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The Computer Journal

An Efficient and Secure Protocol for Multi-party Key Establishment

Gwoboa Horng

Published May 1, 2001• 22 citations
Publisher

Abstract

In this paper, a multi-party key establishment protocol based on the difficulty of calculating discrete logarithms in a finite field is proposed with the following features. It requires a constant number (independent of the number of participants) of rounds. All messages have the same constant size. All participants perform a constant number of exponential operations. All participants agree on a key together with two random integers simultaneously. Furthermore, to establish a new key when the set of participants is changed is easy. We also show that this new scheme is secure against passive attacks provided that the Diffie–Hellman key agreement protocol is secure in the sense that the established key is computationally indistinguishable from a random value.

DOI
10.1093/comjnl/44.5.463

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In this paper, a multi-party key establishment protocol based on the difficulty of calculating discrete logarithms in a finite field is proposed with the following features. It requires a constant number (independent of the number of participants) of rounds. All messages have the same constant size. All participants perform a constant number of exponential operations. All participants agree on a key together with two random integers simultaneously. Furthermore, to establish a new key when the set of participants is changed is easy. We also show that this new scheme is secure against passive attacks provided that the Diffie–Hellman key agreement protocol is secure in the sense that the established key is computationally indistinguishable from a random value.
By its very nature, a non-authenticated multi-party key agreement protocol cannot provide participant and message authentication, so it must rely on an authenticated network channel. This paper presents the inability of two famous multi-party key agreement protocols to withstand malicious participant attacks, even though their protocols are based on the authenticated network channel. This attack involves a malicious participant disrupting the multi-party key agreement among honest participants. In this case, other honest participants do not correctly agree on a common key. Obviously, the malicious participant cannot obtain the common key either, and the communication confidentiality among participants is not breached. However, in some emergency situations or applications, a multi-party key agreement protocol design that is resistant to malicious participants is useful. Therefore, in this paper, a non-authenticated multi-party key agreement protocol resistant to malicious participants is proposed. The proposed robust protocol requires constant rounds to establish a common key. Each participant broadcasts a constant number of messages. Under the assumption of the Decision Diffie–Hellman problem and the random oracle model, we will show that the proposed protocol is provably secure against passive adversaries and malicious participants.
Abstract. Key establishment protocols based on hardness assumptions, such as the discrete logarithm problem and the integer factorization problem, are vulnerable to quantum computer attacks, whereas the protocols based on other hardness assumptions, such as the conjugacy search problem and the decomposition search problem, can resist such attacks. The existing protocols based on the hardness assumptions which can resist quantum computer attacks are only passively secure. Compilers are used to convert a passively secure protocol to an actively secure protocol. Compilers involve some tools such as a signature scheme and a collision-resistant hash function. If there are only passively secure protocols but not a signature scheme based on the same assumption, then the application of existing compilers requires the use of such tools based on different assumptions. But the introduction of new tools, based on different assumptions, makes the new actively secure protocol rely on more than one hardness assumption. We offer an approach to derive an actively secure two-party protocol from a passively secure two-party protocol without introducing further hardness assumptions. This serves as a useful formal tool to transform any basic algebraic method of public key cryptography to the real world applicable cryptographic scheme.
A group key agreement protocol is designed to efficiently implement secure multicast channels for a group of parties communicating over an untrusted, open network by allowing them to agree on a common secret key. In the past decade many problems related to group key agreement have been tackled and solved (diminished if not solved), and recently some constant-round protocols have been proven secure in concrete, realistic setting. However, all forward-secure protocols so far are still too expensive for small mobile devices. In this paper we propose a new constant-round protocol well suited for a mobile environment and prove its security under the Decisional Diffie-Hellman assumption. The protocol meets simplicity, efficiency, and all the desired security properties.
For a secure communication through the public network, cryptographic encryption must be applied. The key establishment issue is the most important part in cryptographic encryption. Only the legitimate principals who have the key can encrypt messages and decrypt cryptograms. A secure multi-party communication held through the public network can only take place after a multi-party key establishment protocol has been executed. The multi-party key establishment protocol is designed so that the principals can receive a common key and use it to securely exchange the messages.\nIn this thesis, the secure multi-party key establishment protocols are discussed. W e start from investigating properties of two-party key establishment protocols such as motivation of using session key, adversaries in the protocols, attacks of the protocol and security analysis of the protocol. Then we give the requirements of a multi-party key establishment protocol and summarize about what should be considered in designing a multi-party key establishment protocol. After that we review some of the previous proposed multi-party key establishment protocol. The existing multi-party key establishment protocols are either impractical ( not efficient enough) or missing some important security goals such as authentication of principals. Three new protocols are proposed in this thesis. The first protocol addresses how to hold a conference for members of two hierarchical groups in an efficient way. The message broadcasting is used to reduce the cost of secure message transport.\nThe second and the third protocols manage the authentication problem by using a secret sharing scheme. We replace the principal authentication with the group authentication so that the computational overhead and communication overhead will be reduced especially in reuse of the protocol for new communication. Again, message broadcasting is used for replacing the expansive secure communication channel.\nPart of this thesis appeared in ACSC'99(Australian Computer Science Conference) and ACISP'99(Australian Conference of Information Security and Privacy).
A group key agreement protocol is designed to efficiently implement secure multicast channels for a group of parties communicating over an distrustful, open network by allowing them to agree on a common secret key. Recently some constant-round protocols have been proposed. However, some of them are too expensive with computational complexity O(n), others with lower computational complexity doesn't ensure the participants to get the same session key. In this paper we propose a new constant-round protocol suited for groups consisting of many hosts with limited computational capability and a host with more computational power. Then we prove its security.
A group key agreement protocol is designed to efficiently implement secure multicast channels for a group of parties communicating over an distrustful, open network by allowing them to agree on a common secret key. Recently some constant-round protocols have been proposed. However, some of them are too expensive with computational complexity O(n), others with lower computational complexity doesn't ensure the participants to get the same session key. In this paper we propose a new constant-round protocol suited for groups consisting of many hosts with limited computational capability and a host with more computational power. Then we prove its security.