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