Encryption Method Based on Codes
This paper proposes an improvement of the McEliece asymmetric cryptosystem based on code-based cryptography by replacing the permutation matrix with a modulo operation and using a finite field $GF(q)$.
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Program model of Reed-Solomon codes
Software is designed for modeling of Reed-Solomon codes on a base of object-oriented technology. Input data for system are blocks of bytes for transmitting through communication channel, where errors can occur in the blocks. Designed program realizes codes of (255,239) and (255,223) type for finite field GF(28) with standard generating polynomials x8+x4+x3+x2+1 and x8+x7+x2+x+1. Moreover, a possibility is provided to add other types of codes and generating polynomials.
Elements of high multiplicative order in extended finite fields on a base of modified GAO approach
The Gao approach to construction of high order elements in arbitrary finite fields is to choose a convenient polynomial, which defines an extension of an initial prime field. This choice depends on one polynomial-parameter. That is why the mentioned approach can be considered as using of a finite field description with one degree of freedom. We explore in the paper the possibility of improvement of lower bound on element orders in finite fields of general form with using of two degrees of freedom.