A New Representation of Elements of Finite Fields GF(2m) Yielding Small Complexity Arithmetic Circuits

—Let F2 denote the binary field and F 2 m an algebraic extension of degree m > 1 over F2 . Traditionally, elements of F 2 m are either represented as powers of a primitive element of F 2 m together with 0, or by an expansion in a basis of the vector space F 2 m over F2 . We propose a new representation based on an isomorphism from F 2 m into the residue polynomial ring modulo X n

• Type: Journal
• Year: 1998
• Where: TC
• Authors: Germain Drolet
• Keywords: Algebraic Extension, Binary Field, Information Technology, Primitive Element, TC 1998