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Mathematical Structures in Computer Science

A second note on the feasibility of generalized universal composability

Alonso González, Alejandro Hevia

Published Jun 8, 2016• 0 citations
Publisher

Abstract

Yao et al. (A note on the feasibility of generalized universal composability.Theory and Applications of Models of Computationpp. 474–485, 2007; A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science,19(1), pp. 193–205) claimed a potential limitation on the class of protocols that could be securely implemented in the generalized universal composability (GUC) framework proposed by Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Specifically, Yao et al. presented a concrete attack on a GUC Zero Knowledge (GUCZK) protocol, a natural adaptation Blum's ZK proof for Directed Hamiltonicity using the general GUC feasibility of Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Interestingly, the attack was not analysed in the GUC model in Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) but in theFUC model, a new UC-like framework proposed in the same work. Nonetheless, Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) argued that, in light of this attack, GUC would lose its concurrent general composability and proof of knowledge properties. Concretely, they argue that GUC composability would now be with respect to some adversaries with limited access to external arbitrary protocols. In this work, we show that the claimed attack from Yao et al. is indeed harmless and does not contradict the security of the mentioned GUCZK protocol, thus restoring the general feasibility for GUC.

DOI
10.1017/s0960129516000074

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Yao et al. (A note on the feasibility of generalized universal composability.Theory and Applications of Models of Computationpp. 474–485, 2007; A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science,19(1), pp. 193–205) claimed a potential limitation on the class of protocols that could be securely implemented in the generalized universal composability (GUC) framework proposed by Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Specifically, Yao et al. presented a concrete attack on a GUC Zero Knowledge (GUCZK) protocol, a natural adaptation Blum's ZK proof for Directed Hamiltonicity using the general GUC feasibility of Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Interestingly, the attack was not analysed in the GUC model in Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) but in theFUC model, a new UC-like framework proposed in the same work. Nonetheless, Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) argued that, in light of this attack, GUC would lose its concurrent general composability and proof of knowledge properties. Concretely, they argue that GUC composability would now be with respect to some adversaries with limited access to external arbitrary protocols. In this work, we show that the claimed attack from Yao et al. is indeed harmless and does not contradict the security of the mentioned GUCZK protocol, thus restoring the general feasibility for GUC.
In this paper we study (interpret) the precise composability guarantee of the generalised universal composability (GUC) feasibility with global setups that was proposed in the recent paper Canetti et al. (2007) from the point of view of full universal composability (FUC), that is, composability with arbitrary protocols, which was the original security goal and motivation for UC. By observing a counter-intuitive phenomenon, we note that the GUC feasibility implicitly assumes that the adversary has limited access to arbitrary external protocols. We then clarify a general principle for achieving FUC security, and propose some approaches for fixing the GUC feasibility under the general principle. Finally, we discuss the relationship between GUC and FUC from both technical and philosophical points of view. This should be helpful in gaining a precise understanding of the GUC feasibility, and for preventing potential misinterpretations and/or misuses in practice.
Modeling security for protocols running in the complex network environment of the Internet can be a daunting task. Ideally, a security model for the Internet should provide the following guarantee: a protocol that implements a particular task specification will retain all the same security properties as the specification itself, even when an arbitrary set of protocols runs concurrently on the same network. This guarantee must hold even when other protocols are maliciously designed to interact badly with the analyzed protocol, and even when the analyzed protocol is composed with other protocols. The popular Universal Composability (UC) security framework aims to provide this guarantee. Unfortunately, such strong security guarantees come with a price: they are impossible to achieve without the use of some trusted setup. Typically, this trusted setup is global in nature, and takes the form of a Public Key Infrastructure (PKI) and/or a Common Reference String (CRS). However, the current approach to modeling security in the presence of such setups falls short of providing expected security guarantees. A quintessential example of this phenomenon is the deniability concern: there exist natural protocols that meet the strongest known security notions (including UC) while failing to provide the same