Creation of Database of Irreducible Polynomial Over A Finite Field GF(2) Based on FPGA


Authors : Bekmuratova AB; Bakytzhan A.B

Volume/Issue : Volume 8 - 2023, Issue 2 - February

Google Scholar : https://bit.ly/3IIfn9N

Scribd : https://bit.ly/3lZ7TcB

DOI : https://doi.org/10.5281/zenodo.7676755

Cryptographic systems based on nonpositional polynomial systems make it possible to create an effective highly reliable cryptographic system that ensures confidentiality, authenticity and integrity of stored and transmitted information. The basis of nonpositional polynomial number systems are irreducible polynomials over the field GF(2). The article discusses a method for creating a database of irreducible polynomials in a finite field GF(2) based on software logic integrated circuits. The main idea of the algorithm for creating a base of irreducible polynomials in a finite field GF(2) is to study the nonlinearity of all polynomials in a finite field GF(2) using the Ben-Or algorithm. The algorithm is implemented in the Verilog HDL language. However, multiplication on finite fields is often a time-consuming task requiring hardware and software. To solve the problem, an FPGA is used, which allows to implement parallel multipliers that perform a full multiplication operation in several cycles. Functional and temporal modeling of the behavioral model algorithm was performed using examples and the correctness of the algorithm was confirmed. The scheme of the device at the register transfer level (RTL) for FPGA is obtained.

Keywords : Irreducible Polynomials, Cryptography, Programmable Logic Integrated Circuits, Ben-or Algorithm.

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