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Abelian and consta-Abelian polyadic codes over affine algebras with a finite commutative chain coefficient ring Cryptogr. Commun. (IF 1.4) Pub Date : 2024-03-15 Gülsüm Gözde Yılmazgüç, Javier de la Cruz, Edgar Martínez-Moro
This paper studies Abelian and consta-Abelian polyadic codes over rings defined as affine algebras over chain rings. For this purpose, we use the classical construction via splittings and multipliers of the underlying Abelian group. We also derive some results on the structure of the associated polyadic codes and the number of codes under these conditions.
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Representing the inverse map as a composition of quadratics in a finite field of characteristic 2 Cryptogr. Commun. (IF 1.4) Pub Date : 2024-03-09 Florian Luca, Santanu Sarkar, Pantelimon Stănică
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An improvement on Weil bounds for character sums of polynomials over finite fields Cryptogr. Commun. (IF 1.4) Pub Date : 2024-03-06 Fengwei Li, Fanhui Meng, Ziling Heng, Qin Yue
Let \(\mathbb {F}_q\) be a finite field with q elements, where q is a power of a prime p. In this paper, we obtain an improvement on Weil bounds for character sums associated to a polynomial f(x) over \(\mathbb {F}_q \), which extends the results of Wan et al. (Des. Codes Cryptogr. 81, 459–468, 2016) and Wu et al. (Des. Codes Cryptogr. 90, 2813–2821, 2022).
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The [1, 0]-twisted generalized Reed-Solomon code Cryptogr. Commun. (IF 1.4) Pub Date : 2024-02-27 Canze Zhu, Qunying Liao
In this paper, we not only give the parity check matrix of the [1, 0]-twisted generalized Reed-Solomon (in short, TGRS) code, but also determine the weight distribution. Especially, we show that the [1, 0]-TGRS code is not GRS or EGRS. Furthermore, we present a sufficient and necessary condition for any punctured code of the [1, 0]-TGRS code to be self-orthogonal, and then construct several classes
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Boolean functions of binary Type-II and Type-III/II complementary array pairs Cryptogr. Commun. (IF 1.4) Pub Date : 2024-02-24 Erzhong Xue, Zilong Wang, Jinjin Chai
The sequence pairs of length \(2^{m}\) projected from Type-II and Type-III/II complementary array pairs of size \(2\times 2\times \cdots \times 2\) (m-times) form Type-II and Type-III complementary sequence pairs, respectively. An exhaustive search for binary Type-II and Type-III complementary sequence pairs of small lengths \(2^{m}\) (\(m=1,2,3,4\)) shows that they are all projected from the aforementioned
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Complete characterization of a class of permutation trinomials in characteristic five Cryptogr. Commun. (IF 1.4) Pub Date : 2024-02-21 Markus Grassl, Ferruh Özbudak, Buket Özkaya, Burcu Gülmez Temür
In this paper, we address an open problem posed by Bai and Xia in [2]. We study polynomials of the form \(f(x)=x^{4q+1}+\lambda _1x^{5q}+\lambda _2x^{q+4}\) over the finite field \({\mathbb F}_{5^{k}}\), which are not quasi-multiplicative equivalent to any of the known permutation polynomials in the literature. We find necessary and sufficient conditions on \(\lambda _1, \lambda _2 \in {\mathbb F}_{5^{k}}\)
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Optimal quinary cyclic codes with three zeros Cryptogr. Commun. (IF 1.4) Pub Date : 2024-02-17 Tingting Wu, Shixin Zhu, Li Liu, Lanqiang Li
Cyclic codes are an important subclass of linear codes, they not only have good algebraic structure, but also are easy to be encoded and decoded. At present, researchers have constructed many optimal ternary cyclic codes, but the study on quinary cyclic codes is less developed. In this paper, by analyzing the solutions of certain equations over \(\mathbb {F}_{5^m}\), we construct some optimal quinary
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A direct construction of cross z-complementary sequence sets with large set size Cryptogr. Commun. (IF 1.4) Pub Date : 2024-02-05 Praveen Kumar, Sudhan Majhi, Subhabrata Paul
