Designs, Codes and Cryptography最新文献_第9页

Hulls of projective Reed–Muller codes 射影里德-穆勒码的船体

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-14 DOI: 10.1007/s10623-024-01543-2

Nathan Kaplan, Jon-Lark Kim

引用次数: 0

On set systems with strongly restricted intersections 在具有强约束交叉口的集合系统上

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-05 DOI: 10.1007/s10623-024-01535-2

Xin Wei, Xiande Zhang, Gennian Ge

{"title":"On set systems with strongly restricted intersections","authors":"Xin Wei, Xiande Zhang, Gennian Ge","doi":"10.1007/s10623-024-01535-2","DOIUrl":"https://doi.org/10.1007/s10623-024-01535-2","url":null,"abstract":"Set systems with strongly restricted intersections, called (alpha )-intersecting families for a vector (alpha ), were introduced recently as a generalization of several well-studied intersecting families including the classical oddtown and eventown. Given a binary vector (alpha =(a_1, ldots , a_k)), a collection ({mathcal {F}}) of subsets over an n element set is an (alpha )-intersecting family modulo 2 if for each (i=1,2,ldots ,k), all i-wise intersections of distinct members in ({mathcal {F}}) have sizes with the same parity as (a_i). Let (f_alpha (n)) denote the maximum size of such a family. In this paper, we study the asymptotic behavior of (f_alpha (n)) when n goes to infinity. We show that if t is the maximum integer such that (a_t=1) and (2tle k), then (f_alpha (n)sim (t! n)^{1/t}). More importantly, we show that for any constant (c>0), as the length k goes larger, (f_alpha (n)) is upper bounded by (O (n^c)) for almost all (alpha ). Equivalently, no matter what k is, there are only finitely many (alpha ) satisfying (f_alpha (n)=Omega (n^c)). This answers an open problem raised by Johnston and O’Neill in 2023. All of our results can be generalized to modulo p setting for any prime p smoothly.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"37 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142776806","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

On 3-dimensional MRD codes of type $$langle X^{q^t},X+delta X^{q^{2t}},G(X) rangle $$ 论型的三维MRD码 $$langle X^{q^t},X+delta X^{q^{2t}},G(X) rangle $$

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-05 DOI: 10.1007/s10623-024-01528-1

Daniele Bartoli, Francesco Ghiandoni

引用次数: 0

Derivative descendants of cyclic codes and constacyclic codes 循环码和恒循环码的派生后代

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01536-1

Li Xu, Cuiling Fan, Chunming Tang, Zhengchun Zhou

引用次数: 0

Codes over $$mathbb {F}_4$$ and $$mathbb {F}_2 times mathbb {F}_2$$ and theta series of the corresponding lattices in quadratic fields 二次域中对应格的$$mathbb {F}_4$$和$$mathbb {F}_2 times mathbb {F}_2$$上的代码和级数

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01537-0

Josline Freed

引用次数: 0

A pair of orthogonal orthomorphisms of finite nilpotent groups 有限幂零群的一对正交正胚

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01540-5

Shikang Yu, Tao Feng, Menglong Zhang

引用次数: 0

Factorization and irreducibility of composed products 合成产物的分解和不可约性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01529-0

Lukas Kölsch, Lucas Krompholz, Gohar Kyureghyan

{"title":"Factorization and irreducibility of composed products","authors":"Lukas Kölsch, Lucas Krompholz, Gohar Kyureghyan","doi":"10.1007/s10623-024-01529-0","DOIUrl":"https://doi.org/10.1007/s10623-024-01529-0","url":null,"abstract":"Brawley and Carlitz introduced diamond products of elements of finite fields and associated composed products of polynomials in 1987. Composed products yield a method to construct irreducible polynomials of large composite degrees from irreducible polynomials of lower degrees. We show that the composed product of two irreducible polynomials of degrees m and n is again irreducible if and only if m and n are coprime and the involved diamond product satisfies a special cancellation property, the so-called conjugate cancellation. This completes the characterization of irreducible composed products, considered in several previous papers. More generally, we give precise criteria when a diamond product satisfies conjugate cancellation. For diamond products defined via bivariate polynomials, we prove simple criteria that characterize when conjugate cancellation holds. We also provide efficient algorithms to check these criteria. We achieve stronger results as well as more efficient algorithms in the case that the polynomials are bilinear. Lastly, we consider possible constructions of normal elements using composed products and the methods we developed.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"3 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142776830","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

