Designs, Codes and Cryptography最新文献_第8页

Quantum sieving for code-based cryptanalysis and its limitations for ISD 基于码的密码分析的量子筛分及其在ISD中的局限性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-02 DOI: 10.1007/s10623-024-01545-0

Lynn Engelberts, Simona Etinski, Johanna Loyer

{"title":"Quantum sieving for code-based cryptanalysis and its limitations for ISD","authors":"Lynn Engelberts, Simona Etinski, Johanna Loyer","doi":"10.1007/s10623-024-01545-0","DOIUrl":"https://doi.org/10.1007/s10623-024-01545-0","url":null,"abstract":"Sieving using near-neighbor search techniques is a well-known method in lattice-based cryptanalysis, yielding the current best runtime for the shortest vector problem in both the classical and quantum setting. Recently, sieving has also become an important tool in code-based cryptanalysis. Specifically, a variant of the information-set decoding (ISD) framework, commonly used for attacking cryptographically relevant instances of the decoding problem, has been introduced that involves a sieving subroutine. The resulting sieving-based ISD framework yields complexities close to the best-performing classical algorithms for the decoding problem. It is therefore natural to ask how well quantum versions perform. In this work, we introduce the first quantum algorithms for code sieving by designing quantum variants of the aforementioned sieving subroutine. In particular, using quantum-walk techniques, we provide a speed-up over classical code sieving and over a variant using Grover’s algorithm. Our quantum-walk algorithm exploits the structure of the underlying search problem by adding a layer of locality sensitive filtering, inspired by a quantum-walk algorithm for lattice sieving. We complement our asymptotic analysis of the quantum algorithms with numerical results, and observe that our quantum speed-ups for code sieving behave similarly as those observed in lattice sieving. In addition, we show that a natural quantum analog of the sieving-based ISD framework does not provide any speed-up over the first quantum ISD algorithm. Our analysis highlights that the framework should be adapted in order to outperform state-of-the-art quantum ISD algorithms.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"20 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142916896","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

Divisible design graphs from the symplectic graph 辛图的可分设计图

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-29 DOI: 10.1007/s10623-024-01557-w

Bart De Bruyn, Sergey Goryainov, Willem H. Haemers, Leonid Shalaginov

{"title":"Divisible design graphs from the symplectic graph","authors":"Bart De Bruyn, Sergey Goryainov, Willem H. Haemers, Leonid Shalaginov","doi":"10.1007/s10623-024-01557-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01557-w","url":null,"abstract":"A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a (group) divisible design. Divisible design graphs were introduced in 2011 as a generalization of ((v,k,lambda ))-graphs. Here we describe four new infinite families that can be obtained from the symplectic strongly regular graph Sp(2e, q) (q odd, (ege 2)) by modifying the set of edges. To achieve this we need two kinds of spreads in (PG(2e-1,q)) with respect to the associated symplectic form: the symplectic spread consisting of totally isotropic subspaces and, when (e=2), a special spread that consists of lines which are not totally isotropic and which is closed under the action of the associated symplectic polarity. Existence of symplectic spreads is known, but the construction of a special spread for every odd prime power q is a main result of this paper. We also show an equivalence between special spreads of Sp(4, q) and certain nice point sets in the projective space (operatorname {PG}(4,q)). We have included relevant background from finite geometry, and when (q=3,5) and 7 we worked out all possible special spreads.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887802","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

Several families of negacyclic BCH codes and their duals 几个负环BCH码族及其对偶

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-27 DOI: 10.1007/s10623-024-01551-2

Zhonghua Sun, Xinyue Liu

引用次数: 0

Fault attacks on multi-prime RSA signatures 针对RSA多素数签名的故障攻击

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-27 DOI: 10.1007/s10623-024-01554-z

Chunzhi Zhao, Jinzheng Cao, Junqi Zhang, Qingfeng Cheng

引用次数: 0

The support designs of several families of lifted linear codes 几种提升线性码族的支撑设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-25 DOI: 10.1007/s10623-024-01549-w

