Arithmetic of Finite Fields

Chapter 1 Generalised Jacobians in Cryptography and Coding Theory

Chapter 2 The Weight Distribution of a Family of Reducible Cyclic Codes

Chapter 3 A New Method for Constructing Small-Bias Spaces from Hermitian Codes

Chapter 4 An Improved Threshold Ring Signature Scheme Based on Error Correcting Codes

Chapter 5 Sequences and Functions Derived from Projective Planes and Their Difference Sets

Chapter 6 On Formally Self-dual Boolean Functions in 2,4 and 6 Variables

Chapter 7 On the Algebraic Normal Form and Walsh Spectrum of Symmetric Functions over Finite Rings

Chapter 8 Verification of Restricted EA-Equivalence for Vectorial Boolean Functions

Chapter 9 Software implementation of modular exponentiation, using advanced vector instructions architectures

Chapter 10 Efficient Multiplication over Extension Fields

Chapter 11 $\textrm{GF}(2^m)$ Finite-Field Multipliers with Reduced Activity Variations

Chapter 12 Finding Optimal Formulae for Bilinear Maps

Chapter 13 Solving Binary Linear Equation Systems over the Rationals and Binaries

Chapter 14 Hashing with Elliptic Curve L -Functions

Chapter 15 Square Root Algorithms for the Number Field Sieve

Chapter 16 Improving the Berlekamp Algorithm for Binomials x n  −  a

Chapter 17 On Some Permutation Binomials of the Form $x^{\frac{2^n-1}{k}+1} +ax$ over $\mathbb{F}_{2^n}$ : Existence and Count