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Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over Z e × k i=0 F q i are obtained. And it shows that all the known ZDB functions using cyclotomic cosets over Z n are special cases of a generic construction. Moreover, applications of these ZDB functions are presented. key words: constant composition code, constant weight code, difference system of sets, frequency-hopping sequence, zero-difference balanced function

Security challenges brought about by the upcoming 5G era should be taken seriously. Code-based cryptography leverages difficult problems in coding theory and is one of the main techniques enabling cryptographic primitives in the postquantum scenario. In this work, we propose the first efficient secure scheme based on polar codes (i.e., polarRLCE) which is inspired by the RLCE scheme, a candidate for the NIST postquantum cryptography standardization in the first round. In addition to avoiding some weaknesses of the RLCE scheme, we show that, with the proper choice of parameters, using polar codes, it is possible to design an encryption scheme to achieve the intended security level while retaining a reasonably small public key size. In addition, we also present a KEM version of the polarRLCE scheme that can attain a negligible decryption failure rate within the corresponding security parameters. It is shown that our proposal enjoys an apparent advantage to decrease the public key size, especially on the high-security level.

In the past decades, considerable attention has been paid to the chaos-based image encryption schemes owing to their characteristics such as extreme sensitivity to initial conditions and parameters, pseudo-randomness, and unpredictability. However, some schemes have been proven to be insecure due to using a single chaotic system. To increase the security, this work proposes a novel image encryption scheme based on the piecewise linear chaotic map (PWLCM) and the standard map. To the best of our knowledge, it is the first chaos-based image encryption scheme combining the PWLCM with the standard map, which adopts permutation-diffusion structure. Unlike the traditional scrambling way, a hierarchical diffusion strategy, which not only changes the pixel position but also modifies the value, is employed in the permutation phase. The operation model of row-by-row and column-by-column is further used to enhance the efficiency in the diffusion process. Consequently, a good trade-off efficiency and security can be achieved. Furthermore, the numerical simulations and performance analyses illustrate that the proposed encryption scheme can be used in practical application scenarios requiring lightweight security.

Difference systems of sets (DSS) and frequency-hopping sequences (FHS) are two objects with many applications in wireless communication. Zero-difference balanced function (ZDBF) and near zero-difference balanced functions (NZDBF) are two types of functions which can be used to obtain optimal DSSs and FHSs. In order to obtain more optimal DSSs and FHSs, zero-difference function (ZDF) as a generalization of ZDBF and NZDBF was recently proposed. In this paper, four classes of ZDFs with good applications are given from some known ZDBFs. It is noticed that these ZDFs are neither ZDBFs nor NZDBFs. As a result, more optimal DSSs and FHSs with new flexible parameters are obtained. INDEX TERMSDifference system of sets, frequency-hopping sequence, zero-difference balanced function, zero-difference function. I. INTRODUCTION Difference systems of sets (DSS) are related with comma-free codes [21], [29], authentication codes and secrete sharing schemes [15], [27]. Frequency-hopping sequences are used to reduce the interferes between the wireless devices in CDMA communication [6], [11], [12], [14]. Definition 1 [8]: Let (A, +) and (B, +) be two finite Abelian groups. A function from A to B is an (n, m, λ) zero-difference balanced function (ZDBF), if there exists a constant number λ such that for any nonzero element a ∈ A, |{x ∈ A | f (x + a) − f (x) = 0}| = λ, where n = |A| and m = |f (A)|. Ding first proposed the concept of ZDBF in 2008 [8], [8]. Since optimal DSSs and FHSs can be obtained from ZDBFs, many researchers have been working on constructing ZDBFs (see [3]-[5], [8], [9], [13], [22], [31], [33], [35], [37]-[39] and the references therein). It is worth mentioning that in The associate editor coordinating the review of this article and approving it for publication was Zilong Liu.