Designs, Codes and Cryptography最新文献

{"title":"Generalized cycle joining method and its application to the construction of long-period Galois NFSRs","authors":"Yingyin Pan, Jianghua Zhong, Dongdai Lin","doi":"10.1007/s10623-024-01500-z","DOIUrl":"https://doi.org/10.1007/s10623-024-01500-z","url":null,"abstract":"<p>Nonlinear feedback shift registers (NFSRs) are used in many recent stream ciphers as their main building blocks. One security criterion for the design of a stream cipher is to assure its used NFSR has a long period. As the period of a Fibonacci NFSR is equal to its largest cycle length, a common way to get a maximum-period Fibonacci NFSR is to join the cycles of an original Fibonacci NFSR into a maximum cycle. Nevertheless, so far only the maximum-period Fibonacci NFSRs with stage numbers no greater than 33 have been found. Considering that Galois NFSRs may have higher implementation efficiency than Fibonacci NFSRs, this paper first generalizes the cycle joining method for Fibonacci NFSRs to Galois NFSRs and establishes some conditions for maximum-period Galois NFSRs. It then reveals the cycle structure of some cascade connections of two Fibonacci NFSRs. Based on both, the paper constructs some long-period Galois NFSRs including maximum-period Galois NFSRs with stage numbers up to 41. Finally, it analyzes their hardware implementation via the technology mapping obtained by synthesizing the NFSRs with Synopsys Design Compiler L<span>(-)</span>2016.03-Sp1 using the TSMC 90nm CMOS library, and the results show that they have good hardware performance.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"46 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142369298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A characterization of complex Hadamard matrices appearing in families of MUB triplets","authors":"Ákos K. Matszangosz, Ferenc Szöllősi","doi":"10.1007/s10623-024-01503-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01503-w","url":null,"abstract":"<p>It is shown that a normalized complex Hadamard matrix of order 6 having three distinct columns each containing at least one <span>(-1)</span> entry, necessarily belongs to the transposed Fourier family, or to the family of 2-circulant complex Hadamard matrices. The proofs rely on solving polynomial systems of equations by Gröbner basis techniques, and make use of a structure theorem concerning regular Hadamard matrices. As a consequence, members of these two families can be easily recognized in practice. In particular, one can identify complex Hadamard matrices appearing in known triplets of pairwise mutually unbiased bases in dimension 6.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142369296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Abelian one-dimensional hull codes in group algebras","authors":"Rong Luo, Mingliang Yan, Sihem Mesnager, Dongchun Han","doi":"10.1007/s10623-024-01504-9","DOIUrl":"https://doi.org/10.1007/s10623-024-01504-9","url":null,"abstract":"<p>This paper focuses on hull dimensional codes obtained by the intersection of linear codes and their dual. These codes were introduced by Assmus and Key and have been the subject of significant theoretical and practical research over the years, gaining increased attention in recent years. Let <span>(mathbb {F}_q)</span> denote the finite field with <i>q</i> elements, and let <i>G</i> be a finite Abelian group of order <i>n</i>. The paper investigates Abelian codes defined as ideals of the group algebra <span>(mathbb {F}_qG)</span> with coefficients in <span>(mathbb {F}_q)</span>. Specifically, it delves into Abelian hull dimensional codes in the group algebra <span>(mathbb {F}_qG)</span>, where <i>G</i> is a finite Abelian group of order <i>n</i> with <span>(gcd (n,q)=1)</span>. Specifically, we first examine general hull Abelian codes and then narrow its focus to Abelian one-dimensional hull codes. Next, we focus on Abelian one-dimensional hull codes and present some necessary and sufficient conditions for characterizing them. Consequently, we generalize a recent result on Abelian codes and show that no binary or ternary Abelian codes with one-dimensional hulls exist. Furthermore, we construct Abelian codes with one-dimensional hulls by generating idempotents, derive optimal ones with one-dimensional hulls, and establish several existing results of Abelian codes with one-dimensional hulls. Finally, we develop enumeration results through a simple formula that counts Abelian codes with one-dimensional hulls in <span>(mathbb {F}_qG)</span>. These achievements exploit the rich algebraic structure of those Abelian codes and enhance and increase our knowledge of them by considering their hull dimensions, reducing the gap between their interests and our understanding of them.