Designs, Codes and Cryptography最新文献

More on codes for combinatorial composite DNA 更多关于组合复合DNA的代码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-15 DOI: 10.1007/s10623-025-01634-8

Zuo Ye, Omer Sabary, Ryan Gabrys, Eitan Yaakobi, Ohad Elishco

{"title":"More on codes for combinatorial composite DNA","authors":"Zuo Ye, Omer Sabary, Ryan Gabrys, Eitan Yaakobi, Ohad Elishco","doi":"10.1007/s10623-025-01634-8","DOIUrl":"https://doi.org/10.1007/s10623-025-01634-8","url":null,"abstract":"In this paper, we focus on constructing unique-decodable and list-decodable codes for the recently studied (t, e)-composite-asymmetric error-correcting codes ((t, e)-CAECCs). Let (mathcal {X}) be an (m times n) binary matrix in which each row has Hamming weight w. If at most t rows of (mathcal {X}) contain errors, and in each erroneous row, there are at most e occurrences of (1 rightarrow 0) errors, we say that a (t, e)-composite-asymmetric error occurs in (mathcal {X}). For general values of m, n, w, t, and e, we propose new constructions of (t, e)-CAECCs with redundancy at most ((t-1)log (m) + O(1)), where O(1) is independent of the code length m. In particular, this yields a class of (2, e)-CAECCs that are optimal in terms of redundancy. When m is a prime power, the redundancy can be further reduced to ((t-1)log (m) - O(log (m))). To further increase the code size, we introduce a combinatorial object called a weak (B_e)-set. When (e = w), we present an efficient encoding and decoding method for our codes. Finally, we explore potential improvements by relaxing the requirement of unique decoding to list-decoding. We show that when the list size is t! or an exponential function of t, there exist list-decodable (t, e)-CAECCs with constant redundancy. When the list size is two, we construct list-decodable (3, 2)-CAECCs with redundancy (log (m) + O(1)).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144066263","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

A combinatorial approach to avoiding weak keys in the BIKE cryptosystem 避免BIKE密码系统中弱密钥的组合方法

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-14 DOI: 10.1007/s10623-025-01643-7

Gretchen L. Matthews, Emily McMillon

引用次数: 0

Evaluation codes arising from symmetric polynomials 由对称多项式产生的计算代码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-12 DOI: 10.1007/s10623-025-01637-5

Barbara Gatti, Gábor Korchmáros, Gábor P. Nagy, Vincenzo Pallozzi Lavorante, Gioia Schulte

引用次数: 0

On tweakable correlation robust hashing against key leakages 针对键泄漏的可调整相关性鲁棒散列

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-12 DOI: 10.1007/s10623-025-01641-9

Chun Guo, Xiao Wang, Kang Yang, Yu Yu

引用次数: 0

On flag-transitive symmetric (v, k, 4) designs 关于标志传递对称（v, k, 4）设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-11 DOI: 10.1007/s10623-025-01642-8

Seyed Hassan Alavi

引用次数: 0

On the coding capacity of reverse-complement and palindromic duplication-correcting codes 反向补码和回文重复纠错码的编码容量研究

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-10 DOI: 10.1007/s10623-025-01627-7

Lev Yohananov, Moshe Schwartz

引用次数: 0

Commutative cryptanalysis as a generalization of differential cryptanalysis 微分密码分析的推广——交换密码分析

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-10 DOI: 10.1007/s10623-025-01625-9

Jules Baudrin, Christof Beierle, Patrick Felke, Gregor Leander, Patrick Neumann, Léo Perrin, Lukas Stennes

{"title":"Commutative cryptanalysis as a generalization of differential cryptanalysis","authors":"Jules Baudrin, Christof Beierle, Patrick Felke, Gregor Leander, Patrick Neumann, Léo Perrin, Lukas Stennes","doi":"10.1007/s10623-025-01625-9","DOIUrl":"https://doi.org/10.1007/s10623-025-01625-9","url":null,"abstract":"Recently, Baudrin et al. analyzed a special case of Wagner’s commutative diagram cryptanalysis, referred to as commutative cryptanalysis. For a family ((E_k)_k) of permutations on a finite vector space G, commutative cryptanalysis exploits the existence of affine permutations (A,B :G rightarrow G), (I notin {A,B}) such that (E_k circ A (x) = B circ E_k(x)) holds with high probability, taken over inputs x, for a significantly large set of weak keys k. Several attacks against symmetric cryptographic primitives can be formulated within the framework of commutative cryptanalysis, most importantly differential attacks, as well as rotational and rotational-differential attacks. Besides, the notion of c-differentials on S-boxes can be analyzed as a special case within this framework. We discuss the relations between a general notion of commutative cryptanalysis, with A and B being arbitrary functions over a finite Abelian group, and differential cryptanalysis, both from the view of conducting an attack on a symmetric cryptographic primitive, as well as from the view of a theoretical study of cryptographic S-boxes.\u0000","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"30 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143931303","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