This paper presents a direct construction of novel type cross Z-complementary sequence sets (CZCSSs), whose aperiodic correlation sums exhibit zero correlation zones at both the front-end and tail-end shifts. CZCSS can be regarded as an extension of the symmetrical Z-complementary code set (SZCCS). The available construction of SZCCS has a limitation on the set size, with a maximum set size of 8. The
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Several constructions of optimal LCD codes over small finite fields Cryptogr. Commun. (IF 1.4) Pub Date : 2024-02-05 Shitao Li, Minjia Shi, Huizhou Liu
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information protection. In this paper, we give some methods for constructing LCD codes over small finite fields by modifying some typical methods for constructing linear codes. We show
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On the parameters of some LCD BCH codes over $$\mathbb {F}_q$$ with length $$(q^m+1)/\lambda $$ Cryptogr. Commun. (IF 1.4) Pub Date : 2024-01-26
Abstract As a particular subclass of cyclic codes, BCH codes have wide applications in storage devices, communication systems, consumer electronics and other fields. However, parameters of BCH codes are unknown in general. In this paper, we investigate parameters of BCH codes of length \(\frac{q^m+1}{\lambda }\) where \(\lambda \mid q+1\) .Some new techniques are employed to study the coset leaders
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Theoretical differential fault attacks on FLIP and FiLIP Cryptogr. Commun. (IF 1.4) Pub Date : 2024-01-25 Pierrick Méaux, Dibyendu Roy
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GL-S-NFSR: A new NFSR structure and its period properties Cryptogr. Commun. (IF 1.4) Pub Date : 2024-01-17 Xiao-Juan Wang, Tian Tian, Wen-Feng Qi
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Combinatorial constructions of repairable ramp schemes Cryptogr. Commun. (IF 1.4) Pub Date : 2024-01-17 Jinghui Zhao, Xiuling Shan, Zihong Tian
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Re-keying analysis in group key management of wireless sensor networks Cryptogr. Commun. (IF 1.4) Pub Date : 2024-01-05 Prity Kumari, Karam Ratan Singh
The exclusion basis system is a combinatorial formulation of group key management that provides long-term and flexible protection for wireless sensor networks while allowing for reasonable adjustment of the number of keys per node and the number of re-key messages. In this paper, we extend the work of Karst and Wicker to near-resolvable design, symmetric balanced incomplete block designs, and balanced
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A class of balanced binary sequences with two-valued non-zero autocorrelation sum and good crosscorrelation sum Cryptogr. Commun. (IF 1.4) Pub Date : 2024-01-03 Shuhui Shen, Xiaojun Zhang
In this paper, we study a class of binary sequences with two-valued non-zero periodic autocorrelation sum and good periodic crosscorrelation sum as well as balanced properties. We make use of the sequences obtained in (No, J. et al., IEEE Trans. Inform. Theory 44(3), 1278-1282 2001) and adopt the extraction method similar to (Lüke, H. IEEE Trans. Inform. Theory 43(1) 1997). The new sequences are proven
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Low-hit-zone frequency hopping sequence sets under aperiodic Hamming correlation Cryptogr. Commun. (IF 1.4) Pub Date : 2024-01-03 Xing Liu
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The 4-adic complexity of interleaved quaternary sequences of even period with optimal autocorrelation Cryptogr. Commun. (IF 1.4) Pub Date : 2023-12-23 Xiaoyan Jing, Zhefeng Xu
Su, Yang, Zhou, and Tang proposed several new classes of optimal autocorrelation interleaved quaternary sequences with period 2n from the twin-prime sequence pairs or GMW sequence pairs. In this paper, we determine the 4-adic complexity of these quaternary sequences by using the correlation function. Our results show that the 4-adic complexity of these quaternary sequences exceeds \(\frac{2n-16}{6}\)
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Minimal linear codes constructed from partial spreads Cryptogr. Commun. (IF 1.4) Pub Date : 2023-12-13 Xia Wu, Wei Lu, Xiwang Cao, Gaojun Luo
