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New Practical Algebraic Public-Key Cryptosystem and Some Related Algebraic and Computational Aspects
Faculty of Mathematics and Mechanics, Tomsk State University, Tomsk, Russia
- 1 Faculty of Mathematics and Mechanics, Tomsk State University, Tomsk, Russia
Applied Mathematics·Volume 04 (2013)·Pages 1043–1049·Published 28 June 2013·DOI10.4236/am.2013.47142
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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 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.
KeywordsPublic-Key CryptosystemModular Matrix Ring
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