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  3. Volume 13, 2023
  4. Analysis of multiplication algorithms in Galuis fields for the cryptographic protection of information

Analysis of multiplication algorithms in Galuis fields for the cryptographic protection of information

SISN.
2023;
Volume 13
: pp. 338 - 349
https://doi.org/10.23939/sisn2023.13.338
Authors:
  1. Ivan Zholubak
1
Lviv Polytechnic National University, Ukraine

The mathematical basis for processing a digital signature is elliptic curves. The processing of the points of an elliptic curve is based on the operations performed in the Galois fields GF(pm). Fields with a simple foundation are not well-studied and very interesting for research. In this paper, a comparison of the complexity of algorithms for the realization of the multiplication operation in Galois fields GF(pm) with different bases is carried out. Conducts a comparison of the 3 most common  multiplication algorithms. Found that fields with a base greater than 2 will have greater complexity of the algorithm.

Galois fields GF(dm)
multiplier
modified Guild cell
LUT
cell generator
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