The 4-adic complexity of quaternary sequences with low autocorrelation and high linear complexity

Recently, Jiang et al. proposed several new classes of quaternary sequences with low autocorrelation and high linear complexity by using the inverse Gray mapping (JAMC, \textbf{69} (2023): 689--706). In this paper, we estimate the 4-adic complexity of these quaternary sequences. Our results show that these sequences have large 4-adic complexity to resist the attack of the rational approximation algorithm

Improved lower bound on the number of balanced symmetric functions over GF(p)

The lower bound on the number of n-variable balanced symmetric functions over finite fields GF(p) presented in {\cite{Cusick}} is improved in this paper

Linear Complexity of a New Class of Quaternary Generalized Cyclotomic Sequence with Period 2pm

Sequences with high linear complexity property are of importance in applications. In this paper, based on the theory of generalized cyclotomy, new classes of quaternary generalized cyclotomic sequences with order 4 and period 2pm are constructed. In addition, we determine their linear complexities over finite field F4 and over ℤ4, respectively

Constructions of binary array set with zero-correlation zone

Based on the perfect binary array and the orthogonal matrix, a new method of constructing zero-correlation zone binary array set is proposed, yielding binary array sets with member sizes almost achieve the theoretical upper bound. A recursive construction of zero-correlation zone binary array set is also proposed and the obtained array sets have even larger sizes as well as additional good correlation properties

Bivariate polynomial-based secret sharing schemes with secure secret reconstruction

A (t,n)-threshold scheme with secure secret reconstruction, or a (t,n)-SSR scheme for short, is a (t,n)-threshold scheme against the outside adversary who has no valid share, but can impersonate a participant to take part in the secret reconstruction phase. We point out that previous bivariate polynomial-based (t,n)-SSR schemes, such as those of Harn et al. (Information Sciences 2020), are insecure, which is because the outside adversary may obtain the secret by solving a system of [Formula presented] linear equations. We revise Harn et al. scheme and get a secure (t,n)-SSR scheme based on a symmetric bivariate polynomial for the first time, where t⩽n⩽2t-1. To increase the range of n for a given t, we construct a secure (t,n)-SSR scheme based on an asymmetric bivariate polynomial for the first time, where n⩾t. We find that the share sizes of our schemes are the same or almost the same as other existing insecure (t,n)-SSR schemes based on bivariate polynomials. Moreover, our asymmetric bivariate polynomial-based (t,n)-SSR scheme is more easy to be constructed compared to the Chinese Remainder Theorem-based (t,n)-SSR scheme with the stringent condition on moduli, and their share sizes are almost the same.Ministry of Education (MOE)The work of Jian Ding and Changlu Lin was supported in part by National Natural Science Foundation of China under Grant Nos. U1705264 and 61572132, in part by Natural Science Foundation of Fujian Province under Grant No. 2019J01275, in part by Guangxi Key Laboratory of Trusted Software under Grant No. KX202039, and in part by University Natural Science Research Project of Anhui Province under Grant No. KJ2020A0779. The work of Pinhui Ke was supported by National Natural Science Foundation of China under Grant Nos. 61772292 and 61772476. The work of Huaxiong Wang was supported by the Singapore Ministry of Education under Grant Nos. RG12/19 and RG21/18 (S)

Further Constructions of Almost Resilient Functions

Almost resilient function is the generalization of resilient function and have important applications in multiple authenticate codes and almost security cryptographic Boolean functions. In this paper,some secondary constructions are provided.In particular, the theorem 3 in [6] is improved. As #-almost(n, 1, k)-CI functions plays an important role in the secondary constructions, we concluded some properties and constructions. Specially we presented a spectrum characterization of balanced almost CI function, which can be used to identify a balanced almost CI function by computing its walsh spectra. Keywords: Almost resilient Functions; Resilient function; Almost correlation immune function