Pub Date : 2026-01-05DOI: 10.1007/s10623-025-01745-2
Andrea C. Burgess, Peter Danziger, Daniel Horsley, Muhammad Tariq Javed
{"title":"Packing designs with large block size","authors":"Andrea C. Burgess, Peter Danziger, Daniel Horsley, Muhammad Tariq Javed","doi":"10.1007/s10623-025-01745-2","DOIUrl":"https://doi.org/10.1007/s10623-025-01745-2","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"28 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902645","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}
Pub Date : 2026-01-05DOI: 10.1007/s10623-025-01764-z
Mohsen Bayat, Nasrin Soltankhah
{"title":"On flag-transitive 2-designs with prime block length and projective special linear groups","authors":"Mohsen Bayat, Nasrin Soltankhah","doi":"10.1007/s10623-025-01764-z","DOIUrl":"https://doi.org/10.1007/s10623-025-01764-z","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902642","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}
Pub Date : 2026-01-05DOI: 10.1007/s10623-025-01752-3
Ivan Landjev, Emiliyan Rogachev, Assia Rousseva
{"title":"Characterization of some minihypers in $${{,textrm{PG},}}(r,3)$$ and the nonexistence of some ternary Griesmer codes","authors":"Ivan Landjev, Emiliyan Rogachev, Assia Rousseva","doi":"10.1007/s10623-025-01752-3","DOIUrl":"https://doi.org/10.1007/s10623-025-01752-3","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902646","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}
Pub Date : 2025-12-24DOI: 10.1007/s10623-025-01740-7
Leijo Jose, Anuradha Sharma
{"title":"On Eisenstein additive codes over chain rings and linear codes over mixed alphabets","authors":"Leijo Jose, Anuradha Sharma","doi":"10.1007/s10623-025-01740-7","DOIUrl":"https://doi.org/10.1007/s10623-025-01740-7","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"22 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145829852","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}
Pub Date : 2025-12-24DOI: 10.1007/s10623-025-01744-3
Giulia Cavicchioni, Alessio Meneghetti, Giovanni Tognolini
Information set decoding (ISD) algorithms currently offer the most powerful tool to solve the two archetypal problems of coding theory, namely the codeword finding problem and the syndrome decoding problem. Traditionally, ISD have primarily been studied for linear codes over finite fields, equipped with the Hamming metric. However, recently, other possibilities have also been explored. These algorithms have been adapted to different ambient spaces and metrics, such as the rank metric or the Lee metric over $$mathbb {Z}_m$$Zm . In this paper, we propose a general framework for decoding ring-linear codes that exploits the underlying ring structure to improve traditional approaches. The core idea is to project the decoding instance onto a smaller alphabet, which may enable more efficient decoding algorithms. The framework applies to coordinate-additive metric including Hamming and Lee, and extends to the rank metric, though its effectiveness strongly depends on the chosen metric. We illustrate how this framework can be leveraged to design decoding algorithms for the two aforementioned problems in Hamming, rank, and Lee metrics, along with their range of effectiveness. For each case, we provide the average computational complexity of the resulting algorithms.
信息集译码（ISD）算法是目前解决编码理论的两个原型问题——码字查找问题和证型译码问题的最有力工具。传统上，ISD主要研究有限域上的线性码，并配有汉明度量。然而，最近也探索了其他可能性。这些算法已经适应了不同的环境空间和度量，例如秩度量或$$mathbb {Z}_m$$ Z m上的Lee度量。在本文中，我们提出了一种解码环线性码的通用框架，利用潜在的环结构来改进传统方法。核心思想是将解码实例投影到更小的字母表上，这可能会使解码算法更有效。该框架适用于包括Hamming和Lee在内的坐标加性度量，并扩展到秩度量，尽管其有效性强烈依赖于所选择的度量。我们说明了如何利用这个框架来设计针对上述两个问题的解码算法，包括Hamming、rank和Lee度量，以及它们的有效性范围。对于每种情况，我们提供了结果算法的平均计算复杂度。
{"title":"Information set decoding for ring-linear codes","authors":"Giulia Cavicchioni, Alessio Meneghetti, Giovanni Tognolini","doi":"10.1007/s10623-025-01744-3","DOIUrl":"https://doi.org/10.1007/s10623-025-01744-3","url":null,"abstract":"Information set decoding (ISD) algorithms currently offer the most powerful tool to solve the two archetypal problems of coding theory, namely the codeword finding problem and the syndrome decoding problem. Traditionally, ISD have primarily been studied for linear codes over finite fields, equipped with the Hamming metric. However, recently, other possibilities have also been explored. These algorithms have been adapted to different ambient spaces and metrics, such as the rank metric or the Lee metric over <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$mathbb {Z}_m$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> . In this paper, we propose a general framework for decoding ring-linear codes that exploits the underlying ring structure to improve traditional approaches. The core idea is to project the decoding instance onto a smaller alphabet, which may enable more efficient decoding algorithms. The framework applies to coordinate-additive metric including Hamming and Lee, and extends to the rank metric, though its effectiveness strongly depends on the chosen metric. We illustrate how this framework can be leveraged to design decoding algorithms for the two aforementioned problems in Hamming, rank, and Lee metrics, along with their range of effectiveness. For each case, we provide the average computational complexity of the resulting algorithms.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"7 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145829884","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}