Characterizations for minimal codes: graph theory approach and algebraic approach over finite chain rings 最小码的刻画：有限链环上的图论方法和代数方法

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-10 DOI: 10.1007/s10623-025-01636-6

Makhan Maji, Sihem Mesnager, Santanu Sarkar, Kalyan Hansda

{"title":"Characterizations for minimal codes: graph theory approach and algebraic approach over finite chain rings","authors":"Makhan Maji, Sihem Mesnager, Santanu Sarkar, Kalyan Hansda","doi":"10.1007/s10623-025-01636-6","DOIUrl":"https://doi.org/10.1007/s10623-025-01636-6","url":null,"abstract":"The concept of minimal linear codes was introduced by Ashikhmin and Barg in 1998, leading to the development of various methods for constructing these codes over finite fields. In this context, minimality is defined as a codeword u in a linear code (mathcal {C}) is considered minimal if u covers the codeword cu for all c in the finite field (mathbb {F}_{q}) of order q but no other codewords in (mathcal {C}). A linear code (mathcal {C}) is said to be minimal if each of its codewords is minimal. Minimal codewords are widely used in decoding linear codes, secret sharing schemes, secure two-party computations, cryptography, and other areas such as combinatorics. They have also facilitated the exploration of codes and research codes over finite commutative rings, which are considered appropriate alphabets for coding theory. Extending the minimality property from finite fields to rings and developing such codes poses significant challenges but presents opportunities for advancing coding theory in the context of finite rings. Firstly, the aim is to create graphs that produce a linear minimal (or nearly minimal) code through their adjacency, and examples will be offered for explicit illustrations. Secondly, there is an investigation of codes over rings generated by minimal codewords and an exploration of related minimal codes over finite chain rings. More specifically, a basis (mathcal {C}) is constructed so that every codeword is minimal. To this end, a linear transformation of (mathcal {C}) with this basis is built, and sufficient and necessary minimal linear codes over finite chain rings are provided. Then, there is a new design of minimality conditions over finite principal ideal rings.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"145 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143932686","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

Trace representation of a family of generalized cyclotomic binary sequences with period $$p^n$$ 一类具有周期的广义分环二值序列的迹表示 $$p^n$$

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-07 DOI: 10.1007/s10623-025-01638-4

Zibi Xiao, Yaya Ye, Zhiye Yang, Xiangyong Zeng

引用次数: 0

Avoiding trusted setup in isogeny-based commitments 在基于等基因的承诺中避免可信设置

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-02 DOI: 10.1007/s10623-025-01633-9

Gustave Tchoffo Saah, Tako Boris Fouotsa, Emmanuel Fouotsa, Célestin Nkuimi-Jugnia

{"title":"Avoiding trusted setup in isogeny-based commitments","authors":"Gustave Tchoffo Saah, Tako Boris Fouotsa, Emmanuel Fouotsa, Célestin Nkuimi-Jugnia","doi":"10.1007/s10623-025-01633-9","DOIUrl":"https://doi.org/10.1007/s10623-025-01633-9","url":null,"abstract":"In 2021, Sterner proposed a commitment scheme based on supersingular isogenies. For this scheme to be binding, one relies on a trusted party to generate a starting supersingular elliptic curve of unknown endomorphism ring. In fact, the knowledge of the endomorphism ring allows one to compute an endomorphism of degree a power of a given small prime. Such an endomorphism can then be split into two to obtain two different messages with the same commitment. This is the reason why one needs a curve of unknown endomorphism ring, and the only known way to generate such supersingular curves is to rely on a trusted party or on some expensive multiparty computation. We observe that if the degree of the endomorphism in play is well chosen, then the knowledge of the endomorphism ring is not sufficient to efficiently compute such an endomorphism and in some particular cases, one can even prove that endomorphism of a certain degree do not exist. Leveraging these observations, we adapt Sterner’s commitment scheme in such a way that the endomorphism ring of the starting curve can be known and public. This allows us to obtain isogeny-based commitment schemes which can be instantiated without trusted setup requirements.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"51 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898087","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