An authenticated group key distribution protocol based on the generalized Chinese remainder theorem

Abstract

The group key distribution protocol is a mechanism for distributing a group key that is used to encrypt the communication data transmitted in an open group. Recently, a novel group key distribution protocol based on secret sharing was proposed. In their protocol, the group key information is broadcast in an open network environment, and only authorized group members can obtain the group key. However, their protocol requires each group member to broadcast a random challenge to the rest of the group members in the construction of the group key, and this may increase communication cost and cause network traffic congestion. In this paper, we propose an authenticated group key distribution protocol based on the generalized Chinese remainder theorem that drastically reduces communication costs while maintaining at least the same degree of security. Our protocol is built on the secret sharing scheme based on Chinese remainder theorem, which requires fewer computation operations than the previous work. 127This paper focuses on how to construct a secure and efficient group key distribution protocol. Although group key distribution [2-6, 12-15] has been deeply researched, it still remains open in cryptography. A secure and efficient group key distribution scheme should allow only authorized members to share a common session key for secure group communication. Some group key distribution protocols [2, 3, 5, 6] have been proposed based on the Diffie-Hellman key agreement protocol.In 2003, Sáze [16] utilized the secret sharing scheme [17] to distribute the group key. A trusted offline server can be used to distribute secret pieces to all authorized group members in the initialization phase. Then, only the authorized members that obtained the secret piece can achieve the secret data in the following group key distribution phase. In 2010, Harn and Lin [12] proposed an efficient authenticated group key transfer protocol based on Shamir's secret sharing scheme [17], in which the group manager transfers the group key among the group members by broadcasting group key information. With Shamir's (t , n) threshold scheme, any authorized group member can obtain the group key, and unauthorized users cannot obtain anything about the group key. Their protocol can withstand outsider attack and insider attack. Furthermore, its security does not rely on unproven assumptions, so its security feature is information theoretically secure. However, Harn and Lin's protocol requires that, when group members want to construct a group key or a member joins or leaves the group, each group member has to broadcast a random challenge as an input of a function used to generate the group key. This requirement may cause network traffic congestion and increase communication cost.The current paper, inspired by Harn and Lin's scheme, proposes a new group key distribution scheme based on the generalized Chinese remainder theorem (GCRT) that drastically reduces computation and communication costs and maintains at least the same security degree. In addition to an...

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An authenticated group key distribution mechanism using theory of numbers

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