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Allerton Conference on Communication, Control, and Computing

Unconditionally secure conference key distribution: Security definitions and their relations

Reihaneh Safavi–Naini, Shaoquan Jiang

Published Sep 1, 2008• 0 citations
Publisher

Abstract

A non-interactive conference key distribution scheme (NICKDS) is a system that allows selected sets of users to securely share a common key without interacting with each other. In this paper, we consider unconditionally secure setting where the is no limit on adversary's computation power. Unconditionally secure NICKDS has been considered with security against an adversary who can corrupt up to w users. We strengthen the security model of the system by allowing the adversary to also obtain conference keys of conferences whose members are honest, and use a game bases approach to define security. We give two other ways of defining security, using probability distance and mutual information and show the relationship between the three definitions of security.

DOI
10.1109/allerton.2008.4797698

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A non-interactive conference key distribution scheme (NICKDS) is a system that allows selected sets of users to securely share a common key without interacting with each other. In this paper, we consider unconditionally secure setting where the is no limit on adversary's computation power. Unconditionally secure NICKDS has been considered with security against an adversary who can corrupt up to w users. We strengthen the security model of the system by allowing the adversary to also obtain conference keys of conferences whose members are honest, and use a game bases approach to define security. We give two other ways of defining security, using probability distance and mutual information and show the relationship between the three definitions of security.
A key distribution scheme is a method by means of which a trusted party distributes pieces of information among a set of users in such a way that each group of them can compute a common key for secure communication. In this paper we present a model for unconditionally secure key distribution schemes, i.e., schemes whose security is independent of the power of the adversary. We prove lower bounds on the amount of information the trusted party has to generate and each user has to keep secret in such schemes, and we show that some previous unconditionally secure models for key distribution fall in our model. As a consequence, the lower bounds given in the literature for these models can be seen as corollaries of our results. Hence, the main contribution of the paper consists in pointing out a sort of common structure underlying some apparently different key distribution techniques.
An original approach to establish a computationally secure and robust conference key between multiple users is presented, which is built on known secret sharing schemes and requires the authenticated and encrypted point-to-point channels between servers and users. By running of the protocol, every honest user of a given conference can get a common key, even if a minority of the servers malfunction or misbehave. This scheme does not rely on any unproven cryptographic assumptions or on the availability of any tamper-proof hardware. By using zero knowledge proof, any corrupted information and incorrect results can be detected. And by distributing the sensitive security information across several servers and never reconstructing any key at a single location, the compromise of a few servers will not compromise the privacy of any key. Analysis shows that under the assumption of a Diffie-Hellman decisional problem, a passive adversary gets zero knowledge about the conference key, and in the random oracle model, an active adversary cannot impersonate successfully. We have implemented the scheme in a distributed environment. By conducting a number of experiments in the fault-free case and various fault scenarios, we show that it has an acceptable performance of practicability.
A computationally secure and robust conference key distribution scheme is presented, which requires only the authenticated and encrypted point-to-point channels between each server and each user. By using it, every honest user of a conference can get a common key after running of the protocol, even if some minority of the servers malfunction or misbehave. Analysis shows that a passive adversary gets zero knowledge about the conference key, and the active adversary cannot impersonate successfully. Because this scheme is noninteractive, both operation and communication overhead are reduced, this make it very efficient.
This paper proposes a computationally secure and fault-tolerant conference key distribution scheme, which only requires the authenticated and encrypted point-to-point channels between each server and each user. By the combined use of knowledge proof and verifiable secret sharing, the scheme has the properties of simple structure and high security. Analysis shows that every honest user of a conference can get a common key after the running of the protocol, even if a minority of the servers malfunction or misbehave. We also show that on the assumption of a Diffie-Hellman decisional problem, a passive adversary gets zero knowledge about the conference key, and the active adversary cannot impersonate someone successfully. Because the knowledge proof method we adopt is non-interactive, both operation and communication overheads are reduced, thus making the schemes very efficient.
We focus on unconditionally secure conference key distribution. Many onetime keys shared by users are needed for perfect secure communication. Our approach is to use a twoparty key agreement system as an underlying cryptographic primitive and extend it to a conference system which is as secure as the twopart system. With the spanning tree in this paper, the conference key distribution system can be executed in parallel to the largest extent and it is efficient for dynmaic changing group.