deniability guarantees that their task specifications imply they should provide. We introduce the Generalized Universal Composability (GUC) framework to extend the UC security notion and enable the re-establishment of its original intuitive security guarantees even for protocols that use global trusted setups. In particular, GUC enables us to guarantee that secure protocols will provide the same level of deniability as the task specification they implement. To demonstrate the usefulness of the GUC framework, we first apply it to the analysis and construction of deniable authentication protocols. Building upon such deniable authentication protocols, we then prove a general feasibility result showing how to construct protocols satisfying our security notion for a large class of two-party and multi-party tasks (assuming the availability of some reasonable trusted setup). Finally, we highlight the practical applicability of GUC by constructing efficient protocols that securely instantiate two common cryptographic tasks: commitments and zero-knowledge proofs.
Introduced by Canetti in 2001, Universal Composability (UC) is a widely adopted security model that enables the specification and proof of security for a broad range of protocols, offering strong security guarantees. At its core lies the universal composition theorem (UC theorem), which ensures that protocols proven secure within the framework remain secure even when deployed in real-world environments with multiple instances of them. In this work, we present two key contributions. First, we identify several problems with the UC framework, in particular the UC Theorem. They include counterexamples, limitations that make it unusable for important classes of protocols, and weaknesses in its proof. These problems reveal flaws in nearly all the fundamental concepts of UC. Second, we propose a revised formulation of the main concepts of UC to address these issues. Although the resulting modifications are nontrivial, our updated definitions are designed to remain as faithful as possible to the structure and intent of the original model.
Abstract. Zero-knowledge proofs of knowledge (ZK-PoK) for discrete logarithms and related problems are indispensable for practical cryptographic protocols. At Eurocrypt 2009, Camenisch, Kiayias, and Yung provided a specification language (the CKY-language) for such protocols, which allows one to modularly design and analyze cryptographic protocols: protocol designers just need to specify the statement they want to prove in zero-knowledge and are ensured that an efficient proof protocol exists and indeed proves the specified statement, provided that the specification was in the CKY-language. However, as specifications in the CKY-language are realized by so-called Σ-protocols, the resulting protocols only satisfy the classical notion of zero-knowledge proofs of knowledge, which not retained if they are composed with themselves or with other protocols, e.g., when used as building blocks for higher-level applications. This problem can be tackled by moving to the Universal Composability (UC) framework, which guarantees retention of security when composing protocols and, in particular, when using them as building blocks in arbitrary contexts. While there exists generic transformations from Σ-protocols to protocols that are secure under this stronger security notion, these transformation are often not efficient enough for the design of practical protocols. In this paper we are aiming for practically efficient ZK-PoK in the UC-framework by introducing
We propose a modification to the framework of Universally Composable (UC) security [3]. Our new notion, involves comparing the protocol executions with an ideal execution involving ideal functionalities (just as in UC-security), but allowing the environment and adversary access to some super-polynomial computational power. We argue the meaningfulness of the new notion, which in particular subsumes many of the traditional notions of security. We generalize the Universal Composition theorem of [3] to the new setting. Then under new computational assumptions, we realize secure multi-party computation (for static adversaries) without a common reference string or any other set-up assumptions, in the new framework. This is known to be impossible under the UC framework. 1
We put forward a framework for the modular design and analysis of multi-party protocols. Our framework is called “GNUC ” (with the recursive meaning “GNUC’s Not UC”), already alluding to the similarity to Canetti’s Universal Composability (UC) framework. In particular, like UC, we offer a universal composition theorem, as well as a theorem for composing protocols with joint state. We deviate from UC in several important aspects. Specifically, we have a rather different view than UC on the structuring of protocols, on the notion of polynomial-time protocols and attacks, and on corruptions. We will motivate our definitional choices by explaining why the definitions in the UC framework are problematic, and how we overcome these problems. Our goal is to offer a framework that is largely compatible with UC, such that previous results formulated in UC carry over to GNUC with minimal changes. We exemplify this by giving explicit formulations for several important protocol tasks, including authenticated and secure communication, as well as commitment and secure function evaluation. 1