发布求助
文献互助 智能选刊 最新文献

Designs, Codes and Cryptography最新文献

筛选
英文 中文
The support designs of several families of lifted linear codes
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-25 DOI: 10.1007/s10623-024-01549-w
Cunsheng Ding, Zhonghua Sun, Qianqian Yan
{"title":"The support designs of several families of lifted linear codes","authors":"Cunsheng Ding, Zhonghua Sun, Qianqian Yan","doi":"10.1007/s10623-024-01549-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01549-w","url":null,"abstract":"<p>A generator matrix of a linear code <span>({mathcal {C}})</span> over <span>({textrm{GF}}(q))</span> is also a matrix of the same rank <i>k</i> over any extension field <span>({textrm{GF}}(q^ell ))</span> and generates a linear code of the same length, same dimension and same minimum distance over <span>({textrm{GF}}(q^ell ))</span>, denoted by <span>({mathcal {C}}(q|q^ell ))</span> and called a lifted code of <span>({mathcal {C}})</span>. Although <span>({mathcal {C}})</span> and their lifted codes <span>({mathcal {C}}(q|q^ell ))</span> have the same parameters, they have different weight distributions and different applications. Few results about lifted linear codes are known in the literature. This paper proves some fundamental theory for lifted linear codes, and studies the 2-designs of the lifted projective Reed–Muller codes, lifted Hamming codes and lifted Simplex codes. In addition, this paper settles the weight distributions of the lifted Reed–Muller codes of certain orders, and investigates the 3-designs supported by these lifted codes. As a by-product, an infinite family of three-weight projective codes over <span>({textrm{GF}}(4))</span> is obtained.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884413","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}
引用次数: 0
Low-weight codewords in cyclic codes
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-24 DOI: 10.1007/s10623-024-01547-y
J. G. Coelho, F. E. Brochero Martínez
{"title":"Low-weight codewords in cyclic codes","authors":"J. G. Coelho, F. E. Brochero Martínez","doi":"10.1007/s10623-024-01547-y","DOIUrl":"https://doi.org/10.1007/s10623-024-01547-y","url":null,"abstract":"<p>We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that connects their weight distribution to the number of solutions of associated systems of polynomial equations. This relationship allows for the computation of weight distributions from known solutions of systems of diagonal equations and vice versa, offering a new insight into the structure and properties of binary cyclic codes.\u0000</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"123 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884410","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}
引用次数: 0
A class of permutations on $${mathbb {Z}}_{p}$$ with differential uniformity at most 3
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-22 DOI: 10.1007/s10623-024-01548-x
Prachi Gupta, P. R. Mishra, Atul Gaur
{"title":"A class of permutations on $${mathbb {Z}}_{p}$$ with differential uniformity at most 3","authors":"Prachi Gupta, P. R. Mishra, Atul Gaur","doi":"10.1007/s10623-024-01548-x","DOIUrl":"https://doi.org/10.1007/s10623-024-01548-x","url":null,"abstract":"<p>In this paper, we give a class of permutations on <span>({mathbb {Z}}_{p})</span> having differential uniformity at most 3, where prime <i>p</i> satisfies <span>(p equiv 1 pmod {4})</span>. Further, we present a sufficient condition for differential uniformity exactly 3 and identify a subclass achieving this value.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142869956","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}
引用次数: 0
Guessing less and better: improved attacks on GIFT-64
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01527-2
Federico Canale, María Naya-Plasencia
{"title":"Guessing less and better: improved attacks on GIFT-64","authors":"Federico Canale, María Naya-Plasencia","doi":"10.1007/s10623-024-01527-2","DOIUrl":"https://doi.org/10.1007/s10623-024-01527-2","url":null,"abstract":"<p>GIFT-64 is a block cipher that has received a lot of attention from the community since its proposal in 2017. The attack on the highest number of rounds is a differential related-key attack on 26 rounds. We studied this attack, in particular with respect to some recent generic frameworks for improving key recovery, and we realised that this framework, combined with an efficient parallel key guessing of interesting subsets of the key and a consequent list merging applied to the partial solutions, can improve the complexity of the attack. We propose two different trade-offs, as a result of the improved key-recovery. We believe that the techniques are quite generic and that it is possible to apply them to improve other differential attacks.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"31 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867061","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}
