Applicable Algebra in Engineering Communication and Computing最新文献

{"title":"Computing the (forcing) strong metric dimension in strongly annihilating-ideal graphs","authors":"M. Pazoki,&nbsp;R. Nikandish","doi":"10.1007/s00200-023-00601-x","DOIUrl":"10.1007/s00200-023-00601-x","url":null,"abstract":"<div><p>The strongly annihilating-ideal graph <span>(textrm{SAG}(R))</span> of a commutative unital ring <i>R</i> is a simple graph whose vertices are non-zero ideals of <i>R</i> with non-zero annihilator and there exists an edge between two distinct vertices if and only if each of them has a non-zero intersection with annihilator of the other one. In this paper, we compute twin-free clique number of <span>(textrm{SAG}(R))</span> and as an application strong metric dimension of <span>(textrm{SAG}(R))</span> is given. Moreover, we investigate the structures of strong resolving sets in <span>(textrm{SAG}(R))</span> to find forcing strong metric dimension in <span>(textrm{SAG}(R))</span>.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"273 - 283"},"PeriodicalIF":0.6,"publicationDate":"2023-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00601-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42668152","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}

{"title":"Using algebraic geometry to reconstruct a darboux cyclide from a calibrated camera picture","authors":"E. Hoxhaj,&nbsp;J. M. Menjanahary,&nbsp;J. Schicho","doi":"10.1007/s00200-023-00600-y","DOIUrl":"10.1007/s00200-023-00600-y","url":null,"abstract":"<div><p>The task of recognizing an algebraic surface from a single apparent contour can be reduced to the recovering of a homogeneous equation in four variables from its discriminant. In this paper, we use the fact that Darboux cyclides have a singularity along the absolute conic in order to recognize them up to Euclidean similarity transformations.\u0000</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"255 - 271"},"PeriodicalIF":0.6,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00600-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42691999","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}

{"title":"The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications","authors":"István András Seres,&nbsp;Máté Horváth,&nbsp;Péter Burcsi","doi":"10.1007/s00200-023-00599-2","DOIUrl":"10.1007/s00200-023-00599-2","url":null,"abstract":"<div><p>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.</p></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}

{"title":"Algebraic and SAT models for SCA generation","authors":"Marlene Koelbing,&nbsp;Bernhard Garn,&nbsp;Enrico Iurlano,&nbsp;Ilias S. Kotsireas,&nbsp;Dimitris E. Simos","doi":"10.1007/s00200-023-00597-4","DOIUrl":"10.1007/s00200-023-00597-4","url":null,"abstract":"<div><p>In this paper, we compute sequence covering arrays (SCAs), which are arrays, consisting of sequences, such that all subsequences with pairwise different entries of some length are covered, via a novel approach based on commutative algebra and symbolic computation. Hereby, we provide various algebraic models being capable to characterize possibly small sets of permutations collectively containing particular shorter subsequences. These models take the form of multivariate polynomial systems of equations and are then processed via supercomputing by a Gröbner Basis solver in order to compute solutions from them. If the variety is not empty, i.e. the Gröbner basis is non-trivial, then each point in the computed variety can be transformed to a SCA. In our experiments, we observed varying computational performance depending on the chosen model, while all of them exhibited scalability issues. Additionally and for comparison, we give new SAT descriptions modelling SCAs. By employing a SAT solver on our provided SAT models, we are able to provide upper bounds, one of which is best among literature results. Lastly, we adapt our SAT approach to answer a question posed by Yuster (Des Codes Cryptogr 88(3):585–593, 2020). As a result, we find a characterization of the dimensions of all perfect SCAs with coverage multiplicity two of strength three.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"173 - 222"},"PeriodicalIF":0.6,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00597-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48363389","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}

