Designs, Codes and Cryptography最新文献_第3页

The complete weight enumerator of the square of one-weight irreducible cyclic codes 一权不可约循环码平方的完全权枚举数

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-22 DOI: 10.1007/s10623-025-01620-0

Canze Zhu

引用次数: 0

Limitations of the decoding-to-LPN reduction via code smoothing 通过代码平滑降低解码到lpn的局限性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-22 DOI: 10.1007/s10623-025-01617-9

Madhura Pathegama, Alexander Barg

引用次数: 0

Binary stretch embedding of weighted graphs 加权图的二元拉伸嵌入

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-21 DOI: 10.1007/s10623-025-01608-w

Javad Ebrahimi Boroojeni, Mehri Oghbaei Bonab

{"title":"Binary stretch embedding of weighted graphs","authors":"Javad Ebrahimi Boroojeni, Mehri Oghbaei Bonab","doi":"10.1007/s10623-025-01608-w","DOIUrl":"https://doi.org/10.1007/s10623-025-01608-w","url":null,"abstract":"In this paper, we introduce and study the problem of binary stretch embedding of edge-weighted graphs in both integer and fractional settings. Roughly speaking, the binary stretch embedding problem for a weighted graph G is to find a mapping from the vertex set of G, to the vertices of a hypercube graph such that the distance between every pair of the vertices is not reduced under the mapping, hence the name binary stretch embedding. The minimum dimension of a hypercube for which such a stretch embedding exists is called the binary addressing number of G. We show that the binary addressing number of weighted graphs is the optimum value of an integer program. The optimum value for the corresponding linear relaxation problem is called the fractional binary addressing number of G. This embedding type problem is closely related to the well-known addressing problem of Graham and Pollak and isometric hypercube embedding problem of Firsov. Using tools and techniques such as Hadamard codes and the linear programming theory help us to find upper and lower bounds, approximations, or exact values of the binary addressing number and the fractional variant of graphs. As an application of our results, we derive improved upper bounds or exact values of the maximum size of Lee metric codes of certain parameters.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"41 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666542","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

Additive combinatorial designs 加性组合设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-20 DOI: 10.1007/s10623-025-01594-z

Marco Buratti, Francesca Merola, Anamari Nakić

{"title":"Additive combinatorial designs","authors":"Marco Buratti, Francesca Merola, Anamari Nakić","doi":"10.1007/s10623-025-01594-z","DOIUrl":"https://doi.org/10.1007/s10623-025-01594-z","url":null,"abstract":"A (2-(v, k, lambda )) design is additive if, up to isomorphism, the point set is a subset of an abelian group G and every block is zero-sum. This definition was introduced in Caggegi et al. (J Algebr Comb 45:271-294, 2017) and was the starting point of an interesting new theory. Although many additive designs have been constructed and known designs have been shown to be additive, these structures seem quite hard to construct in general, particularly when we look for additive Steiner 2-designs. One might generalize additive Steiner 2-designs in a natural way to graph decompositions as follows: given a simple graph (Gamma ), an additive ((K_v,Gamma ))-design is a decomposition of the graph (K_v) into subgraphs (blocks) (B_1,dots ,B_t) all isomorphic to (Gamma ), such that the vertex set (V(K_v)) is a subset of an abelian group G, and the sets (V(B_1), dots , V(B_t)) are zero-sum in G. In this work we begin the study of additive ((K_v,Gamma ))-designs: we develop different tools instrumental in constructing these structures, and apply them to obtain some infinite classes of designs and many sporadic examples. We will consider decompositions into various graphs (Gamma ), for instance cycles, paths, and k-matchings. Similar ideas will also allow us to present here a sporadic additive 2-(124, 4, 1) design.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"34 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143661406","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

An attack on p-adic lattice public-key encryption cryptosystems and signature schemes 对 p 演算网格公钥加密密码系统和签名方案的攻击

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-18 DOI: 10.1007/s10623-025-01618-8

Chi Zhang

引用次数: 0

A new framework for fast homomorphic matrix multiplication 一个新的快速同态矩阵乘法框架

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-15 DOI: 10.1007/s10623-025-01614-y

Xiaopeng Zheng, Hongbo Li, Dingkang Wang

引用次数: 0

Resolution of the exceptional APN conjecture in the Gold degree case 金度情况下异常APN猜想的解决

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-14 DOI: 10.1007/s10623-025-01607-x

Carlos Agrinsoni, Heeralal Janwa, Moises Delgado

{"title":"Resolution of the exceptional APN conjecture in the Gold degree case","authors":"Carlos Agrinsoni, Heeralal Janwa, Moises Delgado","doi":"10.1007/s10623-025-01607-x","DOIUrl":"https://doi.org/10.1007/s10623-025-01607-x","url":null,"abstract":"A function (f: {mathbb {F}}_q rightarrow {mathbb {F}}_q), is called an almost perfect nonlinear (APN) if (f(X+a)-f(X) =b) has at most 2 solutions for every (b,a in {mathbb {F}}_q), with a nonzero. Furthermore, it is called an exceptional APN if it is an APN on infinitely many extensions of ({mathbb {F}}_q). These problems are equivalent to finding rational points on the corresponding variety ({mathcal {X}}_f:=phi _f(X,Y,Z)=0). The Lang–Weil, Deligne, and Ghorpade–Lachaud bounds help solve these problems when (phi _f) contains an absolutely irreducible factor in the defining field. The exceptional monomial APN functions had been classified up to CCZ equivalence by Hernando and McGuire (J Algebra 343:78–92, 2011), proving the conjecture of Janwa, Wilson, and McGuire (JMW) (1993, 1995). The main tools used were the computation and classification of the singularities of ({mathcal {X}}_f) and the algorithm of JMW for the absolute irreducibility testing using Bezout’s Theorem. Aubry et al. (2010) conjectured that the only exceptional APN functions of odd degree up to CCZ equivalence are the Gold ((2^k+1)) and the Kasami-Welch ((2^{2k}-2^k+1)) monomial functions. Here, we settle the first case (Theorem 20). We also prove a part of a conjecture on exceptional crooked functions. One of the main tools in our proofs is our new absolute irreducibility criterion (Theorem 9).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"22 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618460","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