Partial spreads are important in finite geometry and can be used to construct linear codes. From the results in (Des. Codes Cryptogr. 90, 1–15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a partial spread is “big enough”, then the corresponding linear code is minimal. This paper used the sufficient condition in (IEEE Trans. Inf. Theory 44(5), 2010–2017, 1998)
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The Griesmer codes of Belov type and optimal quaternary codes via multi-variable functions Cryptogr. Commun. (IF 1.4) Pub Date : 2023-12-07 Jong Yoon Hyun, Nayoung Han, Yoonjin Lee
We study the Griesmer codes of specific Belov type and construct families of distance-optimal linear codes over \({\mathbb {Z}_4}\) by using multi-variable functions. We first show that the pre-images of specific Griesmer codes of Belov type under a Gray map \(\phi \) from \({\mathbb {Z}_4}\) to \(\mathbb {Z}_2^2\) are non-linear except one case. Therefore, we are interested in finding subcodes of
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MDS multi-twisted Reed-Solomon codes with small dimensional hull Cryptogr. Commun. (IF 1.4) Pub Date : 2023-12-04 Harshdeep Singh, Kapish Chand Meena
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New construction of optimal ZCZ sequence sets with inter-set zero cross-correlation zone Cryptogr. Commun. (IF 1.4) Pub Date : 2023-11-21 Zheng Wang, Zhifan Ye, Chunming Tang, Yang Yang
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A new construction of almost-optimal multiple ZCZ sequence sets for multi-cell QS-CDMA system Cryptogr. Commun. (IF 1.4) Pub Date : 2023-11-20 Nishant Kumar, Sudhan Majhi, Sushant K. Jha
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The Homogeneous Gray image of linear codes over the Galois ring GR(4, m) Cryptogr. Commun. (IF 1.4) Pub Date : 2023-11-17 Hamidreza Eyvazi, Karim Samei, Batoul Savari
Let R be the Galois ring of characteristic 4 and cardinality \(4^{m}\), where m is a natural number. Let \( \mathcal {C} \) be a linear code of length n over R and \(\Phi \) be the Homogeneous Gray map on \(R^n\). In this paper, we show that \(\Phi (\mathcal {C})\) is linear if and only if for every \(\varvec{X}, \varvec{Y}\in \mathcal {C} \), \(2(\varvec{X} \odot \varvec{Y})\in \mathcal {C}\). Using
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On the $$\sigma $$ duals and $$\sigma $$ hulls of linear codes Cryptogr. Commun. (IF 1.4) Pub Date : 2023-11-13 Meng Cao, Jing Yang, Fuchuan Wei
Let \(\text{SLAut}(\mathbb{F}_{q}^{n})\) denote the group of all semilinear isometries on \(\mathbb{F}_{q}^{n}\), where \(q=p^{e}\) is a prime power. In this paper, we investigate some general properties of linear codes associated with the \(\sigma \) duals for \(\sigma \in \text{SLAut}(\mathbb {F}_{q}^{n})\). We show that the dimension of the intersection of two linear codes can be determined by generator
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Frameproof codes, separable codes and $$B_2$$ codes: Bounds and constructions Cryptogr. Commun. (IF 1.4) Pub Date : 2023-11-10 Marcel Fernandez, John Livieratos, Sebastià Martín
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Locally repairable codes with multiple repair sets based on packings of block size 4 Cryptogr. Commun. (IF 1.4) Pub Date : 2023-11-09 Xiaopan Han, Guojun Han, Han Cai, Linxin Yin
In distributed storage systems, the utilization of locally repairable codes offers the potential to reduce the complexity and bandwidth required for repairs. This paper focuses on a scenario where each information symbol is associated with several distinct repair sets, each of which includes a single parity check symbol. By leveraging various combinatorial designs, such as resolvable balanced incomplete
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Periodic autocorrelation of sequences Cryptogr. Commun. (IF 1.4) Pub Date : 2023-11-03 François Rodier, Florian Caullery, Eric Férard
The autocorrelation of a sequence is a useful criterion, among all, of resistance to cryptographic attacks. The behavior of the autocorrelations of random Boolean functions (studied by Rodier et al., (Crypt. Commun. 15, 995–1009, 2023) shows that they are concentrated around a point. We show that the same is true for the evaluation of the periodic autocorrelations of random binary sequences.
