Carl Bracken

TL;DR: Two new infinite families of APN functions are introduced, one on fields of order 2^2^k for k not divisible by 2, and the other on field of order2^3^k with polynomials between three and k+2 terms.

TL;DR: This article demonstrates that the highly nonlinear permutation f(x)=x^2^^^2^k^+^ 2^^^k+^1 on the field F"2" ^"4"^"k, discovered by Hans Dobbertin (1998), has differential uniformity of four and hence, with respect to differential and linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem as the inverse function.

TL;DR: This paper constructs the first class of binomial differentially 4 uniform permutations with high nonlinearity on F 2 6 m, where m is an odd integer and gives a positive answer to an open problem proposed in Bracken and Leander (2010).

TL;DR: An infinite family of quadrinomial APN functions on GF(2n) where n is divisible by 3 but not 9 is presented, and the inequivalence proof which shows that these functions are new is discussed.

TL;DR: The Walsh spectrum is computed and hence the nonlinearity of a new family of quadratic multi-term APN functions is shown and it is shown that the distribution of values in the Walsh spectrum of these functions is the same as the Gold function.