  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.
