Designs, Codes and Cryptography最新文献_第6页

A class of ternary codes with few weights 一类少权值的三元码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-06 DOI: 10.1007/s10623-025-01605-z

Kaimin Cheng

{"title":"A class of ternary codes with few weights","authors":"Kaimin Cheng","doi":"10.1007/s10623-025-01605-z","DOIUrl":"https://doi.org/10.1007/s10623-025-01605-z","url":null,"abstract":"Let (ell ^m) be a power with (ell ) a prime greater than 3 and (m) a positive integer such that 3 is a primitive root modulo (2ell ^m). Let (mathbb {F}_3) be the finite field of order 3, and let (mathbb {F}) be the (ell ^{m-1}(ell -1))-th extension field of (mathbb {F}_3). Denote by (text {Tr}) the absolute trace map from (mathbb {F}) to (mathbb {F}_3). For any (alpha in mathbb {F}_3) and (beta in mathbb {F}), let (D) be the set of nonzero solutions in (mathbb {F}) to the equation (text {Tr}(x^{frac{q-1}{2ell ^m}} + beta x) = alpha ). In this paper, we investigate a ternary code (mathcal {C}) of length (n), defined by (mathcal {C}:= {(text {Tr}(d_1x), text {Tr}(d_2x), dots , text {Tr}(d_nx)): x in mathbb {F}}) when we rewrite (D = {d_1, d_2, dots , d_n}). Using recent results on explicit evaluations of exponential sums, the Weil bound, and combinatorial techniques, we determine the Hamming weight distribution of the code (mathcal {C}). Furthermore, we show that when (alpha = beta = 0), the dual code of (mathcal {C}) is optimal with respect to the Hamming bound.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"17 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143569770","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 class of triple-twisted GRS codes 一类三绞GRS码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-05 DOI: 10.1007/s10623-025-01595-y

Kapish Chand Meena, Piyush Pachauri, Ambrish Awasthi, Maheshanand Bhaintwal

引用次数: 0

Constructing k-ary orientable sequences with asymptotically optimal length 构造长度渐近最优的k元可定向序列

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-28 DOI: 10.1007/s10623-025-01581-4

Daniel Gabrić, Joe Sawada

{"title":"Constructing k-ary orientable sequences with asymptotically optimal length","authors":"Daniel Gabrić, Joe Sawada","doi":"10.1007/s10623-025-01581-4","DOIUrl":"https://doi.org/10.1007/s10623-025-01581-4","url":null,"abstract":"An orientable sequence of order n over an alphabet({0,1,ldots , k{-}1}) is a cyclic sequence such that each length-n substring appears at most once in either direction. When (k= 2), efficient algorithms are known to construct binary orientable sequences, with asymptotically optimal length, by applying the classic cycle-joining technique. The key to the construction is the definition of a parent rule to construct a cycle-joining tree of asymmetric bracelets. Unfortunately, the parent rule does not generalize to larger alphabets. Furthermore, unlike the binary case, a cycle-joining tree does not immediately lead to a simple successor-rule when (k ge 3) unless the tree has certain properties. In this paper, we derive a parent rule to derive a cycle-joining tree of k-ary asymmetric bracelets. This leads to a successor rule that constructs asymptotically optimal k-ary orientable sequences in O(n) time per symbol using O(n) space. In the special case when (n=2), we provide a simple construction of k-ary orientable sequences of maximal length.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"28 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143518771","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

Meet-in-the-middle attack on round-reduced SCARF under single pair-of-tweaks setting 在单对调整设置下，对圆形缩小围巾进行中路攻击

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-27 DOI: 10.1007/s10623-025-01596-x

