The most popular present-day public-key
cryptosystems are RSA and ElGamal cryptosystems. Some practical algebraic
generalization of the ElGamal cryptosystem is considered-basic modular matrix
cryptosystem (BMMC) over the modular matrix ring M2(Zn).
An example of computation for an artificially small number n is presented. Some possible attacks on the cryptosystem and
mathematical problems, the solution of which are necessary for implementing
these attacks, are studied. For a small number n, computational time for compromising some present-day public-key
cryptosystems such as RSA, ElGamal, and Rabin, is compared with the
corresponding time for the ВММС. Finally, some open mathematical and computational problems are
Cite this paper
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