Cunsheng Ding, Zhonghua Sun, Qianqian Yan

{"title":"The support designs of several families of lifted linear codes","authors":"Cunsheng Ding, Zhonghua Sun, Qianqian Yan","doi":"10.1007/s10623-024-01549-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01549-w","url":null,"abstract":"A generator matrix of a linear code ({mathcal {C}}) over ({textrm{GF}}(q)) is also a matrix of the same rank k over any extension field ({textrm{GF}}(q^ell )) and generates a linear code of the same length, same dimension and same minimum distance over ({textrm{GF}}(q^ell )), denoted by ({mathcal {C}}(q|q^ell )) and called a lifted code of ({mathcal {C}}). Although ({mathcal {C}}) and their lifted codes ({mathcal {C}}(q|q^ell )) have the same parameters, they have different weight distributions and different applications. Few results about lifted linear codes are known in the literature. This paper proves some fundamental theory for lifted linear codes, and studies the 2-designs of the lifted projective Reed–Muller codes, lifted Hamming codes and lifted Simplex codes. In addition, this paper settles the weight distributions of the lifted Reed–Muller codes of certain orders, and investigates the 3-designs supported by these lifted codes. As a by-product, an infinite family of three-weight projective codes over ({textrm{GF}}(4)) is obtained.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884413","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

Low-weight codewords in cyclic codes 循环码中的低权重码字

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-24 DOI: 10.1007/s10623-024-01547-y

J. G. Coelho, F. E. Brochero Martínez

引用次数: 0

Guessing less and better: improved attacks on GIFT-64 猜测更少，更好：改进对GIFT-64的攻击

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01527-2

Federico Canale, María Naya-Plasencia

引用次数: 0

On automorphism groups of binary cyclic codes 论二元循环码的自形群

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01539-y

Jicheng Ma, Guiying Yan

引用次数: 0

Several new classes of optimal ternary cyclic codes with two or three zeros 几种新的具有两个或三个零的最优三元循环码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-19 DOI: 10.1007/s10623-024-01541-4

Gaofei Wu, Zhuohui You, Zhengbang Zha, Yuqing Zhang

{"title":"Several new classes of optimal ternary cyclic codes with two or three zeros","authors":"Gaofei Wu, Zhuohui You, Zhengbang Zha, Yuqing Zhang","doi":"10.1007/s10623-024-01541-4","DOIUrl":"https://doi.org/10.1007/s10623-024-01541-4","url":null,"abstract":"Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let (alpha ) be a generator of (mathbb F_{3^m}setminus {0}), where m is a positive integer. Denote by (mathcal {C}_{(i_1,i_2,cdots , i_t)}) the cyclic code with generator polynomial (m_{alpha ^{i_1}}(x)m_{alpha ^{i_2}}(x)cdots m_{alpha ^{i_t}}(x)), where ({{m}_{alpha ^{i}}}(x)) is the minimal polynomial of ({{alpha }^{i}}) over ({{mathbb {F}}_{3}}). In this paper, by analyzing the solutions of certain equations over finite fields, we present four classes of optimal ternary cyclic codes (mathcal {C}_{(0,1,e)}) and (mathcal {C}_{(1,e,s)}) with parameters ([3^m-1,3^m-frac{3m}{2}-2,4]), where (s=frac{3^m-1}{2}). In addition, by determining the solutions of certain equations and analyzing the irreducible factors of certain polynomials over (mathbb F_{3^m}), we present four classes of optimal ternary cyclic codes (mathcal {C}_{(2,e)}) and (mathcal {C}_{(1,e)}) with parameters ([3^m-1,3^m-2m-1,4]). We show that our new optimal cyclic codes are not covered by known ones.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858387","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

Optimal combinatorial neural codes via symmetric designs 通过对称设计的最优组合神经编码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-18 DOI: 10.1007/s10623-024-01534-3

Xingyu Zheng, Shukai Wang, Cuiling Fan

引用次数: 0