Designs, Codes and Cryptography最新文献_第6页

On two non-existence results for Cameron–Liebler k-sets in $${{,mathrm{textrm{PG}},}}(n,q)$$ 论 $${{,mathrm{textrm{PG}},}}(n,q)$$ 中卡梅隆-利勃勒 k 集的两个不存在结果

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-10 DOI: 10.1007/s10623-024-01505-8

Jan De Beule, Jonathan Mannaert, Leo Storme

{"title":"On two non-existence results for Cameron–Liebler k-sets in $${{,mathrm{textrm{PG}},}}(n,q)$$","authors":"Jan De Beule, Jonathan Mannaert, Leo Storme","doi":"10.1007/s10623-024-01505-8","DOIUrl":"https://doi.org/10.1007/s10623-024-01505-8","url":null,"abstract":"This paper focuses on non-existence results for Cameron–Liebler k-sets. A Cameron–Liebler k-set is a collection of k-spaces in ({{,mathrm{textrm{PG}},}}(n,q)) or ({{,mathrm{textrm{AG}},}}(n,q)) admitting a certain parameter x, which is dependent on the size of this collection. One of the main research questions remains the (non-)existence of Cameron–Liebler k-sets with parameter x. This paper improves two non-existence results. First we show that the parameter of a non-trivial Cameron–Liebler k-set in ({{,mathrm{textrm{PG}},}}(n,q)) should be larger than (q^{n-frac{5k}{2}-1}), which is an improvement of an earlier known lower bound. Secondly, we prove a modular equality on the parameter x of Cameron–Liebler k-sets in ({{,mathrm{textrm{PG}},}}(n,q)) with (x<frac{q^{n-k}-1}{q^{k+1}-1}), (nge 2k+1), (n-k+1ge 7) and (n-k) even. In the affine case we show a similar result for (n-k+1ge 3) and (n-k) even. This is a generalization of earlier known modular equalities in the projective and affine case.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142405484","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

Efficient error-correcting codes for the HQC post-quantum cryptosystem HQC 后量子密码系统的高效纠错码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-09 DOI: 10.1007/s10623-024-01507-6

Carlos Aguilar-Melchor, Nicolas Aragon, Jean-Christophe Deneuville, Philippe Gaborit, Jérôme Lacan, Gilles Zémor

{"title":"Efficient error-correcting codes for the HQC post-quantum cryptosystem","authors":"Carlos Aguilar-Melchor, Nicolas Aragon, Jean-Christophe Deneuville, Philippe Gaborit, Jérôme Lacan, Gilles Zémor","doi":"10.1007/s10623-024-01507-6","DOIUrl":"https://doi.org/10.1007/s10623-024-01507-6","url":null,"abstract":"The HQC post-quantum cryptosystem enables two parties to share noisy versions of a common secret binary string, and an error-correcting code is required to deal with the mismatch between both versions. This code is required to deal with binary symmetric channels with as large a transition parameter as possible, while guaranteeing, for cryptographic reasons, a decoding error probability of provably not more than 2-128. This requirement is non-standard for digital communications, and modern coding techniques are not amenable to this setting. This paper explains how this issue is addressed in the last version of HQC: precisely, we introduce a coding scheme that consists of concatenating a Reed–Solomon code with the tensor product of a Reed–Muller code and a repetition code. We analyze its behavior in detail and show that it significantly improves upon the previous proposition for HQC, which consisted of tensoring a BCH and a repetition code. As additional results, we also provide a better approximation of the weight distribution for HQC error vectors, and we remark that the size of the exchanged secret in HQC can be reduced to match the protocol security which also significantly improves performance.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"46 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142397918","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

Infinite families of 3-designs from special symmetric polynomials 来自特殊对称多项式的无穷 3 设计族

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-05 DOI: 10.1007/s10623-024-01508-5

Guangkui Xu, Xiwang Cao, Gaojun Luo, Huawei Wu

引用次数: 0

Interactive aggregate message authentication equipped with detecting functionality from adaptive group testing 配备自适应小组测试检测功能的交互式汇总信息验证