引用次数: 0
On automorphism groups of binary cyclic codes 论二元循环码的自形群
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01539-y
Jicheng Ma, Guiying Yan
{"title":"On automorphism groups of binary cyclic codes","authors":"Jicheng Ma, Guiying Yan","doi":"10.1007/s10623-024-01539-y","DOIUrl":"https://doi.org/10.1007/s10623-024-01539-y","url":null,"abstract":"<p>Cyclic codes, as a significant subclass of linear codes, can be constructed and analyzed using algebraic methods. Due to its cyclic nature, they have efficient encoding and decoding algorithms. To date, cyclic codes have found applications in various domains, including consumer electronics, data storage systems, and communication systems. In this paper, we investigate the full automorphism groups of binary cyclic codes. A matrix presentation technique of cyclic codewords is introduced, which subsequently serves well for presenting binary cyclic codes of long lengths. These constructions are significantly useful in facilitating the determination of the full automorphism groups of binary cyclic codes of specified lengths.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"8 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867031","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}
引用次数: 0
A construction of optimal quasi-cyclic locally recoverable codes using constituent codes
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01532-5
Gustavo Terra Bastos, Angelynn Álvarez, Zachary Flores, Adriana Salerno
{"title":"A construction of optimal quasi-cyclic locally recoverable codes using constituent codes","authors":"Gustavo Terra Bastos, Angelynn Álvarez, Zachary Flores, Adriana Salerno","doi":"10.1007/s10623-024-01532-5","DOIUrl":"https://doi.org/10.1007/s10623-024-01532-5","url":null,"abstract":"<p>A locally recoverable code of locality <i>r</i> over <span>(mathbb {F}_{q})</span> is a code where every coordinate of a codeword can be recovered using the values of at most <i>r</i> other coordinates of that codeword. Locally recoverable codes are efficient at restoring corrupted messages and data which make them highly applicable to distributed storage systems. Quasi-cyclic codes of length <span>(n=mell )</span> and index <span>(ell )</span> are linear codes that are invariant under cyclic shifts by <span>(ell )</span> places. In this paper, we decompose quasi-cyclic locally recoverable codes into a sum of constituent codes where each constituent code is a linear code over a field extension of <span>(mathbb {F}_q)</span>. Using these constituent codes with set parameters, we propose conditions which ensure the existence of almost optimal and optimal quasi-cyclic locally recoverable codes with increased dimension and code length.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"20 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867030","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}
引用次数: 0
Several new classes of optimal ternary cyclic codes with two or three zeros
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-19 DOI: 10.1007/s10623-024-01541-4
Gaofei Wu, Zhuohui You, Zhengbang Zha, Yuqing Zhang
{"title":"Several new classes of optimal ternary cyclic codes with two or three zeros","authors":"Gaofei Wu, Zhuohui You, Zhengbang Zha, Yuqing Zhang","doi":"10.1007/s10623-024-01541-4","DOIUrl":"https://doi.org/10.1007/s10623-024-01541-4","url":null,"abstract":"<p>Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let <span>(alpha )</span> be a generator of <span>(mathbb F_{3^m}setminus {0})</span>, where <i>m</i> is a positive integer. Denote by <span>(mathcal {C}_{(i_1,i_2,cdots , i_t)})</span> the cyclic code with generator polynomial <span>(m_{alpha ^{i_1}}(x)m_{alpha ^{i_2}}(x)cdots m_{alpha ^{i_t}}(x))</span>, where <span>({{m}_{alpha ^{i}}}(x))</span> is the minimal polynomial of <span>({{alpha }^{i}})</span> over <span>({{mathbb {F}}_{3}})</span>. In this paper, by analyzing the solutions of certain equations over finite fields, we present four classes of optimal ternary cyclic codes <span>(mathcal {C}_{(0,1,e)})</span> and <span>(mathcal {C}_{(1,e,s)})</span> with parameters <span>([3^m-1,3^m-frac{3m}{2}-2,4])</span>, where <span>(s=frac{3^m-1}{2})</span>. In addition, by determining the solutions of certain equations and analyzing the irreducible factors of certain polynomials over <span>(mathbb F_{3^m})</span>, we present four classes of optimal ternary cyclic codes <span>(mathcal {C}_{(2,e)})</span> and <span>(mathcal {C}_{(1,e)})</span> with parameters <span>([3^m-1,3^m-2m-1,4])</span>. We show that our new optimal cyclic codes are not covered by known ones.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858387","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}
引用次数: 0
