A universal composability framework for analysis of proxy threshold signature

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.

It is well-known that most cryptographic tasks do not have universally composable (UC) secure protocols, if no trusted setup is available in the framework. On the other hand, if a task like fair coin-tossing is available as a trusted setup, then all cryptographic tasks have UC-secure protocols. What other trusted setups allow UC-secure protocols for all tasks? More generally, given a particular setup, what tasks have UC-secure protocols? We show that, surprisingly, every trusted setup is either useless (equivalent to having no trusted setup) or all-powerful (allows UC-secure protocols for all tasks). There are no intermediate trusted setups in the UC framework. We prove this zero-one law under a natural intractability assumption, and consider the class of deterministic, finite, 2-party functionalities as candidate trusted setups. One important technical contribution in this work is to initiate the comprehensive study of the cryptographic properties of reactive functionalities. We model these functionalities as finite automata and develop an automata-theoretic methodology for classifying and studying their cryptographic properties. Consequently, we completely characterize the reactive behaviors that lead to cryptographic non-triviality. Another contribution of independent interest is to optimize the hardness assumption used by Canetti et al. (STOC 2002) in showing that the common random string functionality is complete (a result independently obtained by Damgard et al. (TCC 2010)).

The relationship of three cryptographic channels, secure channels (SC), anonymous channels (AC) and direction-indeterminable channels (DIC), was investigated by Okamoto. He showed that the three cryptographic channels are reducible to each other, but did not consider communication schedules clearly as well as composable security. This paper refines the relationship of the three channels in the light of communication schedules and composable security. We model parties by the task-probabilistic input/output automata (PIOA) to treat communication schedules, and adopt the universally composable (UC) framework by Canetti to treat composable security. We show that a class of anonymous channels, two-anonymous channels (2AC), and DIC are reducible to each other under any schedule and that DIC and SC are reducible to each other under some types of schedules, in the UC framework with the PIOA model.KeywordsSecure Channel (SC)Two-Anonymous Channel (2AC)Direction-Indeterminable Channel (DIC)Universal Composability (UC)Probabilistic Input/Output Automaton (PIOA)

Adaptively code-correlation robustness functions and its applications to private set intersection

Universal composability and concurrent general composition consider a setting where secure protocols are run concurrently with each other and with arbitrary other possibly insecure protocols. Protocols that meet the definition of universal composability are guaranteed to remain secure even when run in this strongly adversarial setting. In the case of an honest majority, or where there is a trusted setup phase of some kind (like a common reference string or the key-registration public-key infrastructure of Barak et al. in FOCS 2004), it has been shown that any functionality can be securely computed in a universally composable way. On the negative side, it has also been shown that in the plain model where there is no trusted setup at all, there are large classes of functionalities which cannot be securely computed in a universally composable way without an honest majority.In this paper, we extend these impossibility results for universal composability. We study a number of public-key models and show for which models the impossibility results of universal composability hold and for which they do not. We also consider a setting where the inputs to the protocols running in the network are fixed before any execution begins. The majority of our results are negative and we show that the known impossibility results for universal composability in the case of no honest majority extend to many other settings.

Three-party password authenticated key exchange (3PAKE) allows two clients, each sharing a password with a trusted server, to establish a session key with the help of the server. It is a quite practical mechanism for establishing secure channels in large communication network. However, most current 3PAKE protocols are analyzed in security models that don’t adequately address protocol composition problem. In this paper, a direct definition of security for 3PAKE within the universal composability framework is proposed, which captures the basic security requirements of the problem and is proven to be stronger than the commonly used security notions. To further justify our formulation of 3PAKE, we prove that a slight variant of a generic 3PAKE protocol by Wang and Hu securely realizes the new security definition.

In this paper, we provide the first scheme that realises an attribute-based access control system for static resources that offers maximal privacy and is secure in the universal composability framework (UC). More precisely, we offer a protocol for adaptive oblivious transfer, where the sender can enforce an attribute-based access control policy for each record and nevertheless learns neither which record a user retrieves nor which attributes a user has. As additional results we provide a new structure-preserving signature scheme from the SXDH assumption and a new universally composable adaptive oblivious transfer protocol that is secure under two DDH-like assumptions and is the most efficient one secure under ``non $q$-type'' assumptions. We believe the new signature scheme to be of independent interest as a building block that is compatible with Groth-Sahai non-interactive zero-knowledge proofs.

SummaryThree‐party password‐authenticated key exchange (3PAKE) allows two clients, each sharing a password with a trusted server, to establish a session key with the help of the server. It is a quite practical mechanism for establishing secure channels in a large communication network. However, most current 3PAKE protocols are analyzed in security models that do not adequately address protocol composition problem. In this paper, an ideal functionality for 3PAKE within the universal composability framework is defined, which not only provides security guarantees under arbitrary composition with other protocols but also achieves contributiveness and explicit authentication. Moreover, we propose a generic construction of contributory 3PAKE protocol and prove that it securely realizes the ideal functionality in the static corruption model. Copyright © 2014 John Wiley & Sons, Ltd.

