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Extension of RSA Cryptosystems to Matrix Rings

A generalization of the RSA cryptosystem in the ring of matrices over Z/mZ is presented. It is shown that factorization of the modulus m is needed to compute the exponent of the group formed by either non-singular matrix messages or upper triangular matrices including diagonal elements thus offering the same level of security as the RSA system. The latter method employing the triangular matrices as messages seems to be more practical than the use of arbitrary non-singular matrix messages. The scheme is as suitable for privacy and authentication as its predecessor.