Dual and Hull code in the first two generic constructions and relationship with the Walsh transform of cryptographic functions

The construction of linear codes from functions in finite fields has been widely studied in the literature. There are two generic construction methods: the first and second generic construction methods for generating linear codes from functions over finite fields. In this paper, we first define the augmented code construction of the variation of the second generic construction method and then present new infinite families of four- and five-weight self-orthogonal divisible codes derived from trace functions. Moreover, by using the augmented code construction based on the first generic construction method, we construct new infinite families of three-weight and four-weight self-orthogonal divisible codes from weakly regular plateaued functions. We determine all parameters of the constructed self-orthogonal codes as well as their dual codes over the odd characteristic finite fields. We present Hamming weights and their weight distributions for the constructed self-orthogonal codes. Additionally, we utilise the constructed p-ary self-orthogonal codes to develop p-ary Linear Complementary Dual (LCD) codes and determine the parameters of the obtained LCD codes and their dual codes.

Linear codes with certain special properties have received renewed attention in recent years due to their practical applications. Among them, binary linear complementary dual (LCD) codes play an important role in implementations against side-channel attacks and fault injection attacks. Self-orthogonal codes can be used to construct quantum codes. In this paper, four classes of binary linear codes are constructed via a generic construction which has been intensively investigated in the past decade. Simple characterizations of these linear codes to be LCD or self-orthogonal are presented. Resultantly, infinite families of binary LCD codes and self-orthogonal codes are obtained. Infinite families of binary LCD codes from the duals of these four classes of linear codes are produced. Many LCD codes and self-orthogonal codes obtained in this paper are optimal or almost optimal in the sense that they meet certain bounds on general linear codes. In addition, the weight distributions of two sub-families of the proposed linear codes are established in terms of Krawtchouk polynomials.

Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many construction methods for linear codes from functions have been proposed in the literature. In this paper, we generalize the recent construction methods given by Tang et al. in [IEEE Transactions on Information Theory, 62(3), 1166-1176, 2016] to weakly regular plateaued functions over finite fields of odd characteristic. We first construct three-weight linear codes from weakly regular plateaued functions based on the second generic construction and then determine their weight distributions. We also give a punctured version and subcode of each constructed code. We note that they may be (almost) optimal codes and can be directly employed to obtain (democratic) secret sharing schemes, which have diverse applications in the industry. We next observe that the constructed codes are minimal for almost all cases and finally describe the access structures of the secret sharing schemes based on their dual codes.

Given a self-dual code over $$\mathbb{F }_q[u]/(u^t)$$ F q [ u ] / ( u t ) we present a method to obtain explicitly new self-dual codes of larger length. Conversely, we also prove that, with the appropriate assumptions on length and number of generators, every self-dual code over $$\mathbb{F }_q[u]/(u^t)$$ F q [ u ] / ( u t ) can be obtained in this manner. We use this construction to produce several optimal self-dual codes over the base field in a manner that generalizes the Lee weight. This construction is based on ideas presented by Han et al. (Bull Korean Math Soc, 49:135---143, 2012) and also by Lee and Kim (An efficient construction of self dual codes, 2012), not only generalizing it, but joining the two different cases from the original paper as special cases of one general construction.

New results on quaternary (Z4 = {0, 1, 2, 3}-valued) cryptographic functions are presented. We define and characterize completely the Z4-balancedness and the Z4-nonlinearity according the Hamming metric and the LEE metric. In the particular case of quaternary Bent functions we show that the maximal nonlinearity of these functions is bounded for the HAMMING metric and we give the exact value of the maximal nonlinearity of these functions for the LEE metric. A general construction, based on Galois ring is detailed and applied to obtain a class of balanced and high nonlinearity quaternary cryptographic functions. We use Gray map to derive these constructed quaternary functions to obtain balanced boolean functions having high nonlinearity.

11 The Relationship Between Antisocial and Prosocial Behaviors in Chinese Preschool Children

Boolean functions with good cryptographic characteristics are needed for the design of robust pseudo-random generators for stream ciphers and of S-boxes for block ciphers. Very few general constructions of such cryptographic Boolean functions are known. The main ones correspond to concatenating affine or quadratic functions. We introduce a general construction corresponding to the concatenation of indicators of flats. We show that the functions it permits to design can present very good cryptographic characteristics.