Pub Date : 2025-12-24DOI: 10.1007/s10623-025-01738-1
Giuseppe D’Alconzo, Andre Esser, Andrea Gangemi, Carlo Sanna
A partial key exposure attack is a key recovery attack where an adversary obtains a priori partial knowledge of the secret key, e.g., through side-channel leakage. While for a long time post-quantum cryptosystems, unlike RSA, have been believed to be resistant to such attacks, recent results by Esser, May, Verbel, and Wen (CRYPTO ’22), and by Kirshanova and May (SCN ’22), have refuted this belief. In this work, we focus on partial key exposure attacks in the context of rank-metric-based schemes, particularly targeting the RYDE, MIRA, and MiRitH digital signatures schemes, which are active candidates in the NIST post-quantum cryptography standardization process. We demonstrate that, similar to the RSA case, the secret key in RYDE can be recovered from a constant fraction of its bits. Specifically, for NIST category I parameters, our attacks remain efficient even when less than 25% of the key material is leaked. Interestingly, our attacks lead to a natural improvement of the best generic attack on RYDE without partial knowledge , reducing security levels by up to 9 bits. For MIRA and MiRitH our attacks remain efficient as long as roughly 57–60% of the secret key material is leaked. Additionally, we initiate the study of partial exposure of the witness in constructions following the popular MPCitH (MPC-in-the-Head) paradigm. We show a generic reduction from recovering RYDE and MIRA’s witness to the MinRank problem, which again leads to efficient key recovery from constant fractions of the secret witness in both cases.
{"title":"Sneaking up the ranks: Partial key exposure attacks on rank-based schemes","authors":"Giuseppe D’Alconzo, Andre Esser, Andrea Gangemi, Carlo Sanna","doi":"10.1007/s10623-025-01738-1","DOIUrl":"https://doi.org/10.1007/s10623-025-01738-1","url":null,"abstract":"A partial key exposure attack is a key recovery attack where an adversary obtains a priori partial knowledge of the secret key, e.g., through side-channel leakage. While for a long time post-quantum cryptosystems, unlike RSA, have been believed to be resistant to such attacks, recent results by Esser, May, Verbel, and Wen (CRYPTO ’22), and by Kirshanova and May (SCN ’22), have refuted this belief. In this work, we focus on partial key exposure attacks in the context of rank-metric-based schemes, particularly targeting the RYDE, MIRA, and MiRitH digital signatures schemes, which are active candidates in the NIST post-quantum cryptography standardization process. We demonstrate that, similar to the RSA case, the secret key in RYDE can be recovered from a constant fraction of its bits. Specifically, for NIST category I parameters, our attacks remain efficient even when less than 25% of the key material is leaked. Interestingly, our attacks lead to a natural improvement of the best generic attack on RYDE <jats:italic>without partial knowledge</jats:italic> , reducing security levels by up to 9 bits. For MIRA and MiRitH our attacks remain efficient as long as roughly 57–60% of the secret key material is leaked. Additionally, we initiate the study of partial exposure of the witness in constructions following the popular MPCitH (MPC-in-the-Head) paradigm. We show a generic reduction from recovering RYDE and MIRA’s witness to the MinRank problem, which again leads to efficient key recovery from constant fractions of the secret witness in both cases.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145829850","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}
Pub Date : 2025-12-20DOI: 10.1007/s10623-025-01743-4
Mahir Bilen Can
Poset metrics in the context of stabilizer codes are investigated. We establish a Singleton-type bound for stabilizer poset codes and introduce the notion of MDS stabilizer poset codes. Several characterizations of these codes are obtained, including criteria in terms of additive codes and perfect codes. We also prove existence results for large families of examples, thereby extending classical results on MDS poset codes to the quantum setting.
{"title":"MDS stabilizer poset codes","authors":"Mahir Bilen Can","doi":"10.1007/s10623-025-01743-4","DOIUrl":"https://doi.org/10.1007/s10623-025-01743-4","url":null,"abstract":"Poset metrics in the context of stabilizer codes are investigated. We establish a Singleton-type bound for stabilizer poset codes and introduce the notion of MDS stabilizer poset codes. Several characterizations of these codes are obtained, including criteria in terms of additive codes and perfect codes. We also prove existence results for large families of examples, thereby extending classical results on MDS poset codes to the quantum setting.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"29 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796149","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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