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Factorization of invariant polynomials under actions of projective linear groups and its applications in coding theory Cryptogr. Commun. (IF 1.4) Pub Date : 2023-10-10 Xia Li, Qin Yue, Daitao Huang
In this paper, let \(\mathbb {F}_q\) be a finite field with \(q=2^n\) elements and let \([A] \in PGL_2(\mathbb {F}_q)\) be of order 2 or 3, where \(A= \left( \begin{array}{cc} a&{}b\\ 1&{}d\end{array}\right) \). We determine all invariant irreducible (monic) polynomials by the action of \([A]\in PGL_2(\mathbb {F}_{q})\) and have irreducible factorizations of polynomials \(F_s(x)=x^{q^s+1}+dx^{q^s}+ax+b\)
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Construction of binary self-orthogonal codes Cryptogr. Commun. (IF 1.4) Pub Date : 2023-10-10 Xiaoshan Kai, Jiayuan Zhang, Ping Li, Shixin Zhu
In this paper, we first give two new methods for constructing self-orthogonal codes from known self-orthogonal codes. On the basis of this, we construct four infinite classes of binary self-orthogonal codes. Moreover, we also determine their weight distributions and the minimum distances of their dual codes. Furthermore, we present a class of optimal linear codes and a class of almost optimal linear
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A direct construction of complete complementary code with zero correlation zone property for prime-power length Cryptogr. Commun. (IF 1.4) Pub Date : 2023-10-06 Nishant Kumar, Sudhan Majhi, Ashish K. Upadhyay
In this paper, we propose a direct construction of a novel type of code set which has combined properties of complete complementary code (CCC) and zero correlation zone (ZCZ) sequence set and which we call complete complementary-ZCZ (CC-ZCZ) code set. The code set is constructed using multivariate functions. The proposed construction also provides Golay-ZCZ codes of prime-power lengths. The proposed
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On generalized spread bent partitions Cryptogr. Commun. (IF 1.4) Pub Date : 2023-09-23 Nurdagül Anbar, Tekgül Kalaycı, Wilfried Meidl
Generalized semifield spreads are partitions \(\Gamma =\{U,A_1,\ldots , A_{p^k}\}\) of \(\mathbb {F}_{p^m}\times \mathbb {F}_{p^m}\) obtained from (pre)semifields with a certain additional property, which generalize semifield spreads. In particular, a generalized semifield spread is a bent partition, i.e., every function \(f:\mathbb {F}_{p^m}\times \mathbb {F}_{p^m}\rightarrow \mathbb {F}_p\), which
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Some classes of permutation binomials and trinomials of index $$q-1$$ over $${\mathbb {F}_{q^n}}$$ Cryptogr. Commun. (IF 1.4) Pub Date : 2023-09-19 Rohit Gupta, Luciane Quoos, Qiang Wang
In this paper, using the classification of degree 7 permutations over \(\mathbb {F}_q\), we classify certain sparse PPs of the form \(P(x)=x^rf(x^{\frac{q^n-1}{q-1}})\) of \(\mathbb {F}_{q^n}\) for \(n=2\) and 3. In particular, we give necessary and sufficient conditions for the polynomial \(f_{a,b}(x):=x(x^{2(q^2+q+1)}+ax^{q^2+q+1}+b)\) in \(\mathbb {F}_{q^3}[x]\) to be a permutation polynomial over
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New constructions of mutually orthogonal complementary sets and Z-complementary code sets based on extended Boolean functions Cryptogr. Commun. (IF 1.4) Pub Date : 2023-09-18 Hongyang Xiao, Xiwang Cao
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A direct construction of optimal 2d-zcacs with flexible array size and large set size Cryptogr. Commun. (IF 1.4) Pub Date : 2023-09-15 Gobinda Ghosh, Sudhan Majhi, Shubhabrata Paul
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Three classes of permutation quadrinomials in odd characteristic Cryptogr. Commun. (IF 1.4) Pub Date : 2023-09-05 Changhui Chen, Haibin Kan, Jie Peng, Lijing Zheng, Yanjun Li
In this paper, we construct three classes of permutation quadrinomials with Niho exponents of the form \(f(x)=\alpha _0x^r+\alpha _1x^{s_1(p^m-1)+r}+\alpha _2x^{s_2(p^m-1)+r}+\alpha _3x^{s_3(p^m-1)+r}\in \mathbb {F}_{p^{n}}[x]\), where p is an odd prime, \(n=2m \) is a positive even integer, and \((r,s_1,s_2,s_3)=(1,\frac{-1}{p^k-2},1,\frac{p^k-1}{p^k-2})\), \((1,\frac{p^k+1}{p^k+2},1,\frac{1}{p^k+2})\)
