TITLE:
New Practical Algebraic Public-Key Cryptosystem and Some Related Algebraic and Computational Aspects
AUTHORS:
S. K. Rososhek
KEYWORDS:
Public-Key Cryptosystem; Modular Matrix Ring
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.7,
July
11,
2013
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.