On translation hyperovals in semifield planes 半场平面上的平移超卵圆

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01533-4

Kevin Allen, John Sheekey

引用次数: 0

Quantum rectangle attack and its application on Deoxys-BC 量子矩形攻击及其在 Deoxys-BC 上的应用

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-11-21 DOI: 10.1007/s10623-024-01526-3

Yin-Song Xu, Yi-Bo Luo, Zheng Yuan, Xuan Zhou, Qi-di You, Fei Gao, Xiao-Yang Dong

{"title":"Quantum rectangle attack and its application on Deoxys-BC","authors":"Yin-Song Xu, Yi-Bo Luo, Zheng Yuan, Xuan Zhou, Qi-di You, Fei Gao, Xiao-Yang Dong","doi":"10.1007/s10623-024-01526-3","DOIUrl":"https://doi.org/10.1007/s10623-024-01526-3","url":null,"abstract":"In recent years, it has become a popular trend to propose quantum versions of classical attacks. The rectangle attack as a differential attack is widely used in symmetric cryptanalysis and applied on many block ciphers. To improve its efficiency, we propose a new quantum rectangle attack firstly. In rectangle attack, it counts the number of valid quartets for each guessed subkeys and filters out subkey candidates according to the counter. To speed up this procedure, we propose a quantum key counting algorithm based on parallel amplitude estimation algorithm and amplitude amplification algorithm. Then, we complete with the remaining key bits and search the right full key by nested Grover search. Besides, we give a strategy to find a more suitable distinguisher to make the complexity lower. Finally, to evaluate post-quantum security of the tweakable block cipher Deoxys-BC, we perform automatic search for good distinguishers of Deoxys-BC according to the strategy, and then apply our attack on 9/10-round Deoxys-BC-256 and 12/13/14-round Deoxys-BC-384. The results show that our attack has some improvements than classical attacks and Grover search.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142684484","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

Almost tight security in lattices with polynomial moduli—PRF, IBE, all-but-many LTF, and more 多项式模网格中的近乎严密的安全性--PRF、IBE、全但多LTF等

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-11-19 DOI: 10.1007/s10623-024-01523-6

Zhedong Wang, Qiqi Lai, Feng-Hao Liu

{"title":"Almost tight security in lattices with polynomial moduli—PRF, IBE, all-but-many LTF, and more","authors":"Zhedong Wang, Qiqi Lai, Feng-Hao Liu","doi":"10.1007/s10623-024-01523-6","DOIUrl":"https://doi.org/10.1007/s10623-024-01523-6","url":null,"abstract":"Achieving tight security is a fundamental task in cryptography. While one of the most important purposes of this task is to improve the overall efficiency of a construction (by allowing smaller security parameters), many current lattice-based instantiations do not completely achieve the goal. Particularly, a super-polynomial modulus seems to be necessary in all prior work for (almost) tight schemes that allow the adversary to conduct queries, such as PRF, IBE, and Signatures. As the super-polynomial modulus would affect the noise-to-modulus ratio and thus increase the parameters, this might cancel out the advantages (in efficiency) brought from the tighter analysis. To determine the full power of tight security/analysis in lattices, it is necessary to determine whether the super-polynomial modulus restriction is inherent. In this work, we remove the super-polynomial modulus restriction for many important primitives—PRF, IBE, all-but-many Lossy Trapdoor Functions, and Signatures. The crux relies on an improvement over the framework of Boyen and Li (Asiacrypt 16), and an almost tight reduction from LWE to LWR, which improves prior work by Alwen et al. (Eurocrypt 13), Bogdanov et al. (TCC 16), and Bai et al. (Asiacrypt 15). By combining these two advances, we are able to derive these almost tight schemes under LWE with a polynomial modulus.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"10 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142671014","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