Galois fields elements processing units for cryptographic data protection in cyber-physical systems
Date
2017-12-03
Journal Title
Journal ISSN
Volume Title
Publisher
Lviv Politechnic Publishing House
Abstract
Currently, elliptic curves are the mathematical
basis for digital signature processing. Elliptic curve points
processing is based on the performance of operations in
Galois field GF(2m) in normal or polynomial bases.
Characteristics of multipliers for these bases are different.
In this paper, the time complexity of software multipliers
for binary Galois fields GF(2m) and fields GF(dn) was
investigated. Fields with approximately the same number of
elements were investigated. Elements of these fields were
represented in a polynomial basis. It is established that the
Galois field GF(3т) provides the greatest time complexity of
software multiplication, and the prime Galois field GF(P)
has the least time complexity. It is also shown that the use
of polynomial basis allows, in contrast to the normal basis,
to realize larger part of multiplier on FPGA chip.
Description
Keywords
Structural complexity, time complexity, Galois fields, extended fields, field degree, field order, normal basis, polynomial basis, multiplier
Citation
Galois fields elements processing units for cryptographic data protection in cyber-physical systems / Valerii Hlukhov, Andrii Kostyk, Ivan Zholubak, Mohammed Rahma // Advances in Cyber-Physical Systems. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 2. — No 2. — P. 47–53.