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Universally Composable Group Signature Protocol

ZHAO Chen,YU Huifang,LI Jianmin

Published Mar 1, 2017• 0 citations
Publisher

Abstract

At present,most group signature is only secure in the standard alone.Its security becomes weak in multiple protocol environment.In view of this,the security of group signature protocol is studied in the multiple concurrent execution under the universally composable framework.Since the protocol can be analyzed modularly under the universally composable framework,an ideal function of group signature protocol is defined in this framework.Then a group signature protocol is proposed to realize the ideal function,and its universally composable security as well as unforgeability is also proved.Furthermore,a concrete instance of this universally composable group signature protocol is given.Analysis results show that this protocol security is suitable for applications in multiple concurrent environment.

DOI
10.3969/j.issn.1000-3428.2017.03.029

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At present,most group signature is only secure in the standard alone.Its security becomes weak in multiple protocol environment.In view of this,the security of group signature protocol is studied in the multiple concurrent execution under the universally composable framework.Since the protocol can be analyzed modularly under the universally composable framework,an ideal function of group signature protocol is defined in this framework.Then a group signature protocol is proposed to realize the ideal function,and its universally composable security as well as unforgeability is also proved.Furthermore,a concrete instance of this universally composable group signature protocol is given.Analysis results show that this protocol security is suitable for applications in multiple concurrent environment.
Since up to now the security of multi-signature protocols has only been considered in a single instance, the security of a multi-signature protocol when it is running with many other protocols concurrently was studied in the universal composable security framework. Firstly, the idea functionality of a multi-signature protocol was defined formally. Then, based on Waters' signature scheme, a multi-signature protocol was presented, which was proved to be Unified Communications (UC) secure. Thus, the presented multi-signature protocol can run safely in multi-protocol executing environments, such as Internet.
Threshold signature allowed any subset of t parties generating a signature,but that disallowed the creation of a valid signature if fewer than t parties participate in the protocol.Since the security of threshold signature was only con-sidered in a single instance before,the universal composability framework was introduced.The framework with its secu-rity preserving composition property allowed for modular design and analysis of the threshold signature.The defined ideal functionality of threshold signature is proved equals to the standard security notion of threshold signature.Further-more,how to applying the ideal functionality is described.The proposed threshold signature protocol and proactive threshold signature protocol are not only provably secure,but also universally composable.
We propose a novel paradigm for defining security of cryptographic protocols, called universally composable security. The salient property of universally composable definitions of security is that they guarantee security even when a secure protocol is composed of an arbitrary set of protocols, or more generally when the protocol is used as a component of an arbitrary system. This is an essential property for maintaining security of cryptographic protocols in complex and unpredictable environments such as the Internet. In particular, universally composable definitions guarantee security even when an unbounded number of protocol instances are executed concurrently in an adversarially controlled manner, they guarantee non-malleability with respect to arbitrary protocols, and more. We show how to formulate universally composable definitions of security for practically any cryptographic task. Furthermore, we demonstrate that practically any such definition can be realized using known techniques, as long as only a minority of the participants are corrupted. We then proceed to formulate universally composable definitions of a wide array of cryptographic tasks, including authenticated and secure communication, key-exchange, public-key encryption, signature, commitment, oblivious transfer, zero knowledge and more. We also make initial steps towards studying the realizability of the proposed definitions in various settings.
Several protocols implementing attribute-based group key exchange, which allows users with certain set of attributes to establish a session key, have been proposed in recent years.However, attacks on attribute-based group key exchange in current research have been considered only in stand-alone fashion.Thus these protocols may be vulnerable when run with other protocol sessions concurrently.We treat the security of attribute-based group key exchange in the universal composability framework to ensure that a protocol remains secure when run with arbitrary protocol sessions concurrently.More specifically, we define an ideal functionality for attribute-based group key exchange first, then propose a two-round protocol based on a primitive called encapsulation policy attribute-based key encapsulation mechanism.In addition, a complete security proof of our protocol in the universal composability framework under random oracle model is given.
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.