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                

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(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.

Keywords

Public-Key Cryptosystem; Modular Matrix Ring

Conflicts of Interest

The authors declare no conflicts of interest.

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