The Construction of Arithmetic Algorithms GF(5m) Generated by Cyclic Group Properties

Abstract

To construct a cryptographic algorithm, many arithmetic concepts are needed. ElGamal encryption for example, can be defined over cyclic group Zp, the usual arithmetic concepts. If the use of this arithmetic is associated with security aspect, then it requires large computational work. This thesis aims to construct arithmetic algorithm as an alternative arithmetic that can be applied to any cryptographic scheme, especially public key scheme. This algorithm is imposed from finite field GF(5m) . Thus, the procedures to construct arithmetic algorithm are as follows. The first step is to choose primitive polynomial M (x)eZ5[x] of lower degree. The second step is to find primitive root M(a)=0, thus the equation M(x)=0 has a root a in GF. The resulted arithmetic algorithms are computational procedures for standard operation in GF(5m) addition, multiplication, division, invertion, and exponentiation. It can be concluded that constructed arithmetic algorithms GF(5m) are better than standard algorithms because some operations can be reduced using primitive polynomial or cyclic group properties, and using reduction of zero. Keywords: arithmetic, cyclic group, GF(5m), primitive polynomial, cryptography. Normal 0 false false false IN X-NONE X-NONE