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The cross-correlation spectrum of ternary perfect sequences and their decimations Cryptogr. Commun. (IF 1.4) Pub Date : 2023-09-04 Xinxin Lv, Cuiling Fan, Yanyan Wang
In this paper, we consider the cross-correlation spectrum between a ternary perfect sequence having terms in \(\{-1,0,1\}\) and its d-decimation, where \(d={3^k+1\over 2}\). We prove that the cross-correlation function between this pair of ternary sequences has three different values. In addition, we propose a new class of ternary perfect sequences, based on the derived cross-correlation.
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Quantum Implementation and Analysis of Default Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-23 Kyungbae Jang, Anubhab Baksi, Jakub Breier, Hwajeong Seo, Anupam Chattopadhyay
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Generalized partially bent functions, generalized perfect arrays, and cocyclic Butson matrices Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-23 J. A. Armario, R. Egan, D. L. Flannery
In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering Butson matrices that are cocyclic rather than strictly group invariant. This result has several applications; for example, to the construction of Boolean functions
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Further Results on Affine Sub-Families of NFSR Sequences Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-21 Cheng Che, Tian Tian
Nonlinear feedback shift registers (NFSRs) have been widely used in hardware-oriented stream ciphers. Whether a family of NFSR sequences includes an affine sub-family of sequences is a fundamental problem for NFSRs. Let f be the characteristic function of an NFSR whose algebraic degree is d. The previous necessary condition on affine sub-families of NFSR sequences given by Zhang et al. [IEEE Trans
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A lower bound for differential uniformity by multiplicative complexity & bijective functions of multiplicative complexity 1 over finite fields Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-15 Matthias Johann Steiner
The multiplicative complexity of an S-box over a finite field is the minimum number of multiplications needed to implement the S-box as an arithmetic circuit. In this paper we fully characterize bijective S-boxes with multiplicative complexity 1 up to affine equivalence over any finite field. We show that under affine equivalence in odd characteristic there are two classes of bijective functions and
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On the construction of near-MDS matrices Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-14 Kishan Chand Gupta, Sumit Kumar Pandey, Susanta Samanta
The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. However, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers offer a better balance between security and efficiency as a diffusion layer, compared to MDS matrices. In this paper, we study NMDS matrices, exploring their construction
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Probabilistic estimation of the algebraic degree of Boolean functions Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-12 Ana Sălăgean, Percy Reyes-Paredes
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Lower bounds on the maximum cross-correlations of 2-D quasi-complementary array sets Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-09 Abhishek Roy, Sudhan Majhi
For one-dimensional (1-D) sequences, many lower bounds on the maximum cross-correlations have been demonstrated. For example, bounds proposed by Welch, Levenstein, Liu et al., and others are the lower bounds on the maximum cross-correlations of aperiodic 1-D sequence sets or quasi-complementary sequence sets (QCSSs). However, in recent times, two-dimensional (2-D) arrays have emerged with promising
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Hyperbent functions from hyperovals Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-07 Kanat Abdukhalikov, Duy Ho
Using polar coordinates, we consider descriptions of translation, Subiaco and Adelaide hyperovals in terms of exponential sums and Kloosterman sums. As an application, we describe a new construction of hyperbent functions that belong to the Charpin and Gong’s family. Explicit examples of this construction are provided as functions with multiple trace terms via Dillon-like exponents.
