Applied Mathematics
Volume 4, Issue 7 (July 2013)
ISSN Print: 2152-7385 ISSN Online: 2152-7393
Google-based Impact Factor: 0.58 Citations
New Practical Algebraic Public-Key Cryptosystem and Some Related Algebraic and Computational Aspects ()
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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.
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