Pub Date : 2021-10-11DOI: 10.1080/23799927.2022.2114381
D. Bertaccini, Fabio Durastante
Some aspects of nonlocal dynamics on directed and undirected networks for an initial value problem whose Jacobian matrix is a variable-order fractional power of a Laplacian matrix are discussed here. This is a new extension to non-stationary behaviour of a class of non-local phenomena on complex networks for which both directed and undirected graphs are considered. Under appropriate assumptions, the existence, uniqueness, and uniform asymptotic stability of the solutions of the underlying initial value problem are proved. Some examples giving a sample of the behaviour of the dynamics are also included.
{"title":"Nonlocal diffusion of variable order on complex networks","authors":"D. Bertaccini, Fabio Durastante","doi":"10.1080/23799927.2022.2114381","DOIUrl":"https://doi.org/10.1080/23799927.2022.2114381","url":null,"abstract":"Some aspects of nonlocal dynamics on directed and undirected networks for an initial value problem whose Jacobian matrix is a variable-order fractional power of a Laplacian matrix are discussed here. This is a new extension to non-stationary behaviour of a class of non-local phenomena on complex networks for which both directed and undirected graphs are considered. Under appropriate assumptions, the existence, uniqueness, and uniform asymptotic stability of the solutions of the underlying initial value problem are proved. Some examples giving a sample of the behaviour of the dynamics are also included.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90096876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-02DOI: 10.1080/23799927.2021.2018115
Samuel Dobson, S. Galbraith, Jason Legrow, Y. Ti, Lukas Zobernig
We present a polynomial-time adaptive attack on the 2-SIDH protocol. The 2-SIDH protocol is a special instance of the countermeasure proposed by Azarderakhsh, Jao and Leonardi to perform isogeny-based key exchange with static keys in the presence of an adaptive attack. This countermeasure has also been recently explicitly proposed by Kayacan. Our attack extends the adaptive attack by Galbraith, Petit, Shani and Ti (GPST) to recover a static secret key using malformed points. The extension of GPST is non-trivial and requires learning additional information. In particular, the attack needs to recover intermediate elliptic curves in the isogeny path, and points on them. We also discuss how to extend the attack to k-SIDH when k>2 and explain that the attack complexity is exponential in k.
{"title":"An adaptive attack on 2-SIDH","authors":"Samuel Dobson, S. Galbraith, Jason Legrow, Y. Ti, Lukas Zobernig","doi":"10.1080/23799927.2021.2018115","DOIUrl":"https://doi.org/10.1080/23799927.2021.2018115","url":null,"abstract":"We present a polynomial-time adaptive attack on the 2-SIDH protocol. The 2-SIDH protocol is a special instance of the countermeasure proposed by Azarderakhsh, Jao and Leonardi to perform isogeny-based key exchange with static keys in the presence of an adaptive attack. This countermeasure has also been recently explicitly proposed by Kayacan. Our attack extends the adaptive attack by Galbraith, Petit, Shani and Ti (GPST) to recover a static secret key using malformed points. The extension of GPST is non-trivial and requires learning additional information. In particular, the attack needs to recover intermediate elliptic curves in the isogeny path, and points on them. We also discuss how to extend the attack to k-SIDH when k>2 and explain that the attack complexity is exponential in k.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79812674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-02DOI: 10.1080/23799927.2021.1988714
Delaram Kahrobaei, V. Shpilrain
The purpose of this short paper is to explain the difference between encrypting real-life data and encrypting elements with a ring structure in the context of fully homomorphic encryption (FHE). Specifically, our encryption of real-life data is in two stages. First, we use a private-key embedding of real-life data in a ring; this embedding does not have to be fully homomorphic. This private embedding, speaking informally, takes most of the security burden off the second part of our encryption procedure, namely FHE between rings. The whole encryption function is then not fully homomorphic, but we show that it still provides for the most popular functionalities one expects from FHE, including private search on encrypted data.
{"title":"A note on fully homomorphic encryption of real-life data","authors":"Delaram Kahrobaei, V. Shpilrain","doi":"10.1080/23799927.2021.1988714","DOIUrl":"https://doi.org/10.1080/23799927.2021.1988714","url":null,"abstract":"The purpose of this short paper is to explain the difference between encrypting real-life data and encrypting elements with a ring structure in the context of fully homomorphic encryption (FHE). Specifically, our encryption of real-life data is in two stages. First, we use a private-key embedding of real-life data in a ring; this embedding does not have to be fully homomorphic. This private embedding, speaking informally, takes most of the security burden off the second part of our encryption procedure, namely FHE between rings. The whole encryption function is then not fully homomorphic, but we show that it still provides for the most popular functionalities one expects from FHE, including private search on encrypted data.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85394880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-19DOI: 10.1080/23799927.2021.1974568
A. Santhakumaran, M. Mahendran, F. Simon Raj, K. Ganesamoorthy
For a connected graph G of order n, a total open monophonic set S of vertices in a graph G is a minimal total open monophonic set if no proper subset of S is a total open monophonic set of G. The upper total open monophonic number of G is the maximum cardinality of a minimal total open monophonic set of G. Certain general properties regarding minimal total open monophonic sets are discussed, and also the upper total open monophonic numbers of certain standard graphs are determined. It is proved that for the Petersen graph G. For integers n and a with , , it is shown that there exists a connected graph G of order n with , and .