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The welch-gong stream cipher - evolutionary path Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-05 N. Zidarič, K. Mandal, G. Gong, M. Aagaard
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Vectorial bent functions and linear codes from quadratic forms Cryptogr. Commun. (IF 1.4) Pub Date : 2023-08-02 Xianhong Xie, Yi Ouyang, Ming Mao
In this paper, we study the vectorial bentness of an arbitrary quadratic form and construct two classes of linear codes of few weights from the quadratic forms. Let q be a prime power, m be a positive integer and \(Q:\mathbb {F}_{q^m}\rightarrow \mathbb {F}_q\) be a quadratic form. We first show that Q is a vectorial bent function if and only if Q is non-degenerate and \((q+1)m\) is even (i.e. either
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A survey of metaheuristic algorithms for the design of cryptographic Boolean functions Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-29 Marko Djurasevic, Domagoj Jakobovic, Luca Mariot, Stjepan Picek
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Distribution of the autocorrelation of random Boolean functions Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-17 François Rodier, Florian Caullery, Eric Férard
The nonlinearity of Boolean functions is well known and the behaviour of the nonlinearity of random Boolean functions has been studied, showing that they concentrate around one point. We show that it is the same for the autocorrelation of Boolean function. As an application, we show that the autocorrelation can distinguish a non random binary sequence from a random one.
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Almost perfect autocorrelation sequences with small number of pauses for applications in magnetic resonance Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-14 Eda Tekin , Oliver Wilhelm Gnilke, Ferruh Özbudak, Bernhard Blümich, Marcus Greferath
It is well known that it is a challenge to find constant amplitude sequences with perfect autocorrelation over small alphabets. In this work we present a construction that provides sequences with perfect cyclic autocorrelation over different alphabets using the value zero only once or twice in their period. The constructions provide a big variety of periods also at moderate lengths and the corresponding
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Construction of Optimal Binary Z-Complementary Code Sets with New Lengths Using Generalized Boolean Function Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-14 Gobinda Ghosh, Sudhan Majhi, Subhabrata Paul
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An infinite family of 0-APN monomials with two parameters Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-10 Nikolay Kaleyski, Kjetil Nesheim, Pantelimon Stănică
We consider an infinite family of exponents e(l, k) with two parameters, l and k, and derive sufficient conditions for e(l, k) to be 0-APN over \({\mathbb F}_{2^n}\). These conditions allow us to generate, for each choice of l and k, an infinite list of dimensions n where \(x^{e(l,k)}\) is 0-APN much more efficiently than in general. We observe that the Gold and Inverse exponents, as well as the inverses
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New constructions of self-dual codes via twisted generalized Reed-Solomon codes Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-10 Junzhen Sui, Qin Yue, Fuqing Sun
In this paper, we give a sufficient and necessary condition that a twisted Reed-Solomon (TRS) code is MDS. Then we give a sufficient and necessary condition that a twisted generalized Reed-Solomon (TGRS) code is self-dual. Moreover, we present some new explicit constructions of self-dual TGRS codes. These self-dual TGRS codes are MDS, Near-MDS, or 2-MDS and most of them are non-GRS.
