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1 Password-Authenticated Constant-Round Group Key Establishment with a Common Reference String

Jens-Matthias Bohli, María Isabel González Vasco, González Vasco, Rainer Steinw

Published Jul 25, 2013• 27 citations
OpenAlex

Abstract

Abstract. A provably secure password-authenticated protocol for group key establishment in the common reference string (CRS) model is presented. Our construction assumes the participating users to share a common password and combines projective hashing as introduced by Cramer and Shoup with a construction of Burmester and Desmedt. Our protocol is constant-round. Namely, it is a three-round protocol that can be seen as generalization of a two-party proposal of Gennaro and Lindell.

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Abstract: Group key management is one of the basic building blocks in securing group communication. A number of solutions to group key exchange have been proposed, but most of them are not scalable and require a number of rounds linear in the number of group members. We formally present a constant-round Identity-based protocol with forward secrecy for group key exchange, which is provably secure in the security model introduced by Bresson et al. Our protocol focuses on round efficiency and the number of communication round is only two. And, the protocol provides a batch verification technique, which simultaneously verifies the validity of messages from other group participants and greatly improves computational efficiency. Moreover, in our protocol, it is no necessary of always-online key generation center during the execution of the protocol compared to other Identity-based protocols. Key-Words:- provable security, identity-based, group key exchange, constant round, secret-share. 1

WSEAS TRANSACTIONS on SYSTEMS archive•Jan 1, 2008•6 citations
Abstract. A provably secure password-authenticated protocol for group key establishment in the common reference string (CRS) model is presented. Our construction assumes the participating users to share a common password and combines projective hashing as introduced by Cramer and Shoup with a construction of Burmester and Desmedt. Our protocol is constant-round. Namely, it is a three-round protocol that can be seen as generalization of a two-party proposal of Gennaro and Lindell.
Group key agreement protocol allows all the members to agree upon a common session key, which may be used for later secure communication among all the participants. Through incorporating ID-based authenticated two-party key agreement protocol proposed by McCullagh et al. and constant round group key agreement proposed by Burmester and Desmedt, we propose a new ID-based two round authenticated group key agreement protocol which is more efficient than previously proposed protocols in terms of both communication and computation cost.
We consider the problem of authenticated group key exchange among n parties communicating over an insecure public network. A number of solutions to this problem have been proposed; however, all prior provably-secure solutions do not scale well and, in particular, require O (n) rounds. Our main contribution is the first scalable protocol for this problem along with a rigorous proof of security in the standard model under the DDH assumption; our protocol uses a constant number of rounds and requires only O (1) \full modular exponentiations per user. Toward this goal (and adapting work of Bellare, Canetti, and Krawczyk), we first present an efficient compiler that transforms any ngroup key-exchange protocol secure against a passive eavesdropper to an authenticated protocol which is secure against an active adversary who controls all communication in the network. This compiler adds only one round and O (1) communication (per user) to the original scheme. We then prove secure | against a passive adversary | a variant of the two-round group key-exchange protocol of Burmester and Desmedt. Applying our compiler to this protocol results in a provably-secure three-round protocol for authenticated group key exchange which also achieves forward secrecy.
Key agreement protocols allow two or more participants exchange information over an open network with each other. In modern collaborative and distributed applications, authenticated group key agreement is one of the important issues. Recently identity-based authenticated key agreement protocol has been increasingly investigated because of the simplicity of a public key management. In this paper, we propose an authenticated three-round identity-based group key agreement protocol. The first round is for identity authentication, the second round is for key agreement, and the third round is for key confirmation. The proposed protocol is based on the protocol of Burmester and Desmedt, and the protocol is provably- secure in the random oracle model. In particular, the proposed authenticated identity-based group key agreement protocol provides a batch verification technique, which verifies the validity of transcripts from other group players simultaneously.
A desirable goal for cryptographic protocols is to guarantee security when the protocol is composed with other protocol instances. Universally composable (UC) protocols provide this guarantee in a strong sense: A protocol remains secure even when composed concurrently with an unbounded number of instances of arbitrary protocols. However, UC protocols for carrying out general tasks are known to exist only if a majority of the participants are honest, or in the common reference string (CRS) model where all parties are assumed to have access to a common string that is drawn from some pre-defined distribution. Furthermore, carrying out many interesting tasks in a UC manner and without honest majority or set-up assumptions is impossible, even if ideally authenticated communication is provided. A natural question is thus whether there exist more relaxed set-up assumptions than the CRS model that still allow for UC protocols. We answer this question in the affirmative: we propose alternative and relaxed set-up assumptions and show that they suffice for reproducing the general feasibility results for UC protocols in the CRS model. These alternative assumptions have the flavor of a "public-key infrastructure": parties have registered public keys, no single registration authority needs to be fully trusted, and no single piece of information has to be globally trusted and available. In addition, unlike known protocols in the CRS model, the proposed protocols guarantee some basic level of security even if the set-up assumption is violated.
A group key establishment protocol is presented and proven secure in the common reference string mode. The protocol builds on a group-theoretic assumption, and a concrete example can be obtained with a decision Diffie–Hellman assumption. The protocol is derived from a two-party solution by means of a protocol compiler presented by Abdalla et al. at TCC 2007, evidencing the possibility of meaningfully integrating cryptographic and group-theoretic tools in cryptographic protocol design. This compiler uses a standard ring configuration, where all users behave symmetrically, exchanging keys with their left and right neighbor, which are later combined to yield a shared group key.
Abstract: Group key management is one of the basic building blocks in securing group communication. A number of solutions to group key exchange have been proposed, but most of them are not scalable and require a number of rounds linear in the number of group members. We formally present a constant-round Identity-based protocol with forward secrecy for group key exchange, which is provably secure in the security model introduced by Bresson et al. Our protocol focuses on round efficiency and the number of communication round is only two. And, the protocol provides a batch verification technique, which simultaneously verifies the validity of messages from other group participants and greatly improves computational efficiency. Moreover, in our protocol, it is no necessary of always-online key generation center during the execution of the protocol compared to other Identity-based protocols. Key-Words:- provable security, identity-based, group key exchange, constant round, secret-share. 1