Siwei Chen, Kai Hu, Guozhen Liu, Zhongfeng Niu, Quan Quan Tan, Shichang Wang

{"title":"Meet-in-the-middle attack on round-reduced SCARF under single pair-of-tweaks setting","authors":"Siwei Chen, Kai Hu, Guozhen Liu, Zhongfeng Niu, Quan Quan Tan, Shichang Wang","doi":"10.1007/s10623-025-01596-x","DOIUrl":"https://doi.org/10.1007/s10623-025-01596-x","url":null,"abstract":"SCARF, an ultra low-latency tweakable block cipher, is the first cipher designed for cache randomization. The block cipher design is significantly different from other common tweakable block ciphers; with a block size of only 10 bits, and yet the input key size is a whopping 240 bits. Notably, the majority of the round key in its round function is absorbed into the data path through AND operations, rather than the typical XOR operations. In this paper, we present a key-recovery attack on a round-reduced version of SCARF with 4 + 4 rounds under the single pair-of-tweaks setting. Our attack is essentially a Meet-in-the-Middle (MitM) attack, where the matching phase is represented by a system of linear equations. Unlike the cryptanalysis conducted by the designers, our attack is effective under both security requirements they have outlined. The data complexity of our attack is (2^{10}) plaintexts, with a time complexity of approximately (2^{60.63}) 4-round of SCARF encryptions. It is important to note that our attack does not threaten the overall security of SCARF.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"38 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507255","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 new family of AMDS symbol-pair constacyclic codes of length $$textbf{4p}$$ and symbol-pair distance $$textbf{9}$$ 一个新的AMDS符号对恒环码族，其长度为$$textbf{4p}$$，符号对距离为0 $$textbf{9}$$

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-27 DOI: 10.1007/s10623-025-01600-4

Hai Q. Dinh, Hieu V. Ha, Bac T. Nguyen, Thieu N. Vo

引用次数: 0

Introducing locality in some generalized AG codes 介绍了一些广义AG码的局部性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-24 DOI: 10.1007/s10623-025-01597-w

Bastien Pacifico

引用次数: 0

Bounds and constructions of optimal symbol-pair codes with constant pair-weight 恒权最优符号对码的界与构造

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-22 DOI: 10.1007/s10623-025-01598-9

Mengzhen Zhao, Yanxun Chang

引用次数: 0

Optimal two-dimensional multilength optical orthogonal codes via compatible mixed difference packing set systems 基于兼容混合差分包装集系统的最优二维多长度光正交码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-18 DOI: 10.1007/s10623-025-01587-y

Hengming Zhao, Rongcun Qin, Minquan Cheng, Dianhua Wu

引用次数: 0

A note on the Walsh spectrum of the Flystel 关于弗里斯特尔的沃尔什谱

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-15 DOI: 10.1007/s10623-025-01589-w

Matthias Johann Steiner

{"title":"A note on the Walsh spectrum of the Flystel","authors":"Matthias Johann Steiner","doi":"10.1007/s10623-025-01589-w","DOIUrl":"https://doi.org/10.1007/s10623-025-01589-w","url":null,"abstract":"Anemoi is a family of compression and hash functions over finite fields (mathbb {F}_q) for efficient Zero-Knowledge applications. Its round function is based on a novel permutation (mathcal {H}: mathbb {F}_q^2 rightarrow mathbb {F}_q^2), called the open Flystel, which is parametrized by a permutation (E: mathbb {F}_q rightarrow mathbb {F}_q) and two functions (Q_gamma , Q_delta : mathbb {F}_q rightarrow mathbb {F}_q). Over a prime field (mathbb {F}_p) with E a power permutation and (Q_gamma ), (Q_delta ) quadratic functions with identical leading coefficient, the Anemoi designers conjectured for the absolute value of the Walsh transform that (max _{textbf{a} in mathbb {F}_p^2, textbf{b} in mathbb {F}_p^2 {setminus } { textbf{0} }} left| mathcal {W}_mathcal {H} (psi , textbf{a}, textbf{b}) right| le p cdot log left( p right) ). By exploiting that the open Flystel is CCZ-equivalent to the closed Flystel, we prove in this note that (max _{textbf{a} in mathbb {F}_p^2, textbf{b} in mathbb {F}_p^2 {setminus } { textbf{0} }} left| mathcal {W}_mathcal {H} (psi , textbf{a}, textbf{b}) right| le (d - 1) cdot p), where (d = deg left( E right) ).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418515","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 generalized construction of variable-length non-overlapping codes 变长非重叠码的一种广义构造

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-02-15 DOI: 10.1007/s10623-025-01585-0

Chunyan Qin, Gaojun Luo

引用次数: 0