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Key Exchange Protocol using Matrix Algebras and its Analysis

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Abstract

A key exchange protocol using commutative subalgebras of a full matrix algebra is considered. The security of the protocol depends on the difficulty of solving matrix equations $XRY=T$, with given matrices $R$ and $T$. We give a polynomial time algorithm to solve $XRY=T$ for the choice of certain types of subalgebras. We also compare the efficiency of the protocol with the Diffie-Hellman key exchange protocol on the key computation time and the key size.

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