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-04 DOI: 10.1007/s10623-024-01498-4

Kazuhiko Minematsu, Shingo Sato, Junji Shikata

{"title":"Interactive aggregate message authentication equipped with detecting functionality from adaptive group testing","authors":"Kazuhiko Minematsu, Shingo Sato, Junji Shikata","doi":"10.1007/s10623-024-01498-4","DOIUrl":"https://doi.org/10.1007/s10623-024-01498-4","url":null,"abstract":"In this paper, we propose a formal security model and a construction methodology of interactive aggregate message authentication codes with detecting functionality (IAMDs). The IAMD is an interactive aggregate MAC protocol which can identify invalid messages with a small amount of tag-size. Several aggregate MAC schemes that can detect invalid messages have been proposed so far by using non-adaptive group testing in the prior work. In this paper, we utilize adaptive group testing to construct IAMD scheme, and we show that the resulting IAMD scheme can identify invalid messages with a small amount of tag-size compared to the previous schemes. To this end, we give the formalization of adaptive group testing and IAMD, and propose a generic construction starting from any aggregate MAC and any adaptive group testing method. In addition, we compare instantiations of our generic constructions, in terms of total tag-size and several properties. Furthermore, we show advantages of IAMD by implementing constructions of (non-)adaptive aggregate message authentication with detecting functionality and comparing these ones in terms of the data-size and running time of verification algorithms.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142377699","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

Intersection distribution of degree four polynomials over finite fields 有限域上四度多项式的交集分布

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-04 DOI: 10.1007/s10623-024-01488-6

Shuxing Li, Maosheng Xiong

引用次数: 0

A quantum-secure partial parallel MAC QPCBC 量子安全部分并行 MAC QPCBC

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-04 DOI: 10.1007/s10623-024-01506-7

Shuping Mao, Tingting Guo, Peng Wang, Ruozhou Xu, Yuchao Chen, Lei Hu

引用次数: 0

Association schemes arising from non-weakly regular bent functions 非弱正则弯曲函数产生的关联方案

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-04 DOI: 10.1007/s10623-024-01495-7

Yadi Wei, Jiaxin Wang, Fang-Wei Fu

{"title":"Association schemes arising from non-weakly regular bent functions","authors":"Yadi Wei, Jiaxin Wang, Fang-Wei Fu","doi":"10.1007/s10623-024-01495-7","DOIUrl":"https://doi.org/10.1007/s10623-024-01495-7","url":null,"abstract":"Association schemes play an important role in algebraic combinatorics and have important applications in coding theory, graph theory and design theory. The methods to construct association schemes by using bent functions have been extensively studied. Recently, in Özbudak and Pelen (J Algebr Comb 56:635–658, 2022), Özbudak and Pelen constructed infinite families of symmetric association schemes of classes 5 and 6 by using ternary non-weakly regular bent functions. They also stated that “constructing 2p-class association schemes from p-ary non-weakly regular bent functions is an interesting problem\", where (p>3) is an odd prime. In this paper, using non-weakly regular bent functions, we construct infinite families of symmetric association schemes of classes 2p, ((2p+1)) and (frac{3p+1}{2}) for any odd prime p. Fusing those association schemes, we obtain t-class symmetric association schemes, where (t=4,5,6,7). In addition, we give the sufficient and necessary conditions for the partitions P, D, T, U and V (defined in this paper) to induce symmetric association schemes.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"59 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374111","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

Transitive path decompositions of Cartesian products of complete graphs 完整图笛卡儿积的传递路径分解

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-03 DOI: 10.1007/s10623-024-01493-9

Ajani De Vas Gunasekara, Alice Devillers

引用次数: 0

Two classes of exceptional m-to-1 rational functions 两类特殊的 m 对 1 有理函数

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-03 DOI: 10.1007/s10623-024-01499-3

Zhiguo Ding, Michael E. Zieve

引用次数: 0

Tactical decompositions in finite polar spaces and non-spreading classical group actions 有限极空间中的战术分解与非展开经典群作用