{"title":"x-superoptimal pairings on elliptic curves with odd prime embedding degrees: BW13-P310 and BW19-P286","authors":"Emmanuel Fouotsa,&nbsp;Laurian Azebaze Guimagang,&nbsp;Raoul Ayissi","doi":"10.1007/s00200-023-00596-5","DOIUrl":"10.1007/s00200-023-00596-5","url":null,"abstract":"<div><p>The choice of the elliptic curve for a given pairing based protocol is primordial. For many cryptosystems based on pairings such as group signatures and their variants (EPID, anonymous attestation, etc) or accumulators, operations in the first pairing group <span>(mathbb {G})</span> of points of the elliptic curve is more predominant. At 128-bit security level two curves <i>BW</i>13-<i>P</i>310 and <i>BW</i>19-<i>P</i>286 with odd embedding degrees 13 and 19 suitable for super optimal pairing have been recommended for such pairing based protocols. But a prime embedding degree (<span>(k=13;19)</span>) eliminates some important optimisation for the pairing computation. However The Miller loop length of the superoptimal pairing is the half of that of the optimal ate pairing but involve more exponentiations that affect its efficiency. In this work, we successfully develop methods and construct algorithms to efficiently evaluate and avoid heavy exponentiations that affect the efficiency of the superoptimal pairing. This leads to the definition of new bilinear and non degenerate pairing on <i>BW</i>13-<i>P</i>310 and <i>BW</i>19-<i>P</i>286 called <i>x</i>-superoptimal pairing where its Miller loop is about <span>(15.3 %)</span> and <span>(39.8 %)</span> faster than the one of the optimal ate pairing previously computed on <i>BW</i>13-<i>P</i>310 and <i>BW</i>19-<i>P</i>286 respectively.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"153 - 171"},"PeriodicalIF":0.6,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00596-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48519380","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}

{"title":"On the 2-adic complexity of cyclotomic binary sequences of order four","authors":"Fuqing Sun,&nbsp;Qin Yue,&nbsp;Xia Li","doi":"10.1007/s00200-023-00598-3","DOIUrl":"10.1007/s00200-023-00598-3","url":null,"abstract":"<div><p>Let <span>(pequiv 1pmod 4)</span> be a prime. In this paper, we support a new method, i.e., a product of 2-adic values for four binary sequences, to determine the maximum evaluations of the 2-adic complexity in all almost balanced cyclotomic binary sequences of order four with period <span>(N=p)</span>, which are viewed as generalizing the results in Hu (IEEE Trans. Inf. Theory 60:5803–5804, 2014) and Xiong et al. (IEEE Trans. Inf. Theory 60:2399–2406, 2014) without the autocorrelation values of cyclotomic binary sequences of order four with period <i>p</i>. By number theory we obtain two necessary and sufficient conditions about the 2-adic complexity of all balanced cyclotomic binary sequences of order four with period <span>(N=2p)</span> and show the 2-adic complexity of several non-balanced cyclotomic binary sequences of order four with period 2<i>p</i>, which are viewed as generalizing the results in Zhang et al. (IEEE Trans. Inf. Theory 66:4613–4620, 2020).</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"133 - 151"},"PeriodicalIF":0.6,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00598-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49026945","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}

{"title":"Two dimensional double cyclic codes over finite fields","authors":"Niloufar Hajiaghajanpour,&nbsp;Kazem Khashyarmanesh","doi":"10.1007/s00200-023-00595-6","DOIUrl":"10.1007/s00200-023-00595-6","url":null,"abstract":"<div><p>A linear code <i>C</i> of length <span>(n = ru + sv)</span> is a two-dimensional <span>({mathbb {F}})</span>-double cyclic code if the set of coordinates can be partitioned into two arrays, such that any cyclic row-shifts and column-shifts of both arrays of a codeword is also a codeword. In this paper, we examine the algebraic structure of these codes and their dual codes in general. Moreover, we are interested in finding out a generating set for these codes (and their dual codes) in case when <span>(u=2)</span>, <span>(v=4)</span> and char<span>((F) ne 2)</span>.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"107 - 131"},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00595-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49092840","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}