{"title":"Minimal total open monophonic sets in graphs","authors":"A. Santhakumaran, M. Mahendran, F. Simon Raj, K. Ganesamoorthy","doi":"10.1080/23799927.2021.1974568","DOIUrl":"https://doi.org/10.1080/23799927.2021.1974568","url":null,"abstract":"For a connected graph G of order n, a total open monophonic set S of vertices in a graph G is a minimal total open monophonic set if no proper subset of S is a total open monophonic set of G. The upper total open monophonic number of G is the maximum cardinality of a minimal total open monophonic set of G. Certain general properties regarding minimal total open monophonic sets are discussed, and also the upper total open monophonic numbers of certain standard graphs are determined. It is proved that for the Petersen graph G. For integers n and a with , , it is shown that there exists a connected graph G of order n with , and .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86836526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-12DOI: 10.1080/23799927.2021.1974569
Rafik Aguech, Sudip Bose, H. Mahmoud, Yi Zhang
Exponential recursive trees and exponential PORTs are introduced in H. Mahmoud (Profile of random exponential recursive trees. Methodology and Computing in Applied Probability (accepted) 2021). In that reference, the author investigates the order and node profile of these species. Several other equally important properties remain to be explored. The aim of the present manuscript is to establish fundamental properties concerning leaves (and their profile level by level) and distances in these trees. Some results fall back on the order of a tree. For the number of leaves in both flavours, we find (under appropriate scaling for each) a limit distribution uniquely characterized by inductively constructed moments. We find an limit for the scaled total (external) path length in an exponential recursive tree (PORT) in terms of the known distribution of the scaled order given in Mahmoud [11]. These total path lengths are indicative of the depth of a randomly chosen node (external node) in an exponential recursive tree (PORT).
{"title":"Some properties of exponential trees","authors":"Rafik Aguech, Sudip Bose, H. Mahmoud, Yi Zhang","doi":"10.1080/23799927.2021.1974569","DOIUrl":"https://doi.org/10.1080/23799927.2021.1974569","url":null,"abstract":"Exponential recursive trees and exponential PORTs are introduced in H. Mahmoud (Profile of random exponential recursive trees. Methodology and Computing in Applied Probability (accepted) 2021). In that reference, the author investigates the order and node profile of these species. Several other equally important properties remain to be explored. The aim of the present manuscript is to establish fundamental properties concerning leaves (and their profile level by level) and distances in these trees. Some results fall back on the order of a tree. For the number of leaves in both flavours, we find (under appropriate scaling for each) a limit distribution uniquely characterized by inductively constructed moments. We find an limit for the scaled total (external) path length in an exponential recursive tree (PORT) in terms of the known distribution of the scaled order given in Mahmoud [11]. These total path lengths are indicative of the depth of a randomly chosen node (external node) in an exponential recursive tree (PORT).","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78166421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-12DOI: 10.1080/23799927.2021.1974567
F. Soliemany, M. Ghasemi, R. Varmazyar
Let and be two graphs. The Kronecker product has vertex set and the edge set In this paper we show that if is a complete multipartite graph, where the parameters satisfying certain conditions and is a path of length n−1, then is not super i-connected, where and . Also we show that is not super connected, where is a cycle of length n and .
{"title":"Super connectivity of a family of direct product graphs","authors":"F. Soliemany, M. Ghasemi, R. Varmazyar","doi":"10.1080/23799927.2021.1974567","DOIUrl":"https://doi.org/10.1080/23799927.2021.1974567","url":null,"abstract":"Let and be two graphs. The Kronecker product has vertex set and the edge set In this paper we show that if is a complete multipartite graph, where the parameters satisfying certain conditions and is a path of length n−1, then is not super i-connected, where and . Also we show that is not super connected, where is a cycle of length n and .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73084953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-03DOI: 10.1080/23799927.2021.1969432
S. Minkevičius, L. Sakalauskas
The purpose of this research in the field of the open queueing network is to prove the Law of the Iterated Logarithm (LIL) for the extreme value of the queue length of customers in an open queueing network. LIL is proved for the extreme values of the queue length of customers the important probability characteristic of the queueing system under conditions of heavy traffic. Also, we present for extreme queue length of jobs Probability Laws ((theorems on the LIL, Fluid Limits Theorem and Diffusion Limit Theorem) in various conditions of traffic and simulating an open queueing network in Appendices 1 and 2.
