Basis Conversion in Composite Field
Intan Muchtadi-Alamsyah, Fajar Yuliawan · International journal of mathematics and computation · 2013
The theory of composite fields has important applications in cryptography. The use of composite field characteristic of dividing one big chunk of operation into smaller ones, allows us to implement in limited resources with adequate level of security. Two type of basis of composite field GF ((2)) over GF (2) are of particular interest, polynomial basis of the form {1, α, α, · · · , αm−1} and type I and type II optimal normal basis of the form {α, α, · · · , α2} for some element α in GF ((2)). Choosing between optimal normal basis and polynomial basis depends on the application. This paper presents a method to convert from the representation of a composite field element in one basis to the representation of a composite field element in another basis.