Xiangyong Zeng

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Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets,(More)
In this paper, three constructions of balanced Boolean functions with optimal algebraic immunity are proposed. It is checked that, at least for small numbers of input variables, these functions have good behavior against fast algebraic attacks as well. Other cryptographic properties such as algebraic degree and nonlinearity of the constructed functions are(More)
In this paper, a new generalized cyclotomy with respect to a positive odd integer is introduced, and a construction of frequency hopping sequence sets and two constructions of frequency hopping sequences are proposed as its applications. The frequency hopping sequence sets and frequency hopping sequences obtained in this paper can be optimal with respect to(More)
In this paper, we present a class of 2k-variable balanced Boolean functions and a class of 2k-variable 1-resilient Boolean functions for an integer k ≥ 2, which both have the maximal algebraic degree and very high nonlinearity. Based on a newly proposed conjecture by Tu and Deng, it is shown that the proposed balanced Boolean functions have optimal(More)
This paper studies a class of binomial functions over the finite fields of odd characteristic and characterizes their bentness in terms of the Kloosterman sums. Numerical results show that the proposed class contains bent functions that are affinely inequivalent to all known monomial and binomial ones.
For a prime power q, let Fq be the finite field with q elements and F ∗ q denote its multiplicative group. A polynomial f ∈ Fq[x] is called a permutation polynomial (PP) if its associated polynomial mapping f : c 7→ f(c) from Fq to itself is a bijection. A permutation polynomial f(x) is referred to as a complete permutation polynomial (CPP) if f(x)+x is(More)
Thanks to a method proposed by Carlet, several classes of balanced Boolean functions with optimum algebraic immunity are obtained. By choosing suitable parameters, for even n ≥ 8, the balanced n-variable functions can have nonlinearity 2n−1− `n−1 n 2−1 ́ + 2 ` n−2 n 2−2 ́ /(n− 2), and for odd n, the functions can have nonlinearity 2n−1 − `n−1 n−1 2 ́ +(More)