Applicable Algebra in Engineering Communication and Computing最新文献_第7页

MWS and FWS codes for coordinate-wise weight functions 坐标加权函数的MWS和FWS代码

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-19 DOI: 10.1007/s00200-023-00608-4

Tim Alderson, Benjamin Morine

{"title":"MWS and FWS codes for coordinate-wise weight functions","authors":"Tim Alderson, Benjamin Morine","doi":"10.1007/s00200-023-00608-4","DOIUrl":"10.1007/s00200-023-00608-4","url":null,"abstract":"<div>A combinatorial problem concerning the maximum size of the (Hamming) weight set of an ([n,k]_q) linear code was recently introduced. Codes attaining the established upper bound are the Maximum Weight Spectrum (MWS) codes. Those ([n,k]_q) codes with the same weight set as (mathbb {F}_q^n) are called Full Weight Spectrum (FWS) codes. FWS codes are necessarily “short”, whereas MWS codes are necessarily “long”. For fixed k, q the values of n for which an ([n,k]_q)-FWS code exists are completely determined, but the determination of the minimum length M(H, k, q) of an ([n,k]_q)-MWS code remains an open problem. The current work broadens discussion first to general coordinate-wise weight functions, and then specifically to the Lee weight and a Manhattan like weight. In the general case we provide bounds on n for which an FWS code exists, and bounds on n for which an MWS code exists. When specializing to the Lee or to the Manhattan setting we are able to completely determine the parameters of FWS codes. As with the Hamming case, we are able to provide an upper bound on (M({mathscr {L}},k,q)) (the minimum length of Lee MWS codes), and pose the determination of (M({mathscr {L}},k,q)) as an open problem. On the other hand, with respect to the Manhattan weight we completely determine the parameters of MWS codes.</div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"367 - 385"},"PeriodicalIF":0.6,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135576353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Correction: Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes 更正：通过重复根循环码的扭转度确定最小符号对和 RT 权重

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-17 DOI: 10.1007/s00200-023-00609-3

Boran Kim

引用次数: 0

The paint pot problem and common multiples in monoids 油漆罐问题和一元群的公倍数

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-13 DOI: 10.1007/s00200-023-00606-6

Hans Zantema, Vincent van Oostrom

引用次数: 0

More classes of optimal quinary cyclic codes of form ({mathcal {C}}_{(1,e,s)}) 更多类形式为$$｛mathcal｛C｝｝_｛（1，e，s）｝的最优五元循环码$$

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-13 DOI: 10.1007/s00200-023-00604-8

Yan Liu, Xiwang Cao, Zhengbang Zha

引用次数: 0

A discrete SIS-model built on the strictly positive scheme 基于严格正格式的离散SIS模型

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-09 DOI: 10.1007/s00200-023-00607-5

Marcin Choiński

引用次数: 0

Fourteen years of cube attacks 立方体攻击14年

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-04 DOI: 10.1007/s00200-023-00602-w

Marco Cianfriglia, Elia Onofri, Silvia Onofri, Marco Pedicini

{"title":"Fourteen years of cube attacks","authors":"Marco Cianfriglia, Elia Onofri, Silvia Onofri, Marco Pedicini","doi":"10.1007/s00200-023-00602-w","DOIUrl":"10.1007/s00200-023-00602-w","url":null,"abstract":"<div>Algebraic Cryptanalysis is a widely used technique that tackles the problem of breaking ciphers mainly relying on the ability to express a cryptosystem as a solvable polynomial system. Each output bit/word can be expressed as a polynomial equation in the cipher’s inputs—namely the key and the plaintext or the initialisation vector bits/words. A part of research in this area consists in finding suitable algebraic structures where polynomial systems can be effectively solved, e.g., by computing Gröbner bases. In 2009, Dinur and Shamir proposed the cube attack, a chosen plaintext algebraic cryptanalysis technique for the offline acquisition of an equivalent system by means of monomial reduction; interpolation on cubes in the space of variables enables retrieving a linear polynomial system, hence making it exploitable in the online phase to recover the secret key. Since its introduction, this attack has received both many criticisms and endorsements from the crypto community; this work aims at providing, under a unified notation, a complete state-of-the-art review of recent developments by categorising contributions in five classes. We conclude the work with an in-depth description of the kite attack framework, a cipher-independent tool that implements cube attacks on GPUs. Mickey2.0 is adopted as a showcase.</div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"285 - 325"},"PeriodicalIF":0.6,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00602-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45636548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes 通过重根循环码的扭转度确定最小符号对和RT权值

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-04-26 DOI: 10.1007/s00200-023-00605-7

Boran Kim

引用次数: 0

Computing the (forcing) strong metric dimension in strongly annihilating-ideal graphs 强湮灭理想图中强度量维数的计算

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-04-22 DOI: 10.1007/s00200-023-00601-x

M. Pazoki, R. Nikandish

引用次数: 0

Using algebraic geometry to reconstruct a darboux cyclide from a calibrated camera picture 利用代数几何从校准的相机图像重建达布克斯自行车

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-03-07 DOI: 10.1007/s00200-023-00600-y

E. Hoxhaj, J. M. Menjanahary, J. Schicho

引用次数: 0

The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications 作为多元二次型密码系统的Legendre伪随机函数:安全性及应用

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-03-01 DOI: 10.1007/s00200-023-00599-2

István András Seres, Máté Horváth, Péter Burcsi

{"title":"The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications","authors":"István András Seres, Máté Horváth, Péter Burcsi","doi":"10.1007/s00200-023-00599-2","DOIUrl":"10.1007/s00200-023-00599-2","url":null,"abstract":"<div>Sequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators were proposed for cryptographic use in 1988. Major interest has been shown towards pseudorandom functions (PRF) recently, based on the Legendre and power residue symbols, due to their efficiency in the multi-party setting. The security of these PRFs is not known to be reducible to standard cryptographic assumptions. In this work, we show that key-recovery attacks against the Legendre PRF are equivalent to solving a specific family of multivariate quadratic (MQ) equation system over a finite prime field. This new perspective sheds some light on the complexity of key-recovery attacks against the Legendre PRF. We conduct algebraic cryptanalysis on the resulting MQ instance. We show that the currently known techniques and attacks fall short in solving these sparse quadratic equation systems. Furthermore, we build novel cryptographic applications of the Legendre PRF, e.g., verifiable random function and (verifiable) oblivious (programmable) PRFs.</div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"223 - 253"},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00599-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82265861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0