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"10 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Binary cyclic-gap constant weight codes with low-complexity encoding and decoding","authors":"Birenjith Sasidharan, Emanuele Viterbo, Son Hoang Dau","doi":"10.1007/s10623-024-01494-8","DOIUrl":"https://doi.org/10.1007/s10623-024-01494-8","url":null,"abstract":"<p>In this paper, we focus on the design of binary constant weight codes that admit low-complexity encoding and decoding algorithms, and that have size <span>(M=2^k)</span> so that codewords can conveniently be labeled with binary vectors of length <i>k</i>. For every integer <span>(ell ge 3)</span>, we construct a <span>((n=2^ell , M=2^{k_{ell }}, d=2))</span> constant weight code <span>({{{mathcal {C}}}}[ell ])</span> of weight <span>(ell )</span> by encoding information in the gaps between successive 1’s of a vector, and call them as cyclic-gap constant weight codes. The code is associated with a finite integer sequence of length <span>(ell )</span> satisfying a constraint defined as <i>anchor-decodability</i> that is pivotal to ensure low complexity for encoding and decoding. The time complexity of the encoding algorithm is linear in the input size <i>k</i>, and that of the decoding algorithm is poly-logarithmic in the input size <i>n</i>, discounting the linear time spent on parsing the input. Both the algorithms do not require expensive computation of binomial coefficients, unlike the case in many existing schemes. Among codes generated by all anchor-decodable sequences, we show that <span>({{{mathcal {C}}}}[ell ])</span> has the maximum size with <span>(k_{ell } ge ell ^2-ell log _2ell + log _2ell - 0.279ell - 0.721)</span>. As <i>k</i> is upper bounded by <span>(ell ^2-ell log _2ell +O(ell ))</span> information-theoretically, the code <span>({{{mathcal {C}}}}[ell ])</span> is optimal in its size with respect to two higher order terms of <span>(ell )</span>. In particular, <span>(k_ell )</span> meets the upper bound for <span>(ell =3)</span> and one-bit away for <span>(ell =4)</span>. On the other hand, we show that <span>({{{mathcal {C}}}}[ell ])</span> is not unique in attaining <span>(k_{ell })</span> by constructing an alternate code <span>(mathcal{{hat{C}}}[ell ])</span> again parameterized by an integer <span>(ell ge 3)</span> with a different low-complexity decoder, yet having the same size <span>(2^{k_{ell }})</span> when <span>(3 le ell le 7)</span>. Finally, we also derive new codes by modifying <span>({{{mathcal {C}}}}[ell ])</span> that offer a wider range on blocklength and weight while retaining low complexity for encoding and decoding. For certain selected values of parameters, these modified codes too have an optimal <i>k</i>.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"103 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142369110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotically optimal aperiodic quasi-complementary sequence sets based on extended Boolean functions","authors":"Bingsheng Shen, Tao Yu, Zhengchun Zhou, Yang Yang","doi":"10.1007/s10623-024-01501-y","DOIUrl":"https://doi.org/10.1007/s10623-024-01501-y","url":null,"abstract":"<p>Quasi-complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. Although several constructions of aperiodic QCSSs have been proposed in the literature, the known optimal aperiodic QCSSs have limited length or have large alphabet. In this paper, based on extended Boolean functions, we present two constructions of aperiodic QCSSs with parameters <span>((q(p_0-1),q,q-t,q))</span> and <span>((q^m(p_0-1),q^m,q^m-t,q^m))</span>, where <span>(qge 3)</span> is an odd integer, <span>(p_0)</span> is the minimum prime factor of <i>q</i>. The proposed constructions can generate asymptotically optimal or near-optimal aperiodic QCSSs with new parameters.\u0000</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"53 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142329172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-linear MRD codes from cones over exterior sets","authors":"Nicola Durante, Giovanni Giuseppe Grimaldi, Giovanni Longobardi","doi":"10.1007/s10623-024-01492-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01492-w","url":null,"abstract":"<p>By using the notion of a <i>d</i>-embedding <span>(Gamma )</span> of a (canonical) subgeometry <span>(Sigma )</span> and of exterior sets with respect to the <i>h</i>-secant variety <span>(Omega _{h}({mathcal {A}}))</span> of a subset <span>({mathcal {A}})</span>, <span>( 0 le h le n-1)</span>, in the finite projective space <span>({textrm{PG}}(n-1,q^n))</span>, <span>(n ge 3)</span>, in this article we construct a class of non-linear (<i>n</i>, <i>n</i>, <i>q</i>; <i>d</i>)-MRD codes for any <span>( 2 le d le n-1)</span>. A code of this class <span>({mathcal {C}}_{sigma ,T})</span>, where <span>(1in T subseteq {mathbb {F}}_q^*)</span> and <span>(sigma )</span> is a generator of <span>(textrm{Gal}({mathbb {F}}_{q^n}|{mathbb {F}}_q))</span>, arises from a cone of <span>({textrm{PG}}(n-1,q^n))</span> with vertex an <span>((n-d-2))</span>-dimensional subspace over a maximum exterior set <span>({mathcal {E}})</span> with respect to <span>(Omega _{d-2}(Gamma ))</span>. We prove that the codes introduced in Cossidente et al (Des Codes Cryptogr 79:597–609, 2016), Donati and Durante (Des Codes Cryptogr 86:1175–1184, 2018), Durante and Siciliano (Electron J Comb, 2017) are suitable punctured ones of <span>({mathcal {C}}_{sigma ,T})</span> and we solve completely the inequivalence issue for this class showing that <span>({mathcal {C}}_{sigma ,T})</span> is neither equivalent nor adjointly equivalent to the non-linear MRD codes <span>({mathcal {C}}_{n,k,sigma ,I})</span>, <span>(I subseteq {mathbb {F}}_q)</span>, obtained in Otal and Özbudak (Finite Fields Appl 50:293–303, 2018).