Cryptography and Communications最新文献

The low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets are commonly applied in quasi-synchronous (QS) frequency-hopping multiple access (FHMA) systems to reduce MA interference. In addition, due to the short synchronization time or sophisticated hardware, the correlation window is typically less than the period of the selected FHS set. In this paper, we construct a class of LHZ FHS sets with strictly optimal partial Hamming correlation (PHC) based on the Chinese Remainder Theorem (CRT) and analyze the PHC of our constructed LHZ FHS sets. It turns out that the new LHZ FHS sets are optimal with respect to the Niu-Peng-Fan bound.

Boukerrou et al. (IACR Trans. Symm. Cryptol. 2020(1), 331–362, 2020) introduced the notion of the Feistel Boomerang Connectivity Table (FBCT), the Feistel counterpart of the Boomerang Connectivity Table (BCT), and the Feistel boomerang uniformity (which is the same as the second-order zero differential uniformity in even characteristic fields). The FBCT is a crucial table for the analysis of the resistance of block ciphers to power attacks such as differential and boomerang attacks. It is worth noting that the coefficients of the FBCT are related to the second-order zero differential spectra of functions and the FBCT of functions can be extended as their second-order zero differential spectra. In this paper, by carrying out certain finer manipulations consisting of solving some specific equations over finite fields, we explicitly determine the second-order zero differential spectra of some power functions with low differential uniformity, and show that these functions also have low second-order zero differential uniformity. Our study further pushes previous investigations on second-order zero differential uniformity and Feistel boomerang uniformity for a power function F.

We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either direction. In particular we establish how two variants of a generalised Lempel homomorphism can be used to recursively construct such sequences, generalising previous work on the binary case. We also derive an upper bound on the period of an orientable sequence.

In (Shi et al. Finite Fields Appl. 80, 102087 2022) studied additive cyclic complementary dual codes with respect to trace Euclidean and trace Hermitian inner products over the finite field (mathbb {F}_4). In this article, we extend their results over (mathbb {F}_{q^2},) where q is an odd prime power. We describe the algebraic structure of additive cyclic codes and obtain the dual of a class of these codes with respect to the trace inner products. We also use generating polynomials to construct several examples of additive cyclic codes over (mathbb {F}_9.) These codes are better than linear codes of the same length and size. Furthermore, we describe the subfield codes and the trace codes of these codes as linear cyclic codes over (mathbb {F}_q).

Constacyclic BCH codes are an interesting subclass of constacyclic codes because of their important theoretical and practical value. The purpose of this paper is to study the parameters of cyclic BCH codes of length (varvec{n = q^{m} - 1}) and negacyclic BCH codes of length (varvec{n = frac{q^{m} - 1}{2}}). We settle completely their dimensions. We also determine the minimum distances of a class of cyclic BCH codes of length (varvec{n = q^m - 1}) and give a lower bound on the minimum distances of other classes of constacyclic BCH codes. As seen by the code examples in this paper, the lower bound on the minimum distances of constacyclic BCH codes we gave is very close to the true minimum distances. These (varvec{q})-ary codes have good parameters in general.

In this paper, we construct a class of (mathbb {Z}_{p^r}mathbb {Z}_{p^s}mathbb {Z}_{p^t})-additive cyclic codes generated by 3-tuples of polynomials, where p is a prime number and (1 le r le s le t). We investigate the algebraic structure of these codes and establish that it is possible to determine generator matrices for a subfamily of codes within this class. We employ a probabilistic approach to analyze the asymptotic properties of these codes. For any positive real number (delta ) satisfying (0< delta < 1) such that the asymptotic Gilbert-Varshamov bound at (left( frac{k+l+n}{3p^{r-1}}delta right) ) is greater than (frac{1}{2}), we demonstrate that the relative distance of the random code converges to (delta ), while the rate of the random code converges to (frac{1}{k+l+n}). Finally, we conclude that the (mathbb {Z}_{p^r}mathbb {Z}_{p^s}mathbb {Z}_{p^t})-additive cyclic codes exhibit asymptotically good properties.

We study the largest minimum weights among quaternary Hermitian LCD codes. We determine the largest minimum weights among quaternary Hermitian LCD codes of length n and dimension k for (k le n le 17). A quaternary Hermitian LCD [21, 5, 13] code and a quaternary Hermitian LCD [21, 9, 9] code are also constructed for the first time. An updated table of the largest minimum weights among quaternary Hermitian LCD [n, k] codes is also given for (k le n le 30).

Subspace codes have attracted a lot of attention in the last few decades due to their applications in noncoherent linear network coding, in particular cyclic subspace codes can be encoded and decoded more efficiently because of their special algebraic structure. In this paper, we present a family of cyclic subspace codes with minimum distance (varvec{2k-2}) and size (varvec{seq^{k}(q^k-1)^{s-1}(q^n-1)+frac{q^n-1}{q^k-1}}), where (varvec{k|n}), (varvec{frac{n}{k}ge 2s+1}), (varvec{sge 1, e=lceil frac{n}{2sk} rceil -1}). In the case of (varvec{n=(2s+1)k}) with (varvec{2le s <q^k}), our cyclic subspace codes have larger size than the known ones in the literature.

The nonlinear invariant attack is a new and powerful cryptanalytic method for lightweight block ciphers. The core step of such cryptanalytic method is to find the nonlinear invariant(s) of its cascade round. Generally, for an (varvec{n})-bit width function, the time complexity (varvec{O}(textbf{2}^{varvec{3n}})) is needed to find its all nonlinear invariants. In this paper, for the positive integer (varvec{m}), we consider the power function (varvec{x}^{varvec{m}}) over the finite field (varvec{GF}(varvec{2}^{varvec{n}})), which is one of the most important cryptographic functions in recent decades. First, the nonlinear invariants of (varvec{x}^{varvec{m}}) is studied and we provide two mathematical toolboxes named (varvec{sim }_{varvec{m}}) periodical point and (varvec{sim }_{varvec{m}}) equivalence class. Second, we present an algorithm to get all the nonlinear invariants of (varvec{x}^{varvec{m}}) over (varvec{GF}(varvec{2}^{varvec{n}})) at the cost of time complexity (varvec{O}(frac{{varvec{2}}^{varvec{n}}varvec{-1}}{varvec{gcd (2}^{varvec{n}}varvec{-1,m)}})). If the growth of n exceeds our tolerance above, another method is provided to get parts of the nonlinear invariants of (varvec{x}^{varvec{m}}). Finally, we consider the nonlinear invariants of (varvec{x}^textbf{3}) over (varvec{GF(2}^{varvec{129}})) as an application, which is used in the block cipher MiMC. It seems impractical by existing methods. The results allow us to find several (but not all) nontrivial nonlinear invariants of such a function for the first time.

In this paper, our main objective is to examine the properties and characteristics of 1-generator ((2 + u))-quasi-twisted (QT) codes and ((2 + u))-generalized quasi-twisted (GQT) codes over the ring (mathbb {Z}_4 +umathbb {Z}_4 ), with (u^2=1). We determine the structure of the generators and minimal generating sets for both 1-generator ((2 + u))-QT and ((2 + u))-GQT codes. Additionally, we establish a lower bound for the minimum distance of free 1-generator ((2 + u))-QT and ((2 + u))-GQT codes over R. Furthermore, we present some numerical examples that illustrate the construction of some optimal (mathbb {Z}_4)-linear codes using the Gray map.