Handbook of Applied Cryptography
Handbook of Applied Cryptography
Covering Sequences of Boolean Functions and Their Cryptographic Significance
Designs, Codes and Cryptography
Connections among nonlinearity, avalanche and correlation immunity
Theoretical Computer Science - Algorithms,automata, complexity and games
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Journal of Complexity - Special issue on coding and cryptography
IEEE Transactions on Information Theory
Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions
Finite Fields and Their Applications
Interpolation of the Double Discrete Logarithm
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
On the nonlinearity of discrete logarithm in F2n
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Boolean functions derived from Fermat quotients
Cryptography and Communications
Boolean functions derived from pseudorandom binary sequences
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
"Provable" security against differential and linear cryptanalysis
FSE'12 Proceedings of the 19th international conference on Fast Software Encryption
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In public-key cryptography the discrete logarithm has gained increasing interest as a one-way function. This paper deals with the particularly interesting case of the discrete logarithm in finite fields of characteristic two. We obtain bounds on the maximal Fourier coefficient, i.e., on the non-linearity, on the degree and the sparsity of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic. The proofs of the results for odd characteristic involve quadratic character sums and are not directly extendable to characteristic two. Here we use a compensation for dealing with the quadratic character.