Abstract
A Key Agreement Protocol is a tool by which two parties can share a common key for their subsequent communication .Many cryptographic protocols are based on the hardness of Integer Factorization and Discrete Logarithm Problem. Very few Protocols are based on search problems in non – abelian groups. In this paper we present a Tripartite Key Agreement Protocol Using Triple Decomposition Search Problem using which three parties may agree on a common shared key in two rounds. We have chosen Discrete Heisenberg group and three cyclic sub groups as our platform to apply the above protocol.
Highlights
A key agreement is a protocol by which two parties, commonly named Alice and Bob, agree on a secret key to use in their subsequent private communication
The first key exchange scheme was introduced by Diffie and Hellman in 1976, and independently by Merkle in 1978.So far, several key exchange protocols have been developed using the concept of combinatorial group theory, namely the Word Problem,Conjugacy Search Problem, Decomposition Problem, Triple Decomposition Problem Membership Search Problem and so on
In this paper we have proposed a Tripartite Key Agreement Protocol (KAP) using triple Decomposition Search Problem and applied it in the discrete Heisenberg group
Summary
The Discrete Heisenberg group may be described as the set of all integer triples endowed with the following multiplication, where p is a prime : (x, y, z) · (u, v, w) = (x + u + yw, y + v, z + w) mod p. The following computational facts about multiplication given above. May be presented as < α,β: [α, [α,β]] = 1 = [β, [α,β]] >, with α (resp.,β) corresponding to the generator (0, 1, 0) (resp.(0, 0, 1)). Result 1: Let L be any group, and let and τ be any elements of L satisfying the two relations given in Proposition 2.5 .there is a unique homomorphism h : → L such that h(0, 1, 0) = σ and h(0, 0, 1) = τ
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