The universal composability (UC) framework is the established standard for analyzing cryptographic protocols in a modular way, such that security is preserved under concurrent composition with arbitrary other protocols. However, although UC is widely used for on-paper proofs, prior attempts at systemizing it have fallen short, either by using a symbolic model (thereby ruling out computational reduction proofs), or by limiting its expressiveness. In this paper, we lay the groundwork for building a concrete, executable implementation of the UC framework. Our main contribution is a process calculus, dubbed the Interactive Lambda Calculus (ILC). ILC faithfully captures the computational model underlying UC—interactive Turing machines (ITMs)—by adapting ITMs to a subset of the π-calculus through an affine typing discipline. In other words, well-typed ILC programs are expressible as ITMs. In turn, ILC’s strong confluence property enables reasoning about cryptographic security reductions. We use ILC to develop a simplified implementation of UC called SaUCy.

The threshold signature scheme is a protocol that allows any subset of t parties out of n to generate a signature. Since the t members can cooperate together to compute the secret key, we introduce the server-aided threshold signature, which provides controllability for activating the signing function in a certain enhanced way. In this study, we present a server-aided threshold RSA signature protocol against the adaptive attacks. We give the universally composable secure model for the server-aided threshold signature primitive and prove that the proposed protocol is claimed to be well-formed, correct and unforgeability. As a separate contribution we also prove that it is also secure in the adaptive universal composability framework. After the discussion about the security and the performance, we claim that the protocol is practical and efficient.

To maintain communications confidentiality, security protocols are widely used in more and more network applications. Moreover, some malwares even leverage these kinds of protocols to evade inspection by IDS. Most security protocols are designed and verified by formalized methods; however, observation shows that protocol implementations commonly contain flaws or vulnerabilities. Therefore, research on reverse engineering of security protocols can play an important role in improving the security of network applications, especially by providing another way to fight against malwares. Nevertheless, previous protocol reverse engineering technologies, which are based on analysis of network traces, encounter great challenges when the network messages transmitted between different protocol principals are encrypted. This paper proposes a taint analysis based method, which aims to infer the message format from dynamic execution of security protocol applications. The proposed approach is based on the observation that the process of message parsing in cryptographic protocol applications reveals rich information about the hierarchical structures and semantics of their messages. Hence, by observing calls to library function and instruction execution in network programs, the proposed approach can reverse derive large amount of information about their protocol, such as message format and protocol model, even the communication is encrypted. Experiments show that the reverse analysis results not only accurately identify message fields, but also unveil the structure of the encrypted message fields.

Secure multi-party computation (SMC) is a cryptographic protocol that allows participants to compute the desired output without revealing their inputs. A variety of results related to increasing the efficiency of SMC protocol have been reported, and thus, SMC can be used in various applications. With the SMC protocol in smart grids, it becomes possible to obtain information for load balancing and various statistics, without revealing sensitive user information. To prevent malicious users from tampering with input values, SMC requires cheater detection. Several studies have been conducted on SMC with cheater detection, but none of these has been able to guarantee the fairness of the protocol. In such cases, only a malicious user can obtain a correct output prior to detection. This can be a critical problem if the result of the computation is real-time information of considerable economic value. In this paper, we propose a fair and secure multi-party computation protocol, which detects malicious parties participating in the protocol before computing the final output and prevents them from obtaining it. The security of our protocol is proven in the universal composability framework. Furthermore, we develop an enhanced version of the protocol that is more efficient when computing an average after detecting cheaters. We apply the proposed protocols to a smart grid as an application and analyze their efficiency in terms of computational cost.

Though much attention has been paid to the research on the security of cryptographic protocols in the last two decades, no perfect solution is a.vailable. In this paper, we firstly present some explicit assumptions, and the properties that a secure protocol should hold, then divide the total security of cryptographic protocols into some partial securities based on those properties, and finally give our protocol which is surprisingly simple and prove its total security based on those assumptions and the capacity of BAN-like of proving the session key safeness of cryptographic protocols.

The geographic area information of smart devices is required for realizing efficient area-based operations in 5G networks, Internet of Things, and so on. Because majority of smart devices are unmanned and are deployed in a hostile environment, secure geographic area verification is one of the important security issues for ensuring the accuracy of geographic area information of smart devices. In this study, we investigate the composition security of geographic area verification in a universally composable (UC) framework. First, we design the ideal functionality of geographic area verification; further, we propose a novel pre-shared secret-free secure geographic area verification protocol CAVδ. We also propose an improved protocol CAVT δ exhibiting a smaller false accept ratio than that exhibited by CAVδ. The proposed protocols can be used for verifying the geographic area information of smart devices without the requirement of any pre-shared secret during the initialization phase and additional key management when the protocols are running. Furthermore, the proposed protocols support the batch verification of multiple smart devices in one run, which is considered to be suitable for several location-critical smart devices. Subsequently, in the UC framework, we proved that our protocols achieve the necessary composition security and that our protocols exhibit an ability to resist colluding attacks.

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.