ELECTROTECHNIC AND COMPUTER SYSTEMS, Odessa national polytechnic university

MULTIPLIERS FOR GALOIS FIELDS TIME COMPLEXITY

Abstract:

Multipliers for binary Galois field GF (2ⁿ) hardware complexity allows to implement in FPGA an operational device with multiple multipliers. But because of the large structural complexity for some combinations of large order n of field and the multipliers number to make it is practically impossible. One of the possible choices of this problem solving is the move to using Galois fields with the base d, greater than 2. Multipliers for such extended Galois field GF (d^m) with approximately the same number of elements d^m » 2ⁿ are estimated in the article in terms of their time complexity to determine the fields in which the multiplier will have the least time complexity.

Authors:

Elias Rodrigue M., PhD ( rodrigue.elias@liu.edu.lb, ORCID ID: 0000-0003-4506-0368 )
Hlukhov Valerij S., Dr. of Science, Professor ( glukhov@polynet.lviv.ua, ORCID ID:0000-0002-0542-7447 )
Rahma Mokhammed K., ( muhamed_kadhem@yahoo.com, ORCID ID: 0000-0002-8377-1833 )

Keywords

time complexity - Galois field - expanded field - base of the field - order of the field – multiplier

DOI

http://dx.doi.org/10.15276/eltecs.22.98.2016.55

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