</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"38 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142245509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Arithmetization-oriented APN permutations","authors":"Lilya Budaghyan, Mohit Pal","doi":"10.1007/s10623-024-01487-7","DOIUrl":"https://doi.org/10.1007/s10623-024-01487-7","url":null,"abstract":"<p>Recently, many cryptographic primitives such as homomorphic encryption (HE), multi-party computation (MPC) and zero-knowledge (ZK) protocols have been proposed in the literature which operate on the prime field <span>({mathbb {F}}_p)</span> for some large prime <i>p</i>. Primitives that are designed using such operations are called <i>arithmetization-oriented</i> primitives. As the concept of arithmetization-oriented primitives is new, a rigorous cryptanalysis of such primitives is yet to be done. In this paper, we investigate arithmetization-oriented APN functions. More precisely, we investigate APN permutations in the CCZ-classes of known families of APN power functions over the prime field <span>({mathbb {F}}_p)</span>. Moreover, we present a class of binomial permutation having differential uniformity at most 5 defined via the quadratic character over finite fields of odd characteristic. Computationally it is confirmed that the latter family contains new APN permutations for some small parameters. We conjecture it to contain an infinite subfamily of APN permutations.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"33 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142236229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A common generalization of hypercube partitions and ovoids in polar spaces","authors":"Jozefien D’haeseleer, Ferdinand Ihringer, Kai-Uwe Schmidt","doi":"10.1007/s10623-024-01489-5","DOIUrl":"https://doi.org/10.1007/s10623-024-01489-5","url":null,"abstract":"<p>We investigate what we call generalized ovoids, that is families of totally isotropic subspaces of finite classical polar spaces such that each maximal totally isotropic subspace contains precisely one member of that family. This is a generalization of ovoids in polar spaces as well as the natural <i>q</i>-analog of a subcube partition of the hypercube (which can be seen as a polar space with <span>(q=1)</span>). Our main result proves that a generalized ovoid of <i>k</i>-spaces in polar spaces of large rank does not exist.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"63 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Capacity of an infinite family of networks related to the diamond network for fixed alphabet sizes","authors":"Sascha Kurz","doi":"10.1007/s10623-024-01485-9","DOIUrl":"https://doi.org/10.1007/s10623-024-01485-9","url":null,"abstract":"<p>We consider the problem of error correction in a network where the errors can occur only on a proper subset of the network edges. For a generalization of the so-called Diamond Network we consider lower and upper bounds for the network’s (1-shot) capacity for fixed alphabet sizes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"53 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Designs in finite classical polar spaces","authors":"Michael Kiermaier, Kai-Uwe Schmidt, Alfred Wassermann","doi":"10.1007/s10623-024-01491-x","DOIUrl":"https://doi.org/10.1007/s10623-024-01491-x","url":null,"abstract":"<p>Combinatorial designs have been studied for nearly 200 years. 50 years ago, Cameron, Delsarte, and Ray-Chaudhury started investigating their <i>q</i>-analogs, also known as subspace designs or designs over finite fields. Designs can be defined analogously in finite classical polar spaces, too. The definition includes the <i>m</i>-regular systems from projective geometry as the special case where the blocks are generators of the polar space. The first nontrivial such designs for <span>(t &gt; 1)</span> were found by De Bruyn and Vanhove in 2012, and some more designs appeared recently in the PhD thesis of Lansdown. In this article, we investigate the theory of classical and subspace designs for applicability to designs in polar spaces, explicitly allowing arbitrary block dimensions. In this way, we obtain divisibility conditions on the parameters, derived and residual designs, intersection numbers and an analog of Fisher’s inequality. We classify the parameters of symmetric designs. Furthermore, we conduct a computer search to construct designs of strength <span>(t=2)</span>, resulting in designs for more than 140 previously unknown parameter sets in various classical polar spaces over <span>(mathbb {F}_2)</span> and <span>(mathbb {F}_3)</span>.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"328 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}