Finite Field Arithmetic

Abstract

11.1 Prime fields of odd characteristic 201 Representations and reductions • Multiplication • Inversion and division • Exponentiation • Squares and square roots 11.2 Finite fields of characteristic 2 213 Representation • Multiplication • Squaring • Inversion and division • Exponentiation • Square roots and quadratic equations 11.3 Optimal extension fields 229 Introduction • Multiplication • Exponentiation • Inversion • Squares and square roots • Specific improvements for degrees 3 and 5