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Cryptography and Communications OnlineFirst articles


Survey on recent trends towards generalized differential and boomerang uniformities

Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block and stream ciphers and cryptographic hash functions. The discovery of differential cryptanalysis is generally attributed to Biham and Shamir in the late …

Sihem Mesnager, Bimal Mandal, Mounira Msahli


New constructions of self-dual generalized reed-solomon codes

A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider new …

Weijun Fang, Jun Zhang, Shu-Tao Xia, Fang-Wei Fu

19.11.2021 Open Access

Improving bounds on probabilistic affine tests to estimate the nonlinearity of Boolean functions

In this paper we want to estimate the nonlinearity of Boolean functions, by probabilistic methods, when it is computationally very expensive, or perhaps not feasible to compute the full Walsh transform (which is the case for almost all functions …

Ana Sălăgean, Pantelimon Stănică

15.11.2021 Open Access

Rational complexity of binary sequences, FSRs, and pseudo-ultrametric continued fractions in

We introduce rational complexity, a new complexity measure for binary sequences. The sequence s ∈ Bω is considered as binary expansion of a real fraction s ≡ ∑ k ∈ ℕ s k 2 − k ∈ [ 0 , 1 ] ⊂ ℝ $s \equiv {\sum }_{k\in \mathbb {N}}s_{k}2^{-k}\in …

Michael Vielhaber, Mónica del Pilar Canales Chacón, Sergio Jara Ceballos


A class of binary cyclic codes with optimal parameters

For positive integers k ≥ 2 and t, let m = 2kt and α be a primitive element of the finite field F 2 m $\mathbb {F}_{2^{m}}$ . In this paper, we study the parameters of a class of cyclic codes C ( 1 , v ) $\mathcal {C}_{(1,v)}$ which has two zeros …

Kaiqiang Liu, Qi Wang, Haode Yan


The second-order zero differential spectra of almost perfect nonlinear functions and the inverse function in odd characteristic

In a prior paper (Boukerrou et al. IACR Trans. Symmetric Cryptol. 2020(1), 331–362 2020), Boukerrou et al. introduced the Feistel Boomerang Connectivity Table (FBCT). FBCT is an important cryptanalytic technique on Feistel ciphers. In fact, the …

Xia Li, Qin Yue, Deng Tang


Some t-designs from BCH codes

Combinatorial t-designs are closely related to coding theory and finite geometries and have nice applications in some engineering areas. One of the major approaches to the construction of combinatorial t-designs is the employment of …

Can Xiang


LCD and ACD codes over a noncommutative non-unital ring with four elements

We study LCD (linear complementary dual) and ACD (additive complementary dual) codes over a noncommutative non-unital ring E with four elements. This is the first attempt to construct LCD codes over a noncommutative non-unital ring. We show that …

Minjia Shi, Shitao Li, Jon-Lark Kim, Patrick Solé


Cryptanalysis of the AEAD and hash algorithm DryGASCON

The DryGASCON scheme was one of authenticated encryption (AE) algorithms submitted to the ongoing NIST Lightweight Cryptography Standardization Process. Such a competition aims to standardize lightweight cryptographic algorithms and determine …

Huicong Liang, Sihem Mesnager, Meiqin Wang


Minimal linear codes from weakly regular bent functions

Minimal linear codes have received much attention in the past decades due to their important applications in secret sharing schemes and secure two-party computation, etc. Recently, several classes of minimal linear codes with w min / w max ≤ ( p − …

Guangkui Xu, Longjiang Qu, Gaojun Luo


The Hermitian dual-containing LCD BCH codes and related quantum codes

Let q be a prime power. In this paper, we investigate the maximum designed distances of LCD BCH codes over F q 2 $\mathbb {F}_{q^{2}}$ such that they contain their Hermitian dual codes, and also calculate their dimensions. As an application, we …

Fengwei Li


Repeated root cyclic codes over and their Lee distances

In this paper we have studied repeated root cyclic codes of length pk over R = ℤ p 2 + u ℤ p 2 $R=\mathbb {Z}_{p^{2}}+u\mathbb {Z}_{p^{2}}$ , u2 = 0, where p is a prime and k is a positive integer. We have determined a unique set of generators for …

Raj Kumar, Maheshanand Bhaintwal

06.10.2021 | Correction

Correction to: New constructions of entanglement-assisted quantum codes

A. Allahmadi, A. AlKenani, R. Hijazi, N. Muthana, F. Özbudak, P. Solé


Resolvable block designs in construction of approximate real MUBs that are sparse

Several constructions of Mutually Unbiased Bases (MUBs) borrow tools from combinatorial objects. In this paper we focus on how one can construct Approximate Real MUBs (ARMUBs) with improved parameters using results from the domain of Resolvable …

Ajeet Kumar, Subhamoy Maitra

12.09.2021 Open Access

Attacking the linear congruential generator on elliptic curves via lattice techniques

In this paper we study the linear congruential generator on elliptic curves from the cryptographic point of view. We show that if sufficiently many of the most significant bits of the composer and of three consecutive values of the sequence are …

Jaime Gutierrez


On equivalence between two known families of APN polynomial functions and APN power functions

Construction and equivalence of APN functions play a significant role in the research of cryptographic functions. On finite fields of characteristic 2, six infinite families of APN power functions and thirteen infinite families of APN polynomial …

Qianhong Wan, Chao Li


The estimate of the linear complexity of generalized cyclotomic binary and quaternary sequences with periods pn and 2pn

In this paper, first we consider the linear complexity of quaternary sequences over the finite ring of order four and the finite field of order four. These sequences are constructed from new generalized cyclotomic classes modulo pn. Second, we …

Vladimir Edemskiy, Nikita Sokolovskiy


Differential and boomerang spectrums of some power permutations

The differential (resp. boomerang) spectrum is an important parameter to estimate the resistance of cryptographic functions against some variants of differential (resp. boomerang) cryptanalysis. This paper aims to determine the differential and …

Sha Jiang, Kangquan Li, Yubo Li, Longjiang Qu


New Galois Hulls of GRS Codes and Application to EAQECCs

Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a general …

Xiaolei Fang, Renjie Jin, Jinquan Luo, Wen Ma


Linear complexity of some sequences derived from hyperelliptic curves of genus 2

For a given hyperelliptic curve C over a finite field with Jacobian JC, we consider the hyperelliptic analogue of the congruential generator defined by Wn = Wn− 1 + D for n ≥ 1 and D, W0 ∈ JC. We show that curves of genus 2 produce sequences with …

Vishnupriya Anupindi, László Mérai