This study examined the extent to which adolescents’behavioral autonomy was predicted by several aspects of the parent‐youth relationship that are encompassed by the general constructs connectedness and restrictiveness. Both of these general relationship constructs are composed of more specific social‐psychological predictors consisting of parental behaviors, parent‐adolescent authority dimensions, and indicators of family ties. A total of 657 adolescents (mean age = 16.3 years) and 753 parents responded to self‐report questionnaires. Hierarchical multiple regression analyses were used to test the hypotheses from both the adolescents’and parents’perspectives in separate models. Many of the predictions were confirmed, indicating that adolescent behavioral autonomy often develops within contexts of relationship connectedness, such as continuing parent‐youth authority and supportiveness. Moreover, as expected, youthful autonomous behavior was inhibited by such aspects of relationship restrictiveness as punitive behavior and the perceived coercive abilities of parents.

Minimal linear codes have important applications in secure communications, including in the framework of secret sharing schemes and secure multi-party computation. A lot of research have been carried out to derive codes with few weights (but more importantly, being minimal) using algebraic or geometric approaches. One of the main power and fructify algebraic methods is based on the design of those codes by employing functions over finite fields. K. Li, C. Li, T. Helleseth, and L. Qu have recently identified in [Binary linear codes with few weights from two-to-one functions, IEEE Trans. Inf. Theory, 2021] some binary linear codes with few weights from two classes of two-to-one functions. In this paper, our ultimate objective is to expand the class of codes derived from the paper of Li <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> . by proposing larger classes of binary linear codes with few weights via generic constructions involving other known families of two-to-one functions over the finite field F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2^<i>n</i></sub> of order 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sup> . We succeed in constructing such codes, and we also completely determine their weight distributions. The linear codes presented in this paper differ in parameters from those known in the literature. Besides, some of them are optimal concerning the well-known Griesmer bound. Notably, we prove that our codes are either optimal or almost optimal with respect to the online Database of Grassl. We next observe that the derived binary linear codes also have the minimality property for most cases. We then describe the access structures of the secret-sharing schemes based on their dual codes. Finally, we solve two problems left open in the paper by Li <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> . (more specifically, a complete solution to Problem 2 and a partial solution to Problem 1).

On rank and kernel of some mixed perfect codes

To resist various attacks, a Boolean function used in symmetric cipher systems should satisfy multiple cryptographic criteria. In this paper, a new generalized construction method for Boolean functions which satisfy multiple cryptographic criteria is provided. These multiple cryptographic criteria include balanced, high nonlinearity, high algebraic degree, propagation criterion of order l (PC(l)) and nonexistence of nonzero linear structures. The construction is based on the use of linear error-correcting code. Given a linear code and its dual code, we show that it is possible to obtain these cryptographic functions.

In this paper, we provide a new generalized construction method for (n, m, t) resilient functions with satisfying synthetical cryptographic criteria. These synthetical cryptographic criteria include high nonlinearity, good resiliency, high algebraic degree, and nonexistence of nonzero linear structure and so on. The construction is based on the use of linear error-correcting code. Given a linear [u, m, t + 1] code and its dual code [u, u - m, t/sup */ + 1], we show that it is possible to construct (n, m, d) resilient functions with satisfying synthetical cryptographic criteria, where d = min(t, t/sup */) and n > u > 2m. The method provides a new idea in designing cryptographic functions.

We consider a model of learning Boolean functions from quantum membership queries. This model was studied in [26], where it was shown that any class of Boolean functions which is information-theoretically learnable from polynomially many quantum membership queries is also information-theoretically learnable from polynomially many classical membership queries. In this paper we establish a strong computational separation between quantum and classical learning. We prove that if any cryptographic one-way function exists, then there is a class of Boolean functions which is polynomial-time learnable from quantum membership queries but not polynomial-time learnable from classical membership queries. A novel consequence of our result is a quantum algorithm that breaks a general cryptographic construction which is secure in the classical setting.

Fully developed turbulence and Brownian motion

How is it possible to prevent the sharing of cryptographic functions? This question appears to be fundamentally hard to address since in this setting the owner of the key is the adversary: she wishes to share a program or device that (potentially only partly) implements her main cryptographic functionality. Given that she possesses the cryptographic key, it is impossible for her to be prevented from writing code or building a device that uses that key. She may though be deterred from doing so. We introduce leakage-deterring public-key cryptosystems to address this problem. Such primitives have the feature of enabling the embedding of owner-specific private data into the owner's public-key so that given access to any (even partially functional) implementation of the primitive, the recovery of the data can be facilitated. We formalize the notion of leakage-deterring in the context of encryption, signature, and identification and we provide efficient generic constructions that facilitate the recoverability of the hidden data while retaining privacy as long as no sharing takes place.