Matrix Extensions of the RSA Algorithm

A new matrix extension of the RSA algorithm is proposed which is based on the Cayley-Hamilton theorem and a one-way function. The security of this algorithm rests upon both that of the RSA algorithm and the one-way function. The computational efficiency of the new algorithm depends on the dimension of the matrix. The most efficient implementation is the 2×2 case in which both encryption and decryption use a single modulo arithmetic multiplication and single evaluation of the one-way function.

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