{"title":"Efficient private PEZ protocols without binary-input restrictions","authors":"Yoshiki Abe, Mitsugu Iwamoto, Kazuo Ohta","doi":"10.1007/s10623-026-01876-0","DOIUrl":"https://doi.org/10.1007/s10623-026-01876-0","url":null,"abstract":"Balogh et al. proposed deterministic secure multiparty computation called <italic>private PEZ protocols</italic>. In their work, a general construction of private PEZ protocols for computing an <italic>arbitrary</italic> function with <italic>n</italic> inputs is presented, but the function’s inputs must be <italic>binary</italic>. Binary domains are sufficient for computing functions with <italic>arbitrary</italic> domains because we can use the binary expansion of the inputs. However, such an expansion makes the protocol inefficient because unnecessary privacy is considered among the expanded bits of each input. Hence, we remove the binary expansion technique in this paper and propose a new private PEZ protocol directly applicable to functions with arbitrary domains. The proposed private PEZ protocol for an arbitrary function is much more efficient than Balogh et al.’s protocol. Concretely, an efficiency measure called <italic>the length of an initial string</italic> is exponentially improved in the domain size <italic>m</italic>: the order obtained from our construction is <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"script\">O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>2</mml:mn><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msup><mml:mi>m</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:msup><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}$$mathcal {O}((2m)^{m^{n-1}})$$end{document}</tex-math></alternatives></inline-formula>, while the construction of Balogh et al. yields <inline-formula><alternatives><mml:math><mml:mrow><mml:mi mathvariant=\"normal\">Ω</mml:mi><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mfrac><mml:mi>m</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:msup><mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:msup><mml:mi>m</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</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}$$mathrm {Omega }bigg (bigg (2^{frac{m}{2}}bigg )^{m^{n-1}}bigg )$$end{document}</tex-math></alternatives></inline-formula>. The key idea of our protocol is called th","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"48 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552124","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}
José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro
{"title":"A knapsack McEliece-based public key cryptosystem","authors":"José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro","doi":"10.1007/s10623-026-01913-y","DOIUrl":"https://doi.org/10.1007/s10623-026-01913-y","url":null,"abstract":"A ROM IND-CCA2 Key Encapsulation Mechanism (KEM) supported by a Public Key Encryption (PKE) scheme based on the Weighted Modular Subset Sum Problem (WMSSP) is proposed. Concretely, it is proven that for certain sets of integers, whose inverses modulo a large predetermined integer have bounded bit size, an algorithm based on a truncated version of the extended Euclidean algorithm can effectively solve the WMSSP. The security analysis is conducted through the connection established between the Binary Subset Sum Problem and the Shortest Vector Problem. Various attacks against our proposal, relying on the computation of a shortest vector, have been analyzed. It is widely accepted that the problem supporting the security of this cryptosystem exhibits resilience against quantum threats. Moreover, the key generation and encryption-decryption processes exhibit remarkable time efficiency, as they rely exclusively on basic integer arithmetic.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612837","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":"Bilateral access control ABE from lattices and application to AB-ME","authors":"Huige Wang, Shuai Han, Jian Weng, Qi Xie","doi":"10.1007/s10623-026-01887-x","DOIUrl":"https://doi.org/10.1007/s10623-026-01887-x","url":null,"abstract":"Attribute-Based Encryption (ABE) is a cryptosystem that can provide flexible access control, which has important application value in the field of fine-grained access control to encrypted data. However, current ABEs only support unilateral access control from the sender to the receiver, and fail to provide data source authentication, which violates the principle of data source identification for sensitive information as mandated by the General Data Protection Regulation (GDPR). To address this problem, the notion of bilateral access control Attribute-Based Encryption (bilateral access control ABE) is introduced, but the existing schemes are constructed under the classical assumptions. In this paper, building upon the WWW+ IBS scheme, we proposed a bilateral access control ABE scheme that is provably secure in the Random Oracle Model (ROM) under the Learning With Errors (LWE) and Short Integer Solution (SIS) assumptions on lattices. In comparison to the existing ABEs based on lattice assumptions, our approach not only enables access control from sender to receiver, but also from receiver to sender. Particularly, our scheme also captures the data source authentication. Furthermore, we prove that our scheme achieves selective Indistinguishable Chosen-Plaintext-Attacks (sIND-CPA) security and authentication under the LWE and SIS assumptions. Beyond that, we also capture the attribute-hiding property (weak attribute-hiding, i.e., the scheme grants access to the attributes to receivers possessing the requisite decryption capability once a match is successful.) to obtain a (plausible) post-quantum secure Attribute-Based Matchmaking Encryption (AB-ME) scheme by using a lockable-obfuscation-based transformation. Compared to the existing AB-ME schemes, our scheme not only achieves privacy and authentication, but also is a lattice-based scheme that is post-quantum secure in the ROM.