{"title":"Vectorial dual-bent functions and association schemes","authors":"Nurdagül Anbar,Tekgül Kalaycı,Wilfried Meidl,Ferruh Özbudak","doi":"10.1007/s10623-026-01946-3","DOIUrl":"https://doi.org/10.1007/s10623-026-01946-3","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149022462","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":"Extending binary sequences to maximum length sequences","authors":"Yupeng Jiang, Ming Li, Junying Liu, Dongdai Lin","doi":"10.1007/s10623-026-01925-8","DOIUrl":"https://doi.org/10.1007/s10623-026-01925-8","url":null,"abstract":"In this paper, we address the problem of determining whether a binary sequence can be extended to a de Bruijn sequence with the same nonlinear complexity. Given a sequence with nonlinear complexity <italic>n</italic>, we can get a partial state graph from it by the inverse process of Golomb’s preference algorithm. Then we propose an algorithm to expand this partial graph to include a maximum component and prove that the sequence can be extended to a de Bruijn sequence of order <italic>n</italic> if and only if the component contains all <inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(n-1)$$end{document}</tex-math></alternatives></inline-formula>-binary tuples. Moreover, employing Golomb’s preference algorithm to the maximum component, we generate a sequence which can be shown to be a maximum length sequence extending this sequence. We also give some properties about the states and period of maximum length sequences. It is interesting that although there may exist many maximum length sequences extending the sequence, the states occurring in each maximum length sequence are the same.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"81 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149003663","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":"An improved method for predicting truncated Fibonacci LFSRs over integer residue rings","authors":"Han-Bing Yu, Qun-Xiong Zheng, Wen-Feng Qi","doi":"10.1007/s10623-026-01943-6","DOIUrl":"https://doi.org/10.1007/s10623-026-01943-6","url":null,"abstract":"Sequences over the residue ring of integers modulo <italic>m</italic> generated by linear feedback shift registers (LFSRs) exhibit ring-level linearity and bit-level nonlinearity, making such kind of LFSRs [denoted as <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {Z}/(m)$$end{document}</tex-math></alternatives></inline-formula>-LFSRs] a key component of stream ciphers. Beyond fundamental cryptographic properties, the unpredictability of truncated <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {Z}/(m)$$end{document}</tex-math></alternatives></inline-formula>-LFSRs has attracted considerable attention as a critical security consideration in the design of stream cipher components. This paper investigates the unpredictability of truncated Fibonacci <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {Z}/(m)$$end{document}</tex-math></alternatives></inline-formula>-LFSRs under various scenarios. First, we provide a practical heuristic estimation for the values of two key parameters based on lattice theory, thereby helping to avoid previous blind search. This estimation is subsequently applied to determine the number of truncated digits required in different scenarios. Next, we develop a heuristic lattice-based method for finding annihilating polynomials over <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidema","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149003665","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":"Near-optimal covering sequences","authors":"Hoang Ta, Van Khu Vu","doi":"10.1007/s10623-026-01934-7","DOIUrl":"https://doi.org/10.1007/s10623-026-01934-7","url":null,"abstract":"An (<italic>n</italic>, <italic>R</italic>)-covering sequence over a finite alphabet <inline-formula><alternatives><mml:math><mml:mrow><mml:msub><mml:mi mathvariant=\"normal\">Σ</mml:mi><mml:mi>q</mml:mi></mml:msub><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>⋯</mml:mo><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Sigma _q{:}{=}{0,1,dots , q-1}$$end{document}</tex-math></alternatives></inline-formula> is a cyclic sequence whose consecutive length-<italic>n</italic> windows form a covering code of radius <italic>R</italic>. Equivalently, every word in <inline-formula><alternatives><mml:math><mml:msubsup><mml:mi mathvariant=\"normal\">Σ</mml:mi><mml:mi>q</mml:mi><mml:mi>n</mml:mi></mml:msubsup></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Sigma _q^n$$end{document}</tex-math></alternatives></inline-formula> is within Hamming distance <italic>R</italic> of at least one window. We give a deterministic and explicit construction of such sequences whose length, for every fixed alphabet size <italic>q</italic>, every fixed radius <italic>R</italic>, and every sufficiently large <italic>n</italic>, attains the sphere-covering lower bound up to a constant factor depending only on <italic>q</italic> and <italic>R</italic>. Thus, in the fixed-radius regime, the construction removes the logarithmic factor in the general probabilistic upper bounds of [Chung and Cooper, <italic>Random Structures & Algorithms</italic>, 2004] and [Vu, <italic>Advances in Applied Mathematics</italic>, 2005]. It also complements the earlier explicit constructions of [Chee, Etzion, Ta, and Vu, <italic>Designs, Codes and Cryptography</italic>, 2025], which include constant factor bounds for the special binary radius-one families <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>a</mml:mi></mml:msup><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n=2^a-1$$end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>a</mml:mi></mml:msup></mm","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"47 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149003666","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":"Linear and group identifying codes in Hamming graphs","authors":"N. V. Shinde, S. A. Mane","doi":"10.1007/s10623-026-01932-9","DOIUrl":"https://doi.org/10.1007/s10623-026-01932-9","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"35 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148883447","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":"Anonymous reputation systems with revocation, revisited","authors":"Ryuya Hayashi,Shuichi Katsumata,Yusuke Sakai","doi":"10.1007/s10623-026-01936-5","DOIUrl":"https://doi.org/10.1007/s10623-026-01936-5","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"38 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894501","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":"The exact parameters of a family of BCH codes","authors":"Zhonghua Sun","doi":"10.1007/s10623-026-01937-4","DOIUrl":"https://doi.org/10.1007/s10623-026-01937-4","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"11 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894498","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 the BUFF security of ECDSA with key recovery","authors":"Keita Emura","doi":"10.1007/s10623-026-01942-7","DOIUrl":"https://doi.org/10.1007/s10623-026-01942-7","url":null,"abstract":"Abstract In the usual syntax of digital signatures, the verification algorithm takes a verification key in addition to a signature and a message, whereas in ECDSA with key recovery, which is used in Ethereum, no verification key is input to the verification algorithm. Instead, a verification key is recovered from a signature and a message. In this paper, we explore the BUFF security of ECDSA with key recovery (KR-ECDSA), where BUFF stands for Beyond UnForgeability Features [7]. As a result, we show that KR-ECDSA provides BUFF security, except weak non-resignability (wNR). It is particularly noteworthy that the KR-ECDSA verification algorithm takes an Ethereum address $$textsf{addr}$$ addr as input. This address is defined as the rightmost 160 bits of the Keccak-256 hash of the corresponding ECDSA verification key. Crucially, the algorithm verifies that the hash of the recovered verification key matches $$textsf{addr}$$ addr . Our security analysis shows that the procedure, namely checking whether the hash value of the recovered verification key matches the address, is essential for achieving provide BUFF security. We also discuss whether wNR is mandatory in Ethereum or not. To clarify which part is mandatory to provide BUFF security in KR-ECDSA, we show that the original ECDSA does not provide any BUFF security. As a by-product of the analysis, we show that one of our BUFF attacks also works against Aumayr et al.’s ECDSA-based adaptor signature scheme [2] and Qin et al.’s blind adaptor signature scheme [35], which is based on Aumayr et al.’s scheme. We emphasize that the attack lies outside their security models.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"55 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894506","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}
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