In this paper, we present a simpler and more restricted variant of the universally composable security (UC) framework that is suitable for “standard ” two-party and multiparty computation tasks. Many of the complications of the UC framework exist in order to enable more general tasks than classic secure computation. This generality may be a barrier to entry for those who are used to the stand-alone model of secure computation and wish to work with universally composable security but are overwhelmed by the differences. The variant presented here (called simplified universally composable security, or just SUC) is closer to the definition of security for multiparty computation in the stand-alone setting. The main difference is that a protocol in the SUC framework runs with a fixed set of parties who know each other’s identities ahead of time, and machines cannot be added dynamically to the execution. As a result, the definitions of polynomial time and protocol composition are much simpler. In addition, the SUC framework has authenticated channels built in, as is standard in previous definitions of security, and all communication is done via the adversary in order to enable arbitrary scheduling of messages. Due to these differences, not all cryptographic tasks can be expressed in the SUC framework.
In this paper, we present a simpler and more restricted variant of the universally composable security (UC) framework that is suitable for “standard ” two-party and multiparty computation tasks. Many of the complications of the UC framework exist in order to enable more general tasks than classic secure computation. This generality may be a barrier to entry for those who are used to the stand-alone model of secure computation and wish to work with universally composable security but are overwhelmed by the differences. The variant presented here (called simplified universally composable security, or just SUC) is closer to the definition of security for multiparty computation in the stand-alone setting. The main difference is that a protocol in the SUC framework runs with a fixed set of parties who know each other’s identities ahead of time, and machines cannot be added dynamically to the execution. As a result, the definitions of polynomial time and protocol composition are much simpler. In addition, the SUC framework has authenticated channels built in, as is standard in previous definitions of security, and all communication is done via the adversary in order to enable arbitrary scheduling of messages. Due to these differences, not all cryptographic tasks can be expressed in the SUC framework.
Secure multi-party computation is a conceptual framework in which distrusting parties engage in a protocol to securely perform a computational task. Depending on the precise model of security, different sets of tasks admit secure protocols. We take a complexity-theoretic approach to studying the inherent difficulty of securely realizing tasks in various standard security models. * We give the first alternate characterization of secure realizability in the framework of universally composable (UC) security. This is the first characterization in any model to consider completely arbitrary computational tasks and completely arbitrary communication channels. * The most long-standing class of computational tasks studied are those in which two parties evaluate a deterministic function. For these tasks, we give the first complete, combinatorial characterizations of secure realizability in the passive, standalone, and universally composable security models, against computationally unbounded adversaries. * Say that a task G has ``as much cryptographic complexity'' as another task F if there is a secure protocol for F that uses access to a secure implementation of G. We show that there is an infinite hierarchy of tasks with strictly increasing cryptographic complexities, with respect to computationally unbounded security. We also show that there exist tasks whose cryptographic complexities are incomparable. * In contrast, we show that under a standard cryptographic assumption, there exist only two distinct levels of cryptographic complexity with respect to polynomial-time security. Every task either has a trivial protocol using plain communication channels, or is complete (i.e., given access to a secure implementation of this task, there are secure protocols for all other tasks). This is the first result to derive a characterization of completeness for a class of arbitrary interactive tasks. In light of these characterizations, the only tasks which are securely realizable in the demanding framework of universal composition are those related to secure communication. Indeed, the framework has been used to define the security of encryption schemes, which has allowed for modular design and analysis of protocols. We consider a similar approach for homomorphic encryption schemes. A homomorphic scheme is one in which anyone can obtain an encryption of f(m_1, ..., m_n), given only the encryptions of unknown messages m_1, ..., m_n, for a specific set of functions f. * We give a construction of a homomorphic encryption scheme in which the allowed homomorphic operation is as full-featured as possible --- namely, one can derive a correctly-distributed encryption of f(m) given an encryption of unknown message m, for some functions f --- yet it is computationally infeasible to generate a ciphertext that is related to other ciphertexts in any other way. Our contributions involve developing new appropriate security definitions as well as new constructions. * We show that schemes with such powerful security guarantees can be used to build conceptually simple, efficient, UC-secure protocols for verifiable computations on encrypted data. We show protocols for two tasks related to aggregating encrypted data.
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
Abstract. To prove security of a multi-party cryptographic protocol, one often reduces attacks on the protocol to attacks on a suitable computational problem. Thus, if the computational problem is hard, then the protocol is secure. But to allow for a security reduction, the protocol itself and the attack on the protocol must be efficient, i.e., polynomialtime. Of course, the obvious way to enforce an overall polynomial runtime of the protocol is to require each individual protocol machine and adversarial entity to be polynomialtime. However, as the specific case of zero-knowledge protocols demonstrates, an a priori polynomial-time bound on all entities may not be an optimal choice because the running time of some machines needs to depend on that of others. As we want to be able to model arbitrary protocol tasks, we work in the Universal Composability framework (UC). This framework additionally provides strong composability guarantees. We will point out that in the UC setting, finding a useful notion of polynomial-time for the analysis of general protocols is a highly non-trivial task. Our goal in this work is to find a good and useful definition of polynomial-time for multiparty protocols in the UC setting that matches the intuition of what is feasible. A good
Concurrent general composition relates to a setting where a secure protocol is run in a network concurrently with other, arbitrary protocols. Clearly, security in such a setting is what is desired, or even needed, in modern computer networks where many different protocols are executed concurrently. Our main result is a proof that security under concurrent general composition is equivalent to a relaxed variant of universal composability (where the only difference relates to the order of quantifiers in the definition). An important corollary of this theorem is that existing impossibility results for universal composability (or actually its relaxed variant) are inherent in any definition achieving security under concurrent general composition. We stress that the impossibility results obtained are not "black-box", and apply even to non-black-box simulation. Our main result also demonstrates that the definition of universal composability is somewhat "minimal", in that the composition guarantee provided by universal composability (almost) implies the definition itself. This indicates that the security definition of universal composability is not overly restrictive.
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
Abstract. The recently proposed universally composable (UC) security framework, for analyzing security of cryptographic protocols, provides very strong security guarantees. In particular, a protocol proven secure in this framework is guaranteed to maintain its security even when deployed in arbitrary multi-party, multi-protocol, multi-execution environments. Protocols for securely carrying out essentially any cryptographic task in a universally composable way exist, both in the case of an honest majority (in the plain model, i.e., without set-up assumptions) and in the case of no honest majority (in the common reference string model). However, in the plain model, little was known for the case of no honest majority and, in particular, for the important special case of two-party protocols. We study the feasibility of universally composable two-party function evaluation in the plain model. Our results show that very few functions can be computed in this model so as to provide the UC security guarantees. Specifically, for the case of deterministic functions, we provide a full characterization of the functions computable in this model. (Essentially, these are the functions that depend on at most one of the parties’ inputs, and furthermore are “efficiently invertible ” in a sense defined within.) For the case of probabilistic functions, we show that the only functions computable in this model are those where one of the parties can essentially uniquely determine the joint output. 1