Quantum security of Trojan message attacks on Merkle–Damgård hash construction
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-18 DOI: 10.1007/s10623-024-01538-z
Ying Xu, Xiaoni Du, Jian Zou
{"title":"Quantum security of Trojan message attacks on Merkle–Damgård hash construction","authors":"Ying Xu, Xiaoni Du, Jian Zou","doi":"10.1007/s10623-024-01538-z","DOIUrl":"https://doi.org/10.1007/s10623-024-01538-z","url":null,"abstract":"<p>In this paper, we promote Trojan message attacks against Merkle–Damgård hash functions and their concatenation combiner in quantum settings for the first time. Two main quantum scenarios are considered, involving the scenarios where a substantial amount of cheap quantum random access memory (qRAM) is available and where qRAM is limited and expensive to access. We first discuss the construction of diamond structures and analyze the corresponding time complexity in both of these quantum scenarios. Secondly, we propose quantum versions of the generic Trojan message attacks on Merkle–Damgård hash functions as well as their improved versions by combining with diamond structures and expandable messages, and then determine their cost. Finally, we propose Trojan message attack against Merkle–Damgård hash concatenation combiner in quantum setting. The results show that Trojan message attacks can be improved significantly with quantum computers under both scenarios, so the security of hash constructions in classical setting requires careful re-evaluation before being deployed to the post-quantum cryptography schemes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"260 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849040","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}
引用次数: 0
Optimal combinatorial neural codes via symmetric designs
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-18 DOI: 10.1007/s10623-024-01534-3
Xingyu Zheng, Shukai Wang, Cuiling Fan
{"title":"Optimal combinatorial neural codes via symmetric designs","authors":"Xingyu Zheng, Shukai Wang, Cuiling Fan","doi":"10.1007/s10623-024-01534-3","DOIUrl":"https://doi.org/10.1007/s10623-024-01534-3","url":null,"abstract":"<p>Combinatorial neural (CN) codes are binary codes introduced firstly by Curto et al. for asymmetric channel, and then are further studied by Cotardo and Ravagnani under the metric <span>(delta _r)</span> (called asymmetric discrepancy) which measures the differentiation of codewords in CN codes. When <span>(r&gt;1)</span>, CN codes are different from the usual error-correcting codes in symmetric channel (<span>(r=1)</span>). In this paper, we focus on the optimality of some CN codes with <span>(r&gt;1)</span>. An upper bound for the size of CN codes with <span>(delta _r=r+1)</span> is deduced, by discussing the relationship between such CN codes and error-detecting codes for asymmetric channels, which is shown to be tight in this case. We also propose an improved Plotkin bound for CN codes. Notably, by applying symmetric designs related with Hadamard matrices, we not only generalize one former construction of optimal CN codes by bent functions obtained by Zhang et al. (IEEE Trans Inf Theory 69:5440–5448, 2023), but also obtain seven classes of new optimal CN codes meeting the improved Plotkin bound.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"8 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841501","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}
引用次数: 0
Relating code equivalence to other isomorphism problems 将代码等价与其他同构问题联系起来
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-16 DOI: 10.1007/s10623-024-01542-3
Huck Bennett, Kaung Myat Htay Win
{"title":"Relating code equivalence to other isomorphism problems","authors":"Huck Bennett, Kaung Myat Htay Win","doi":"10.1007/s10623-024-01542-3","DOIUrl":"https://doi.org/10.1007/s10623-024-01542-3","url":null,"abstract":"<p>We study the complexity of the <i>Code Equivalence Problem</i> on linear error-correcting codes by relating its variants to isomorphism problems on other discrete structures—graphs, lattices, and matroids. Our main results are a fine-grained reduction from the Graph Isomorphism Problem to the Linear Code Equivalence Problem over any field <span>(mathbb {F})</span>, and a reduction from the Linear Code Equivalence Problem over any field <span>(mathbb {F}_p)</span> of prime, polynomially bounded order <i>p</i> to the Lattice Isomorphism Problem. Both of these reductions are simple and natural. We also give reductions between variants of the Code Equivalence Problem, and study the relationship between isomorphism problems on codes and linear matroids.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"2021 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142832039","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}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信