supported by the National Natural Science Foundation of China (60573032,60773092 and 61073149);Research Fund for the Doctoral Program of Higher Education of China (20090073110027)
Keccak is one of the five hash functions selected for the final round of the SHA-3 competition,and its inner primitive is a permutation called Keccak-f.In this paper,we observe that for the inverse of the only nonline...
Two criteria for orthogonal systems over finite fields are presented. The first one is an algorithm by use of Gr*ibner bases. The second one is a formula of the numbers of adjoint morphisms.
Let m, n and k be positive integers, m>1 and k≤n . Let Z m =Z/ m Z denote the residue class ring modulo m . Let Z denote the group of additive characters of ring Z m , x 0 denote the identity of Z . A necessary and s...
In the’recent decade, one-way functions have very. important applications in cryptograpy, especially in public key systems and generators of pseudorandom number. In fact, modem cryptograph is developed based on the a...
In [1], Shevrin posed two open problems on semigroups: (1) Is a semigroup every subsemigroup of which can be included in a finite ideal series nilpotent? (2) Is a semigroup whose proper subsemigroups all are nilpotent...
Let D and R be two finite sets, R^D={f; f: D→R} the set of all functions from D into R, G a permutation group acting on D, H a permutation group acting on R. L. Carlitz defined the strongly equivalent relation of fun...
A two-dimensional quasicrystal pattern with an eight-fold rotational axis has been found by N. Wang et al. (Phys. Rev. Lett., 59(1987), 1010). It is obvious that one-dimensional quasilattice with eight-fold rotational...
In November of 1984, D. Shechtman et al. obtained the first electron micrograph of a quasicrystal. In the high resolution electron micrograph, the bright dots along any straight line have Fibonacci permutations with t...
In November 1984, D. Shechtman et al. reported the first quasicrystal electron diffraction patterns in a splat-cooled Mn-Al alloy. This discovery has broken through