Abstract. Symbolic analysis of cryptographic protocols is dramatically simpler than full-fledged cryptographic analysis. In particular, it is simple enough to be automated. However, symbolic analysis does not, by itself, provide any cryptographic soundness guarantees. Following recent work on cryptographically sound symbolic analysis, we demonstrate how Dolev-Yao style symbolic analysis can be used to assert the security of cryptographic protocols within the universally composable (UC) security framework. Consequently, our methods enable security analysis that is completely symbolic, and at the same time cryptographically sound with strong composability properties. More specifically, we concentrate on mutual authentication and keyexchange protocols. We restrict attention to protocols that use public-key encryption as their only cryptographic primitive and have a specific restricted format. We define a mapping from such protocols to Dolev-Yao style symbolic protocols, and show that the symbolic protocol satisfies a certain symbolic criterion if and only if the corresponding cryptographic protocol is UC-secure. For mutual authentication, our symbolic criterion is similar to the traditional Dolev-Yao criterion. For key exchange, we demonstrate that the traditional Dolev-Yao style symbolic criterion is insufficient, and formulate an adequate symbolic criterion. Finally, to demonstrate the viability of our treatment, we use an existing tool to automatically verify whether some prominent key-exchange protocols are UC-secure. 1

Abstract. Both the formal and the computational models of cryptography contain the notion of message equivalence or indistinguishability. An encryption scheme provides soundness for indistinguishability if, when mapping formal messages into the computational model, equivalent formal messages are mapped to indistinguishable computational distributions. Previous soundness results are limited in that they do not apply when key-cycles are present. We demonstrate that an encryption scheme provides soundness in the presence of key-cycles if it satisfies the recently-introduced notion of key-dependent message (KDM) security. We also show that soundness in the presence of key-cycles (and KDM security) neither implies nor is implied by security against chosen ciphertext attack (CCA-2). Therefore, soundness for key-cycles is possible using a new notion of computational security, not possible using previous such notions, and the relationship between the formal and computational models extends beyond chosen-ciphertext security. 1

We consider expansions of the Abadi-Rogaway logic of indistinguishability of formal cryptographic expressions. We expand the logic in order to cover cases when partial information of the encrypted plaintext is revealed. We consider not only computational, but also purely probabilistic, information-theoretic interpretations. We present a general, systematic treatment of the expansions of the logic for symmetric encryption. We establish general soundness and completeness theorems for the interpretations. We also present applications to specific settings not covered in earlier works: a purely probabilistic one based on One-Time Pad, and computational settings of the so-called type-2 (which-key revealing) and type-3 (which-key and length revealing) encryption schemes based on computational complexity.

Some promising recent schemes for XML access control employ encryption for implementing security policies on published data, avoiding data duplication. In this paper we study one such scheme, due to Miklau and Suciu. That scheme was introduced with some intuitive explanations and goals, but without precise definitions and guarantees for the use of cryptography (specifically, symmetric encryption and secret sharing). We bridge this gap in the present work. We analyze the scheme in the context of the rigorous models of modern cryptography. We obtain formal results in simple, symbolic terms close to the vocabulary of Miklau and Suciu. We also obtain more detailed computational results that establish security against probabilistic polynomial-time adversaries. Our approach, which relates these two layers of the analysis, continues a recent thrust in security research and may be applicable to a broad class of systems that rely on cryptographic data protection. 1.

Abstract. We define a framework to reason about implementations of equational theories in the presence of an adaptive adversary. We particularly focus on soundess of static equivalence. We illustrate our framework on several equational theories: symmetric encryption, XOR, modular exponentiation and also joint theories of encryption and modular exponentiation. This last example relies on a combination result for reusing proofs for the separate theories. Finally, we define a model for symbolic analysis of dynamic group key exchange protocols, and show its computational soundness. 1

We prove, under the strong RSA assumption, that the group of invertible integers modulo the product of two safe primes is pseudo-free. More specifically, no polynomial time algorithm can output (with non negligible probability) an unsatisfiable system of equations over the free abelian group generated by the symbols g1,...,gn, together with a solution modulo the product of two randomly chosen safe primes when g1,..., gn are instantiated to randomly chosen quadratic residues. Ours is the first provably secure construction of pseudo-free abelian groups under a standard cryptographic assumption, and resolves a conjecture of Rivest (TCC 2004).

Abstract. In this paper, we introduce a symbolic model to analyse protocols that use a bilinear pairing between two cyclic groups. This model consists in an extension of the Abadi-Rogaway logic and we prove that the logic is still computationally sound: symbolic indistinguishability implies computational indistinguishability provided that the Bilinear Decisional Diffie-Hellman assumption holds and that the encryption scheme is IND-CPA secure. We illustrate our results on classical protocols using bilinear pairing like Joux tripartite Diffie-Hellman protocol or the TAK-2 and TAK-3 protocols.

Abstract. In this paper, we study the Dynamic Decisional Diffie-Hellman (3DH) problem, a powerful generalization of the Decisional Diffie-Hellman (DDH) problem. Our main result is that DDH implies 3DH. This result leads to significantly simpler proofs for protocols by relying directly on the more general problem. Our second contribution is a computationally sound symbolic technique for reasoning about protocols that use symmetric encryption and modular exponentiation. We show how to apply our results in the case of the Burmester & Desmedt protocol.

Abstract. We study the link between formal and cryptographic models for security protocols in the presence of passive and adaptive adversaries. We first describe the seminal result by Abadi and Rogaway and shortly discuss some of its extensions. Then we describe a general model for reasoning about the soundness of implementations of equational theories. We illustrate this model on several examples of computationally sound implementations of equational theories. 1

We prove computational soundness results for cryptographic expressions with pseudo-random keys, as used, for example, in the design and analysis of secure multicast key distribution protocols. In particular, we establish a symbolic notion of independence (for pseudo-random keys) that exactly matches the standard computational security definition (namely, indistinguishability from the uniform distribution) for pseudo-random generators. As a conceptual contribution, we initiate the study of partial information in the context of computationally sound symbolic security analysis. Specifically, we show that (within our admittedly simple, but hopefully evocative setting) partial information can be taken into account in the symbolic model, in a computationally sound way, by simply annotating each key with a label which specifies that the key is either known, unknown, or partially known, without further details about the amount and type of partial information.