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"239 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148552125","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":"Block-transitive 3-designs with small λdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$lambda $$end{document} on sporadic simple groups","authors":"Ting Lan, Weijun Liu, Fu-Gang Yin","doi":"10.1007/s10623-026-01909-8","DOIUrl":"https://doi.org/10.1007/s10623-026-01909-8","url":null,"abstract":"In this paper, we study non-complete <italic>G</italic>-block-transitive 3-<inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</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}$$(v,k,lambda )$$end{document}</tex-math></alternatives></inline-formula> designs with small values of <inline-formula><alternatives><mml:math><mml:mi>λ</mml:mi></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}$$lambda $$end{document}</tex-math></alternatives></inline-formula>, where <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>T</mml:mi><mml:mo>≤</mml:mo><mml:mi>G</mml:mi><mml:mo>≤</mml:mo><mml:mtext>Aut</mml:mtext><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>T</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}$$T le G le textrm{Aut}(T)$$end{document}</tex-math></alternatives></inline-formula> and <italic>T</italic> is a sporadic simple group. When <italic>G</italic> acts primitively on the point set and <inline-formula><alternatives><mml:math><mml:mrow><mml:mi>λ</mml:mi><mml:mo>≤</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mn>000</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}$$lambda le 10,000$$end{document}</tex-math></alternatives></inline-formula>, we obtain a list of possible parameter tuples <inline-formula><alternatives><mml:math><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</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}$$(G,v,k,lambda )$$end{document}</tex-math></alternatives></inline-formula> and explicitly construct several new designs for the Mathieu group <inline-formula><alternatives><mml:math><mml:msub><mml:mtext>M</mml:mtext><mml:mn>22</mml:mn></mml:msub></mml:math><tex-math>documentclass[12pt]{minimal} u","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148612839","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}
Dylan Fillmore, Bennet Goeckner, Rachel Kirsch, Kirin Martin, Daniel McGinnis
{"title":"The existence and structure of universal partial cycles","authors":"Dylan Fillmore, Bennet Goeckner, Rachel Kirsch, Kirin Martin, Daniel McGinnis","doi":"10.1007/s10623-026-01841-x","DOIUrl":"https://doi.org/10.1007/s10623-026-01841-x","url":null,"abstract":"A universal partial cycle (or upcycle) for <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$mathcal {A}^n$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>A</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> </jats:alternatives> </jats:inline-formula> is a cyclic sequence that covers each word of length <jats:italic>n</jats:italic> over the alphabet <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$mathcal {A}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> exactly once—like a De Bruijn cycle, except that we also allow a wildcard symbol <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$mathord {diamond }$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>⋄</mml:mo> </mml:math> </jats:alternatives> </jats:inline-formula> that can represent any letter of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$mathcal {A}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> . Chen et al. (Discret Math Theor Comput Sci 2017. https://doi.org/10.23638/DMTCS-19-1-16) and Goeckner et al. (Theor Comput Sci 713:56–65, 2018. https://doi.org/10.1016/j.tcs.2017.12.022) showed that the existence and structure of upcycles are highly constrained, unlike those of De Bruijn cycles, which exist for every alphabet size and word length. Moreover, it was not known whether any upcycles existed for <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$n ge 5$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> . We present several examples of upcycles over both binary and non-binary alphabets for <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$n = 8$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> . We generalize two graph-theoretic representations of De Bruijn cycles to upcycles. We then introduce novel approaches to constructing new upcycles from old ones. Notably, given any upcycle for an alphabet of size <jats:italic>a</jats:italic> , we show how to construct an upcycle for an alphabet of size <jats:italic>ak</jats:italic> for any <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$k in mathbb {N}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> , so each example generates an infinite family of upcycles. We also define folds and lifts of u","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148408879","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 reducibility of minihypers","authors":"Ivan Landjev, Assia Rousseva, Leo Storme","doi":"10.1007/s10623-026-01900-3","DOIUrl":"https://doi.org/10.1007/s10623-026-01900-3","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"44 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148408881","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}
Elisa Gorla, Lorenzo García Elisa, Umberto Martínez-Peñas, Flavio Salizzoni
{"title":"Integer sequences that are generalized weights of a linear code","authors":"Elisa Gorla, Lorenzo García Elisa, Umberto Martínez-Peñas, Flavio Salizzoni","doi":"10.1007/s10623-026-01872-4","DOIUrl":"https://doi.org/10.1007/s10623-026-01872-4","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"23 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148408878","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}
Yanyan Zhou, Lin Jiao, Senpeng Wang, Yunong Wu, Bin Hu, Tairong Shi, Kai Zhang
{"title":"An improved automatic framework for searching for differential-linear distinguishers with applications to SPN and Feistel block ciphers","authors":"Yanyan Zhou, Lin Jiao, Senpeng Wang, Yunong Wu, Bin Hu, Tairong Shi, Kai Zhang","doi":"10.1007/s10623-026-01867-1","DOIUrl":"https://doi.org/10.1007/s10623-026-01867-1","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"62 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148408880","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 subcodes of the generalized Reed-Solomon codes","authors":"Yu Ning","doi":"10.1007/s10623-026-01893-z","DOIUrl":"https://doi.org/10.1007/s10623-026-01893-z","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"40 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148408884","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}