Implementasi dan Pengukuran Kinerja Operasi Aritmatika Finite Field Berbasis Polinomial Biner

Abstract

Cryptography is one of the security techniques that secure information confidentiality and information integrity while electronic transaction processing. There are three kinds of cryptograpy protocols, Symmetric Algorithms, Asymmetric (Public Key) Algorithms, and Cryptographic Protocols. Elliptic Curve Cryptography (ECC) is one of the public key encryption. ECC requires high computation for solving arithmetic operations.Finite field has important role in ECC implementation, which curve operations requires finite field. Finite field has several arithmetic operations, add, multiplication, squaring, and invers. There are many method or algorithm for each arithmetic operation. Finite field can be representation in prime field GF(p) and binary field GF(2m). There are two representation in binary field, polynomial basis and normal basis. This research presents implementation of arithmetic operation algorithms for adding, multiplication, squaring, and invers on polynomial basis with maximum key 299 bits. Besides that, this research presents the measurement of algorithm performance based on processing time and memory usage. Keywords — cryptography, elliptic curve, finite field, polynomial basis, binary field