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

S. K. Rososhek

Faculty of Mathematics and Mechanics, Tomsk State University, Tomsk, Russia.

**DOI: **10.4236/am.2013.47142
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Faculty of Mathematics and Mechanics, Tomsk State University, Tomsk, Russia.

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.

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S. Rososhek, "New Practical Algebraic Public-Key Cryptosystem and Some Related Algebraic and Computational Aspects," *Applied Mathematics*, Vol. 4 No. 7, 2013, pp. 1043-1049. doi: 10.4236/am.2013.47142.

Conflicts of Interest

The authors declare no conflicts of interest.

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