{"title":"Algorithmic counting of nonequivalent compact Huffman codes","authors":"Christian Elsholtz,&nbsp;Clemens Heuberger,&nbsp;Daniel Krenn","doi":"10.1007/s00200-022-00593-0","DOIUrl":"10.1007/s00200-022-00593-0","url":null,"abstract":"<div><p>It is known that the following five counting problems lead to the same integer sequence <span>({f_t}({n}))</span>: </p><ol>\u0000 <li>\u0000 <span>(1)</span>\u0000 \u0000 <p>the number of nonequivalent compact Huffman codes of length <i>n</i> over an alphabet of <i>t</i> letters,</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(2)</span>\u0000 \u0000 <p>the number of “nonequivalent” complete rooted <i>t</i>-ary trees (level-greedy trees) with <i>n</i> leaves,</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(3)</span>\u0000 \u0000 <p>the number of “proper” words (in the sense of Even and Lempel),</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(4)</span>\u0000 \u0000 <p>the number of bounded degree sequences (in the sense of Komlós, Moser, and Nemetz), and</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(5)</span>\u0000 \u0000 <p>the number of ways of writing </p><div><div><span>$$begin{aligned} 1= frac{1}{t^{x_1}}+ dots + frac{1}{t^{x_n}} end{aligned}$$</span></div></div><p> with integers <span>(0 le x_1 le x_2 le dots le x_n)</span>.</p>\u0000 \u0000 </li>\u0000 </ol><p>In this work, we show that one can compute this sequence for <b>all</b> <span>(n&lt;N)</span> with essentially one power series division. In total we need at most <span>(N^{1+varepsilon })</span> additions and multiplications of integers of <i>cN</i> bits (for a positive constant <span>(c&lt;1)</span> depending on <i>t</i> only) or <span>(N^{2+varepsilon })</span> bit operations, respectively, for any <span>(varepsilon &gt;0)</span>. This improves an earlier bound by Even and Lempel who needed <span>({O}({{N^3}}))</span> operations in the integer ring or <span>(O({N^4}))</span> bit operations, respectively.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 6","pages":"887 - 903"},"PeriodicalIF":0.6,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-022-00593-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47254023","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}

{"title":"The automorphism group of projective norm graphs","authors":"Tomas Bayer,&nbsp;Tamás Mészáros,&nbsp;Lajos Rónyai,&nbsp;Tibor Szabó","doi":"10.1007/s00200-022-00590-3","DOIUrl":"10.1007/s00200-022-00590-3","url":null,"abstract":"<div><p>The projective norm graphs are central objects to extremal combinatorics. They appear in a variety of contexts, most importantly they provide tight constructions for the Turán number of complete bipartite graphs <span>(K_{t,s})</span> with <span>(s&gt;(t-1)!)</span>. In this note we deepen their understanding further by determining their automorphism group.\u0000</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 6","pages":"875 - 886"},"PeriodicalIF":0.6,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-022-00590-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45591908","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}

{"title":"Bounds on the maximum nonlinearity of permutations on the rings ({mathbb {Z}}_p) and ({mathbb {Z}}_{2p})","authors":"Prachi Gupta,&nbsp;P. R. Mishra,&nbsp;Atul Gaur","doi":"10.1007/s00200-022-00594-z","DOIUrl":"10.1007/s00200-022-00594-z","url":null,"abstract":"<div><p>In 2016, Y. Kumar et al. in the paper ‘<i>Affine equivalence and non-linearity of permutations over</i> <span>({mathbb {Z}}_n)</span>’ conjectured that: <i>For</i> <span>(nge 3)</span>, <i>the nonlinearity of any permutation on</i> <span>({mathbb {Z}}_n)</span>, <i>the ring of integers modulo</i> <i>n</i>, <i>cannot exceed</i> <span>(n-2)</span>. For an odd prime <i>p</i>, we settle the above conjecture when <span>(n=2p)</span> and for <span>(pequiv 3 pmod {4})</span> we prove the above conjecture with an improved upper bound. Further, we derive a lower bound on <span>(max {mathcal {N}}{mathcal {L}}_n)</span> when <i>n</i> is an odd prime or twice of an odd prime where <span>(max {mathcal {N}}{mathcal {L}}_n)</span> denotes the maximum possible nonlinearity of any permutation on <span>({mathbb {Z}}_n)</span>.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 6","pages":"859 - 874"},"PeriodicalIF":0.6,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49231409","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}