Generalized impossible differential attacks on block ciphers: application to SKINNY and ForkSKINNY 分组密码的广义不可能差分攻击：在SKINNY和ForkSKINNY上的应用

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-14 DOI: 10.1007/s10623-025-01611-1

Ling Song, Qinggan Fu, Qianqian Yang, Yin Lv, Lei Hu

{"title":"Generalized impossible differential attacks on block ciphers: application to SKINNY and ForkSKINNY","authors":"Ling Song, Qinggan Fu, Qianqian Yang, Yin Lv, Lei Hu","doi":"10.1007/s10623-025-01611-1","DOIUrl":"https://doi.org/10.1007/s10623-025-01611-1","url":null,"abstract":"Impossible differential cryptanalysis is a crucial cryptanalytical method for symmetric ciphers. Given an impossible differential, the key recovery attack typically proceeds in two steps: generating pairs of data and then identifying wrong keys using the guess-and-filtering method. At CRYPTO 2023, Boura et al. first proposed a new key recovery technique—the differential meet-in-the-middle attack, which recovers the key in a meet-in-the-middle manner. Inspired by this technique, we incorporate the meet-in-the-middle technique into impossible cryptanalysis and propose a generic impossible differential meet-in-the-middle attack (IDMA) framework. We apply IDMA to block ciphers SKINNY, SKINNYe-v2, and ForkSKINNY and achieve remarkably efficient attacks. We improve the impossible differential attack on SKINNY-n-3n by 2 rounds in the single-tweakey setting and 1 round in the related-tweakey setting. For SKINNYe-v2, the impossible differential attacks now can cover 2 more rounds in the related-tweakey setting and the first 23/24/25-round attacks in the single-tweakey model are given. For ForkSKINNY-n-3n, we improve the attacks by 2 rounds in the limited setting specified by the designers and 1 round in relaxed settings. These results confirm that the meet-in-the-middle technique can result in more efficient key recovery, reaching beyond what traditional methods can achieve on certain ciphers.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"183 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618461","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

Galois subcovers of the Hermitian curve in characteristic p with respect to subgroups of order dp with $$dnot =p$$ prime 特征为p的厄米曲线的伽罗瓦子盖关于dp阶具有$$dnot =p$$素数的子群

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-14 DOI: 10.1007/s10623-025-01613-z

Arianna Dionigi, Barbara Gatti

{"title":"Galois subcovers of the Hermitian curve in characteristic p with respect to subgroups of order dp with $$dnot =p$$ prime","authors":"Arianna Dionigi, Barbara Gatti","doi":"10.1007/s10623-025-01613-z","DOIUrl":"https://doi.org/10.1007/s10623-025-01613-z","url":null,"abstract":"A problem of current interest, also motivated by applications to Coding theory, is to find explicit equations for maximal curves, that are projective, geometrically irreducible, non-singular curves defined over a finite field (mathbb {F}_{q^2}) whose number of (mathbb {F}_{q^2})-rational points attains the Hasse-Weil upper bound (q^2+2mathfrak {g}q+1) where (mathfrak {g}) is the genus of the curve (mathcal {X}). For curves which are Galois covered of the Hermitian curve, this has been done so far ad hoc, in particular in the cases where the Galois group has prime order and also when has order the square of the characteristic. In this paper we obtain explicit equations of all Galois covers of the Hermitian curve with Galois group of order dp where p is the characteristic of (mathbb {F}_{q^2}) and d is a prime other than p. We also compute the generators of the Weierstrass semigroup at a special (mathbb {F}_{q^2})-rational point of some of the curves, and discuss some possible positive impacts on the minimum distance problems of AG-codes.\u0000","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"68 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618462","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

Admissible parameters for the Crossbred algorithm and semi-regular sequences over finite fields 有限域上克罗斯比德算法和半规则序列的可容许参数

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-03-11 DOI: 10.1007/s10623-025-01610-2

John Baena, Daniel Cabarcas, Sharwan K. Tiwari, Javier Verbel, Luis Villota

{"title":"Admissible parameters for the Crossbred algorithm and semi-regular sequences over finite fields","authors":"John Baena, Daniel Cabarcas, Sharwan K. Tiwari, Javier Verbel, Luis Villota","doi":"10.1007/s10623-025-01610-2","DOIUrl":"https://doi.org/10.1007/s10623-025-01610-2","url":null,"abstract":"Multivariate public key cryptography (MPKC) is one of the most promising alternatives to build quantum-resistant signature schemes, as evidenced in NIST’s call for additional post-quantum signature schemes. The main assumption in MPKC is the hardness of the Multivariate Quadratic (MQ) problem, which seeks for a common root to a system of quadratic polynomials over a finite field. Although the Crossbred algorithm is among the most efficient algorithms to solve MQ over small fields, its complexity analysis stands on shaky ground. In particular, it is not clear for what parameters it works and under what assumptions. In this work, we provide a rigorous analysis of the Crossbred algorithm over any finite field. We provide a complete explanation of the series of admissible parameters proposed in previous literature and explicitly state the regularity assumptions required for its validity. Moreover, we show that the series does not tell the whole story, hence we propose an additional condition for Crossbred to work. Additionally, we define and characterize a notion of regularity for systems over a small field, which is one of the main building blocks in the series of admissible parameters.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"11 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143599669","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