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IEEE Transactions on Information Theory

Provably Secure Constant Round Contributory Group Key Agreement in Dynamic Setting

Ratna Dutta, Rana Barua

Published Apr 28, 2008• 104 citations

Abstract

In this paper, we present and analyze a variant of Burmester-Desmedt group key agreement protocol (BD) and enhance it to dynamic setting where a set of users can leave or join the group at any time during protocol execution with updated keys. In contrast to BD protocol, let us refer to our protocol as DB protocol. Although the DB protocol is similar to BD protocol, there are subtle differences between them: 1) Key computation in DB protocol is different and simpler than in BD protocol with same complexity of BD protocol; 2) Number of rounds required in our authenticated DB protocol is one less than that in authenticated BD protocol introduced by Katz-Yung; 3) DB protocol is more flexible than BD protocol in the sense that DB protocol is dynamic. The reusability of user's precomputed data in previous session enables the join and leave algorithms of our DB protocol to reduce most user's computation complexities which can be useful in real life applications; and 4) DB protocol has the ability to detect the presence of corrupted group members, although one can not detect who among the group members are behaving improperly.

DOI: 10.1109/tit.2008.920224

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Comments on "Provably Secure Constant Round Contributory Group Key Agreement in Dynamic Setting

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In a recent paper, Dutta and Barua presented a group key agreement protocol in dynamic setting. The protocol allows users to efficiently join or leave a group and was believed to be provably secure. In this letter, we point out a flaw in the Dutta-Barua dynamic group key agreement protocol.

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A group key agreement protocol provides a set of users with a shared secret key to achieve cryptographic goal. When membership changes, group session key should be updated efficiently and securely. Hence, dynamic group key agreement protocols are of practical significance. Identity-based group key agreement protocols are preferred to certificate-based ones since identity-based protocols can simplify public key management procedure. Most of previous dynamic group key agreement protocols need at least two rounds to establish or refresh group session keys. In this paper, an identity-based dynamic authenticated group key agreement (DAGKA) protocol is presented. It is round-optimal, since: 1) in setup and join algorithms, only one round of communication is required; 2) in leave algorithm, there is no message exchange among group members. Joining members cannot compute previous session keys and leaving members cannot compute subsequent session keys. The protocol is provably secure. Its AKE-security is proved under decisional bilinear Diffie-Hellman (DBDH) assumption. In addition, the protocol resists key control attack and achieves forward security.

A group key agreement protocol provides a set of users with a shared secret key to achieve cryptographic goal. When membership changes, group session key should be updated efficiently and securely. Hence, dynamic group key agreement protocols are of practical significance. Identity-based group key agreement protocols are preferred to certificate-based ones since identity-based protocols can simplify public key management procedure. Most of previous dynamic group key agreement protocols need at least two rounds to establish or refresh group session keys. In this paper, an identity-based dynamic authenticated group key agreement (DAGKA) protocol is presented. It is round-optimal, since: 1) in setup and join algorithms, only one round of communication is required; 2) in leave algorithm, there is no message exchange among group members. Joining members cannot compute previous session keys and leaving members cannot compute subsequent session keys. The protocol is provably secure. Its AKE-security is proved under decisional bilinear Diffie-Hellman (DBDH) assumption. In addition, the protocol resists key control attack and achieves forward security.

This paper presents an identity-based dynamic authenticated group key agreement (DAGKA) protocol with following advantages. The algorithms of Setup and Join has only one round communication. There is no message exchange among members in Leave algorithm. Joining members cannot know previous session keys and leaving members cannot know future session keys. Its AKE-security is proved under Decisional Bilinear Diffie-Hellman (DBDH) assumption. The protocol can resist key control attack and has forward security.

The members in the dynamic peer group (DPG) are divided into several clusters according to linker cluster architecture (J.B. Dennis and E. Anthony, 1981). In each cluster, the members perform the BD protocol (M. Burmester and Y. Desmedt, 1994) to establish the cluster key and the TGDH protocol (Y. Kim et al., 2004) is performed among the clusters to generate the group key. This method can not only avoid the weakness of AKA (auxiliary key agreement) of BD, but also reduce the computation cost of TGDH scheme. In our scheme the members have been authenticated based identity, and we prove the security in random oracle model.