A Novel Provably Secure Key Agreement Protocol Based On Binary Matrices

In this paper, a new key agreement protocol is presented. The protocol uses exponentiations of matrices over GF(2) to establish the key agreement in only single step of message exchange. Security analysis of the protocol shows that the shared secret key is indistinguishable from the random under Decisional Diffie-Hellman (DDH) Assumption for subgroup of matrices over GF(2) with prime order, and furthermore, the analysis shows that, unlike many other exponentiation based protocols, security of the protocol goes beyond the level of security provided by (DDH) Assumption and intractability of Discrete Logarithm Problem (DLP). Actually, security of the protocol completely transcends the reliance on the DLP in the sense that breaking the DLP does not mean breaking the protocol. Complexity of brute force attack on the protocol is equivalent to exhaustive search for the secret key. Analysis of the performance demonstrates that the protocol is applicable to real-time applications.