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Informatica

Analysis and Improvement on a Contributory Group Key Exchange Protocol Based on the Diffie–Hellman Technique

Yuh‐Min Tseng, Tsu‐Yang Wu

Published Jan 1, 2010• 10 citations
Publisher

Abstract

In 2008, based on the two-party Diffie–Hellman technique, Biswas proposed a contributory group key exchange protocol called the Group-DH protocol. This contributory property is an important one of group key agreement. Unfortunately, in this paper we show that the proposed Group-DH protocol is not a contributory group key exchange protocol. Therefore, we propose an improved group key exchange protocol with verifiably contributory property based on the same Diffie–Hellman technique. When an identical group key is constructed, each participant can confirm that his/her contribution is actually included in the group key. We show that the improved protocol is provably secure against passive attacks under the decisional Diffie–Hellman assumption. As compared to the previously proposed group key exchange protocols, our protocol provides contributiveness and the required computational cost is suitable for low-power participants in a network environment.

DOI
10.15388/informatica.2010.286

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In 2008, based on the two-party Diffie–Hellman technique, Biswas proposed a contributory group key exchange protocol called the Group-DH protocol. This contributory property is an important one of group key agreement. Unfortunately, in this paper we show that the proposed Group-DH protocol is not a contributory group key exchange protocol. Therefore, we propose an improved group key exchange protocol with verifiably contributory property based on the same Diffie–Hellman technique. When an identical group key is constructed, each participant can confirm that his/her contribution is actually included in the group key. We show that the improved protocol is provably secure against passive attacks under the decisional Diffie–Hellman assumption. As compared to the previously proposed group key exchange protocols, our protocol provides contributiveness and the required computational cost is suitable for low-power participants in a network environment.
Authenticated key-exchange protocols allow two participants A and B , communicating over a public network and each holding an authentication means to exchange a shared secret value. Methods designed to deal with this cryptographic problem ensure A (resp. B ) that no other participants aside from B (resp. A ) can learn any information about the agreed value and often also ensure A and B that their respective partner has actually computed this value. A natural extension to this cryptographic method is to consider a pool of participants exchanging a shared secret value and to provide a formal treatment for it. Starting from the famous two-party Diffie--Hellman (DH) key-exchange protocol and from its authenticated variants, security experts have extended it to the multiparty setting for over a decade and, in the past few years, completed a formal analysis in the framework of modern cryptography. The present paper synthesizes this body of work on the provably-secure authenticated group DH key exchange.
Abstract We propose the first tight security proof for the ordinary two-message signed Diffie–Hellman key exchange protocol in the random oracle model. Our proof is based on the strong computational Diffie–Hellman assumption and the multiuser security of a digital signature scheme. With our security proof, the signed DH protocol can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate any security loss. We abstract our approach with a new notion called verifiable key exchange. In contrast to a known tight three-message variant of the signed Diffie–Hellman protocol (Gjøsteen and Jager, in: Shacham, Boldyreva (eds) CRYPTO 2018, Part II. LNCS, Springer, Heidelberg, 2018), we do not require any modification to the original protocol, and our tightness result is proven in the “Single-Bit-Guess” model which we know can be tightly composed with symmetric cryptographic primitives to establish a secure channel. Finally, we extend our approach to the group setting and construct the first tightly secure group authenticated key exchange protocol.
Abstract. Authenticated Diffie-Hellman key exchange allows two principals communicating over a public network, and each holding public/private keys, to agree on a shared secret value. In this paper we study the natural extension of this cryptographic problem to a group of principals. We begin from existing formal security models and refine them to incorporate major missing details (e.g., strong-corruption and concurrent sessions). Within this model we define the execution of a protocol for authenticated dynamic group Diffie-Hellman and show that it is provably secure under the decisional Diffie-Hellman assumption. Our security result holds in the standard model and thus provides better security guarantees than previously published results in the random oracle model. 1
Group key exchange protocols play main role in group applications such as computer networks, telecommunication and military systems. Given the wide range of usage of group applications, research and design of these protocols can play an important role in securing international exchanges, trade and military issues. Most existing group key exchange protocols establish multi-party or group key exchange protocols based on extending the two party well known Diffie- Hellman key exchanges. The security of these protocols is based on this assumption that difficulty of solving group Dif- fie-Hellman problem can be reduced to the difficulty of two party Diffie-Hellman problems. In spite of this assumption, Group key exchanges are not simply extension of two party protocols. In fact there are many differences and challenges that must be considered in design and implementation of these protocols. This difference is due to essential difference between peer to peer communication and group communication. In group communication in addition to considering the main goal e.g. obtaining group session key, consideration of group member changing is important too. In this paper, a Dynamic ID-based Group Key Agreement protocol based on Weil pairing is proposed. This complete ternary tree struc- ture is used and dynamic changes in group are considered too. Finally we show that the proposed protocol is more effi- cient than other protocols with similar structure and also satisfies all known security requirements .
Certificateless public key cryptography (CL-PKC) avoids the inherent escrow of identity-based cryptography and does not require certificates to guarantee the authenticity of public keys. Based on CL-PKC, we present an efficient constant-round group key exchange protocol, which is provably secure under the intractability of computation Diffie-Hellman problem. Our protocol is a contributory key exchange with perfect forward secrecy and has only two communication rounds. So it is more efficient than other protocols. Moreover, our protocol provides a method to design efficient constant-round group key exchange protocols and most secret sharing schemes could be adopted to construct our protocol.
Authenticated group key exchange (AGKE) enable a set of participants in a public network to share a key which can be further used to achieve confidentiality and authentication. Most of the schemes required a linear number of communications round with respect to the number of group members, such schemes are not practical. Others are inefficient being required some additional condition such as central authority or logic structure. After analyzed the security of bresson's protocol, a improved scheme is proposed, which is simple and efficient. The scheme is proven secure under Decisional Diffie-Hellman assumption.