAPTER 5. SATURATED DEDUCTION
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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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208 BIBLIOGRAPHY [83] H. Comon-Lund
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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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