Designs, Codes and Cryptography最新文献_第5页

Association schemes and orthogonality graphs on anisotropic points of polar spaces 极空间各向异性点上的关联方案和正交图谱

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-24 DOI: 10.1007/s10623-024-01514-7

Sam Adriaensen, Maarten De Boeck

引用次数: 0

Algebraic hierarchical locally recoverable codes with nested affine subspace recovery 具有嵌套仿射子空间恢复功能的代数分层局部可恢复编码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-24 DOI: 10.1007/s10623-024-01510-x

Kathryn Haymaker, Beth Malmskog, Gretchen Matthews

引用次数: 0

DNA codes over groups 组上的 DNA 编码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-23 DOI: 10.1007/s10623-024-01515-6

Cain Álvarez-García, Carlos Alberto Castillo-Guillén, Mohamed Badaoui, Andriy Kryvko

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Equivalence of constacyclic codes with shift constants of different orders 具有不同阶移位常量的常环码的等价性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-18 DOI: 10.1007/s10623-024-01512-9

Reza Dastbasteh, Farzad Padashnick, Pedro M. Crespo, Markus Grassl, Javad Sharafi

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Truncated differential cryptanalysis: new insights and application to QARMAv1-n and QARMAv2-64 截断差分密码分析：QARMAv1-n 和 QARMAv2-64 的新见解和应用

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-18 DOI: 10.1007/s10623-024-01486-8

Zahra Ahmadian, Akram Khalesi, Dounia M’foukh, Hossein Moghimi, María Naya-Plasencia

引用次数: 0

Conjunctive hierarchical secret sharing by finite geometry 通过有限几何实现连接式分层秘密共享

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-16 DOI: 10.1007/s10623-024-01496-6

Máté Gyarmati, Péter Ligeti, Peter Sziklai, Marcella Takáts

引用次数: 0

Revisiting products of the form X times a linearized polynomial L(X) 重温形式为 X 乘以线性化多项式 L(X) 的乘积

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-16 DOI: 10.1007/s10623-024-01511-w

Christof Beierle

{"title":"Revisiting products of the form X times a linearized polynomial L(X)","authors":"Christof Beierle","doi":"10.1007/s10623-024-01511-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01511-w","url":null,"abstract":"For a q-polynomial L over a finite field (mathbb {F}_{q^n}), we characterize the differential spectrum of the function (f_L:mathbb {F}_{q^n} rightarrow mathbb {F}_{q^n}, x mapsto x cdot L(x)) and show that, for (n le 5), it is completely determined by the image of the rational function (r_L :mathbb {F}_{q^n}^* rightarrow mathbb {F}_{q^n}, x mapsto L(x)/x). This result follows from the classification of the pairs (L, M) of q-polynomials in (mathbb {F}_{q^n}[X]), (n le 5), for which (r_L) and (r_M) have the same image, obtained in Csajbók et al. (Ars Math Contemp 16(2):585–608, 2019). For the case of (n>5), we pose an open question on the dimensions of the kernels of (x mapsto L(x) - ax) for (a in mathbb {F}_{q^n}). We further present a link between functions (f_L) of differential uniformity bounded above by q and scattered q-polynomials and show that, for odd values of q, we can construct CCZ-inequivalent functions (f_M) with bounded differential uniformity from a given function (f_L) fulfilling certain properties.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142440633","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

Decoding error probability of random parity-check matrix ensemble over the erasure channel 擦除信道上随机奇偶校验矩阵集合的解码误差概率

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-16 DOI: 10.1007/s10623-024-01516-5

Chin Hei Chan, Fang-Wei Fu, Maosheng Xiong

引用次数: 0

The sequence reconstruction of permutations with Hamming metric 含汉明度量的排列序列重构

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-16 DOI: 10.1007/s10623-024-01509-4

Xiang Wang, Fang-Wei Fu, Elena V. Konstantinova

{"title":"The sequence reconstruction of permutations with Hamming metric","authors":"Xiang Wang, Fang-Wei Fu, Elena V. Konstantinova","doi":"10.1007/s10623-024-01509-4","DOIUrl":"https://doi.org/10.1007/s10623-024-01509-4","url":null,"abstract":"In the combinatorial context, one of the key problems in sequence reconstruction is to find the largest intersection of two metric balls of radius r. In this paper we study this problem for permutations of length n distorted by Hamming errors and determine the size of the largest intersection of two metric balls with radius r whose centers are at distance (d=2,3,4). Moreover, it is shown that for any (ngeqslant 3) an arbitrary permutation is uniquely reconstructible from four distinct permutations at Hamming distance at most two from the given one, and it is proved that for any (ngeqslant 4) an arbitrary permutation is uniquely reconstructible from (4n-5) distinct permutations at Hamming distance at most three from the permutation. It is also proved that for any (ngeqslant 5) an arbitrary permutation is uniquely reconstructible from (7n^2-31n+37) distinct permutations at Hamming distance at most four from the permutation. Finally, in the case of at most r Hamming errors and sufficiently large n, it is shown that at least ({varTheta }(n^{r-2})) distinct erroneous patterns are required in order to reconstruct an arbitrary permutation.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"14 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142444009","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

Constructions of plateaued correctors with high correction order and good nonlinearity via Walsh spectral neutralization technique 通过沃尔什谱中和技术构建具有高校正阶和良好非线性的高原校正器

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-16 DOI: 10.1007/s10623-024-01497-5

Shuyu Luo, Weiqiong Wang, Qi Zhang, Zhenjie Song

{"title":"Constructions of plateaued correctors with high correction order and good nonlinearity via Walsh spectral neutralization technique","authors":"Shuyu Luo, Weiqiong Wang, Qi Zhang, Zhenjie Song","doi":"10.1007/s10623-024-01497-5","DOIUrl":"https://doi.org/10.1007/s10623-024-01497-5","url":null,"abstract":"A corrector is a critical component of True Random Number Generators (TRNGs), serving as a post-processing function to reduce statistical weaknesses in raw random sequences. It is important to note that a (textit{t})-resilient Boolean function is a (textit{t})-corrector, while the converse is not necessarily true. Building upon the pioneering method introduced by Zhang in 2023 for constructing nonlinear correctors with correction order one greater than resiliency order, this paper presents for the first time two approaches for constructing nonlinear plateaued correctors with correction order at least two greater than resiliency order via Walsh spectral neutralization technique, and the resulting correctors have algebraic degree at least (text {2}). The first approach yields (textit{n})-variable plateaued correctors with correction order (textit{n}-text {2}) and resiliency order approximately (textit{n}- text {log}_text {2} textit{n}). The nonlinearity and algebraic degree of the resulting correctors are also analyzed, demonstrating that they meet both Siegenthaler’s and Sarkar-Maitra’s bounds. Another approach based on Walsh spectral neutralization technique for constructing (textit{n})-variable plateaued correctors is proposed. This approach facilitates the design of semi-bent correctors with algebraic degree (lceil frac{textit{n}}{text {2}} rceil ), correction order (lfloor frac{textit{n}}{text {2}} rfloor -text {1}) and resiliency order approximately ( frac{textit{n}}{text {4}} ).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"2 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142444001","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