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

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DOI: 10.4236/am.2013.47142    2,760 Downloads   3,962 Views   Citations
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ABSTRACT

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 formulated.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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