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Information Security and Communications Privacy

Ideal Functionality and Sequential Composition of Zero-knowledge

Dai Yiqi

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

UC security is the framework in treating a stand-alone protocol and guaranteeing the secure composition.This means that a protocol may run concurrently with many other protocols,on arbitrary inputs and in adversarial controlled way,if it is UC security in the sense that it emulates an ideal functionality,it can be treated as a piece of that ideal functionality in overall system security analysis.In this paper,ZK under UC framework is studied,and the study proves that Blum protocol is closed under sequential composition in the Fwzk-hybrid model.

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UC security is the framework in treating a stand-alone protocol and guaranteeing the secure composition.This means that a protocol may run concurrently with many other protocols,on arbitrary inputs and in adversarial controlled way,if it is UC security in the sense that it emulates an ideal functionality,it can be treated as a piece of that ideal functionality in overall system security analysis.In this paper,ZK under UC framework is studied,and the study proves that Blum protocol is closed under sequential composition in the Fwzk-hybrid model.
The Universal Composability (UC) framework provides provable security guaranties for harsh application environment, where we want to construct protocols which keep security guarantees even when they are concurrently composed with arbitrary number of arbitrary (even hostile) protocols.This is a very strong guarantee.The UC-framework inherently supports the modular design, which allows secure composition of arbitrary number of UC-secure components with an arbitrary protocol.In contrast, traditional analysis and design is a stand alone analysis where security of a single instance is considered, i.e. an instance which is not in potential interaction with any concurrent instances.Furthermore, a typical traditional analysis is informal, i.e. without a formal proof.In spite of these facts, beyond the task of key-exchange this technology have not really took the attention of the community of applied cryptography.From practitioner's point of view the UC-world may seem more or less an academic interest of theoretical cryptographers.Accordingly we take a pragmatic approach, where we concentrate on meaningful compromises between the assumed adversarial strength, ideality wishes and realization complexity while keeping provable security guarantees within the UC-framework.We believe that even modest but provable goals (especially, if tunable to application scenarios) are interesting if a wider penetration of the UC-technology is desired into the daily-practice of protocol applications.
Abstract. How to define the security of undeniable signature schemes is a challenging task. This paper presents two security definitions of undeniable signature schemes which are more useful or natural than the existing definition. It then proves their equivalence. We first define the UC-security, where UC means universal composability. We next show that there exists a UC-secure undeniable signature scheme which does not satisfy the standard definition of security that has been believed to be adequate so far. More precisely, it does not satisfy the invisibility defined by [10]. We then show a more adequate definition of invisibility which captures a wider class of (naturally secure) undeniable signature schemes. We finally prove that the UC-security against non-adaptive adversaries is equivalent to this definition of invisibility and the strong unforgeability in FZK-hybrid model, where FZK is the ideal ZK functionality. Our result of equivalence implies that all the known proven secure undeniable signature schemes (including Chaum’s scheme) are UC-secure if the confirmation/disavowal protocols are both UC zero-knowledge.
This work presents a general framework for describing cryptographic protocols and analyzing their security. The framework allows specifying the security requirements of practically any cryptographic task in a unified and systematic way. Furthermore, in this framework the security of protocols is preserved under a general composition operation, called universal composition. The proposed framework with its security-preserving composition operation allows for modular design and analysis of complex cryptographic protocols from simpler building blocks. Moreover, within this framework, protocols are guaranteed to maintain their security in any context, even in the presence of an unbounded number of arbitrary protocol sessions that run concurrently in an adversarially controlled manner. This is a useful guarantee, which allows arguing about the security of cryptographic protocols in complex and unpredictable environments such as modern communication networks.
Universal composition framework, UC, provides a methodology for designing and analyzing protocols. A secure protocol/task can be formulated to an ideal functionality, translate some realistic schemes into an ideal protocol so that it can securely emulate the ideal functionality. UC theory ensures the security of protocols is maintained under a general protocol composition operation. Signature is a primary cryptographic task. The present formulation of ideal signature functionality is introduced and some flaws are pointed out, and then an improved signature functionality is presented and proven that it is securely realized by precisely those signature scheme that is equivalent to existential unforgery against chosen- message attacks, EU-CMA.
Universal composition framework, UC, provides a methodology for designing and analyzing protocols. A secure protocol/task can be formulated to an ideal functionality, translate some realistic schemes into an ideal protocol so that it can securely emulate the ideal functionality. UC theory ensures the security of protocols is maintained under a general protocol composition operation. Signature is a primary cryptographic task. The present formulation of ideal signature functionality is introduced and some flaws are pointed out, and then an improved signature functionality is presented and proven that it is securely realized by precisely those signature scheme that is equivalent to existential unforgery against chosen- message attacks, EU-CMA.
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.