Learn More
a r t i c l e i n f o a b s t r a c t Differentially 4 uniform permutations with high nonlinearity on fields of even degree are crucial to the design of S-boxes in many symmetric cryptographic algorithms. Until now, there are not many known such functions and all functions known are power functions. In this paper, we construct the first class of binomial(More)
Differentially 4-uniform permutations on F 2 2k with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred functions, to construct a lot of infinite families of such permutations [14]. In this paper, we propose a particular type of Boolean(More)
Keccak was seleted as SHA-3 by NIST among 64 submissions in 2012. The submitted version of Keccak has an internal state size of b = 1600 bits, and the output size of 224, 256, 384, 512 bits. Recently, the differential cryptanalysis on Keccak has been received a lot of attention for building a distinguisher and for producing (near-)collisions. In these(More)
In this paper, we introduce a recursive construction of p-ary bent functions, where p is an odd prime. Several new non-quadratic bent functions over fields with characteristic 5, 7, 11, 13, 17, 19, 23 are found by computer search, all of which are homogeneous. A ternary bent function whose algebraic degree attains the upper bound is given. So far it is the(More)
Recently, a family of quadratic APN functions was demonstrated by Bracken et al. to exist over $\mathbb{F}_{2^{2k} } $ with k even and 3 ∤ k. This family of APN functions was firstly proposed by Budaghyan et al. and they exist provided the existence of a quadratic polynomial of the type $x^{2^s + 1} + cx^{2^s } + c^{2^k } x + 1$ with no zeros in(More)