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Circular Costas maps: A multidimensional analog of circular Costas sequences Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-05 Jaziel Torres, Ivelisse Rubio
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Linear complexity and trace representation of balanced quaternary cyclotomic sequences of prime period p Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-05 Zhiye Yang, Zibi Xiao, Xiangyong Zeng
Let \(p=ef+1\) be an odd prime, where \({e}\equiv 0\,(\bmod \,4)\). A family of balanced quaternary sequences is defined by using the classical cyclotomic classes of order e with respect to p in this paper. We derive the formulas for their linear complexity and trace representation over \(\mathbb {Z}_4\) by computing the discrete Fourier transform of these sequences. As an application, the linear complexity
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A practical-quantum differential attack on block ciphers Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-01 Tarun Yadav, Manoj Kumar, Amit Kumar, S K Pal
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Two classes of ternary LCD constacyclic BCH codes Cryptogr. Commun. (IF 1.4) Pub Date : 2023-07-01 Yajing Zhou, Xiaoshan Kai, Shixin Zhu
Linear codes with complementary duals (LCD codes) have attracted a lot of interest in recent years because of their applications in implementations against side-channel attacks and fault injection attacks. In this paper, we investigate the parameters of ternary LCD constacyclic BCH codes of lengths \(\left({3}^{m}-1\right)/2\) and \(\left({3}^{m}+1\right)/2.\) For length \(n=\left({3}^{m}-1\right)/2
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New upper bounds on the size of permutation codes under Kendall $$\tau$$ -metric Cryptogr. Commun. (IF 1.4) Pub Date : 2023-06-22 Alireza Abdollahi, Javad Bagherian, Fatemeh Jafari, Maryam Khatami, Farzad Parvaresh, Reza Sobhani
We give two methods that are based on the representation theory of symmetric groups to study the largest size P(n, d) of permutation codes of length n, i.e., subsets of the set \(S_n\) of all permutations on \(\{1,\dots ,n\}\) with the minimum distance (at least) d under the Kendall \(\tau\)-metric. The first method is an integer programming problem obtained from the transitive actions of \(S_n\).
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Classification of some cosets of the Reed-Muller code Cryptogr. Commun. (IF 1.4) Pub Date : 2023-06-20 Valérie Gillot, Philippe Langevin
This paper presents a descending method to classify Boolean functions in 7 variables under the action of the affine general linear group. The classification determines the number of classes, a set of orbits representatives and a generator set of the stabilizer of each representative. The method consists in the iteration of the classification process of \(RM(k, m)/RM(r-1, m)\) from that of RM(k, m)/RM(r
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Analysis of boolean functions related to binary input binary output two-party nonlocal games Cryptogr. Commun. (IF 1.4) Pub Date : 2023-06-09 Jyotirmoy Basak, Subhamoy Maitra, Prabal Paul, Animesh Roy
The famous CHSH game can be interpreted with Boolean functions while understanding the success probability in the classical scenario. In this paper, we have exhaustively studied all the Boolean functions on four variables to express binary input binary output two-party nonlocal games and explore their performance in both classical and quantum scenarios. Our analysis finds out some other games (other
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Cryptographic functions with interesting properties from CCZ-equivalence Cryptogr. Commun. (IF 1.4) Pub Date : 2023-06-07 Yanjun Li, Haibin Kan, Jie Peng, Lijing Zheng
In the last decades, because of their significantly important applications, a large number of papers were devoted to constructing cryptographic functions with interesting properties by various methods. In this paper, our motivation is to construct more families of such functions up to EA-equivalence (extended affine equivalence) by using the properties of CCZ-equivalence (Carlet-Charpin-Zinoviev equivalence)