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 AM  Vol.4 No.7 , July 2013
New Practical Algebraic Public-Key Cryptosystem and Some Related Algebraic and Computational Aspects
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.
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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