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New Practical Algebraic Public-Key Cryptosystem and Some Related Algebraic and Computational Aspects

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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 *M*_{2}(Z_{n}).
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
formulated.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*Applied Mathematics*, Vol. 4 No. 7, 2013, pp. 1043-1049. doi: 10.4236/am.2013.47142.

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