The Efficient Multiplier GF(2^(8)) is Formed by The
NAYK Algorithm
Muhamad Nursalman
1
, Arif Sasongko
2
{mnursalman@upi.edu
1
, asasongko@stei.itb.ac.id
2
}
Department of Computer Science Education, FPMIPA, Universitas Pendidikan Indonesia
1
School of Electronics and informatics Engineering, Institut Teknologi Bandung
2
Abstract. The efficient multiplier in Finite Field is needed in its implementation in the
cryptography field. The NAIK algorithm provides fast steps and efficient solutions in
forming the desired multiplier. The formation of an efficient multiplier GF(2^8) will be
formed with the NAYK algorithm without being constructed from the smallest values, but
directly from the value 8 itself. In comparison the NAYK algorithm provides a more
efficient solution.
Keywords: Efficient multiplier, Finite field, GF(2^8), NAYK algorithm, Generalization
of karatsuba algorithm
1 Introduction
This research developed two methods, these are the methods to reduce of sum of
multiplication and to find solution for all formula by exhaustive search. Both the development
of formula and algorithm that if executed one by one in the process of reducing the
multiplication does not give better results, due to the constraints of the selection of products to
be combined quite difficult [4], especially for large n, moreover the memory size is bounded
and processing time is very long. But if we combine both and by utilizing the properties of
algebra which appeared in the multiplication of polynomials in GF(2
n
), then both the
development of formula and algorithm give the process much better than the research that has
been done [3,5-9,]. In addition, when compared with the previous researches [3,5,9], the
combination of both formula and algorithm provides a process much easier.
2 Related Research and Theory
2. 1 Algorithm of Karatsuba Improved by Christof Paar
The formula in polynomial with degree (n-1) [1,2], then calculate
MSCEIS 2019, October 12, Bandung, Indonesia
Copyright © 2020 EAI
DOI 10.4108/eai.12-10-2019.2296349