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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Security Analysis of Provably Secure Constant Round Dynamic Group Key Agreement

J. C. M. TEO, Chaowei Tan, J.M. Ng

Published Nov 1, 2006• 6 citations
Publisher

Abstract

Recently, Dutta and Barua proposed provably secure constant round authenticated group key agreement protocols in dynamic scenario. In this letter, we show that their Leave Protocol does not provide forward secrecy, that is, a leaving user can still obtain the new session key used in subsequent sessions.
DOI
10.1093/ietfec/e89-a.11.3348

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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.
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.
The two round dynamic group key agreement protocol(DB08 protocol) proposed by Dutta and Barua doesn't provide key independence.To improve DB08 protocol,an ID-based authenticated key agreement protocol in dynamic peer groups is presented by using Sakai R and Kasahara M's key construction.To avoid the correlation of the sub-keys for different sessions,hash functions and session identifiers are included while computing the sub-keys in the new protocol.So the new protocol achieves key independence,and it provides perfect forward secrecy,KGC-forward secrecy and resistance to passive and active attacks as well.Compared with DB08 protocol,the computation and communication costs are greatly reduced in the new protocol.So the new protocol is more efficient and applicable for dynamic peer network.