{"title":"On the law of iterated logarithm for extreme queue length in an open queueing network","authors":"S. Minkevičius, L. Sakalauskas","doi":"10.1080/23799927.2021.1969432","DOIUrl":"https://doi.org/10.1080/23799927.2021.1969432","url":null,"abstract":"The purpose of this research in the field of the open queueing network is to prove the Law of the Iterated Logarithm (LIL) for the extreme value of the queue length of customers in an open queueing network. LIL is proved for the extreme values of the queue length of customers the important probability characteristic of the queueing system under conditions of heavy traffic. Also, we present for extreme queue length of jobs Probability Laws ((theorems on the LIL, Fluid Limits Theorem and Diffusion Limit Theorem) in various conditions of traffic and simulating an open queueing network in Appendices 1 and 2.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78633670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-03DOI: 10.1080/23799927.2021.1963999
R. Mary, N. Parthiban, I. Rajasingh, P. Manuel
Graph is a mathematical model represented by points and lines joining certain pairs of points. These points are addressed as vertices or nodes and the lines are addressed as edges or links. Graph embedding is a mapping of guest graph G into host graph H satisfying certain conditions. Embedding has been studied for many networks in the literature. The Recursive Circulant has several attractive topological properties. Though the embedding of parallel architectures such as Hypercubes and Mesh into Recursive Circulant has been studied, the embedding of Recursive Circulant into other architectures has not been taken up so far. In this paper, we compute the wirelength of embedding even into paths (MinLA), 1-rooted complete binary trees, regular caterpillars and ladders.
{"title":"Optimal layout of recursive circulant graphs","authors":"R. Mary, N. Parthiban, I. Rajasingh, P. Manuel","doi":"10.1080/23799927.2021.1963999","DOIUrl":"https://doi.org/10.1080/23799927.2021.1963999","url":null,"abstract":"Graph is a mathematical model represented by points and lines joining certain pairs of points. These points are addressed as vertices or nodes and the lines are addressed as edges or links. Graph embedding is a mapping of guest graph G into host graph H satisfying certain conditions. Embedding has been studied for many networks in the literature. The Recursive Circulant has several attractive topological properties. Though the embedding of parallel architectures such as Hypercubes and Mesh into Recursive Circulant has been studied, the embedding of Recursive Circulant into other architectures has not been taken up so far. In this paper, we compute the wirelength of embedding even into paths (MinLA), 1-rooted complete binary trees, regular caterpillars and ladders.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83179034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-15DOI: 10.1080/23799927.2021.1942991
Khadija Achkoun, Charifa Hanin, Anas Sadak, Fatima Ezzahra Ziani, F. Omary
In this article, an enhanced version of SPF is presented. SPF is a previously developed cellular automata-based block cipher that combines Substitution-Permutation Networks (SPN) with a Feistel scheme using key-dependent S-boxes. SPF system has satisfying cryptographic properties against attacks. However, the rule 30 used in the Feistel round function was subject to an attack by Meier and Staffelbach (MS-attack). In order to avoid this attack, a new construction of SPF, namely SPF-CA 1.2, is proposed using a new ruleset combining linear and non-linear rules. In addition, a robust and fast key scheduling algorithm is employed to improve key efficiency. Moreover, the number of rounds has been reduced while conserving the high confusion and diffusion properties of the previous version. A thorough security analysis reveals the efficiency and robustness of the proposed construction.
本文提出了一种增强版本的SPF。SPF是先前开发的基于元胞自动机的分组密码，它将替换置换网络(SPN)与使用依赖密钥的s盒的Feistel方案结合在一起。SPF系统具有良好的抗攻击加密性能。然而，在Feistel回合函数中使用的规则30受到了Meier和Staffelbach的攻击(MS-attack)。为了避免这种攻击，本文提出了一种新的SPF结构SPF- ca 1.2，使用线性和非线性规则相结合的新规则集。此外，采用了鲁棒快速的密钥调度算法来提高密钥效率。此外，减少了弹数，同时保留了前一版本的高混淆和扩散特性。全面的安全性分析揭示了所提出的结构的效率和鲁棒性。
{"title":"SPF-CA-1.2: an enhanced version of cellular automata-based block cipher system","authors":"Khadija Achkoun, Charifa Hanin, Anas Sadak, Fatima Ezzahra Ziani, F. Omary","doi":"10.1080/23799927.2021.1942991","DOIUrl":"https://doi.org/10.1080/23799927.2021.1942991","url":null,"abstract":"In this article, an enhanced version of SPF is presented. SPF is a previously developed cellular automata-based block cipher that combines Substitution-Permutation Networks (SPN) with a Feistel scheme using key-dependent S-boxes. SPF system has satisfying cryptographic properties against attacks. However, the rule 30 used in the Feistel round function was subject to an attack by Meier and Staffelbach (MS-attack). In order to avoid this attack, a new construction of SPF, namely SPF-CA 1.2, is proposed using a new ruleset combining linear and non-linear rules. In addition, a robust and fast key scheduling algorithm is employed to improve key efficiency. Moreover, the number of rounds has been reduced while conserving the high confusion and diffusion properties of the previous version. A thorough security analysis reveals the efficiency and robustness of the proposed construction.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82295334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-14DOI: 10.1080/23799927.2021.1934900
Ke Wang, Jiannan Zhou, Dong He, Qin Tong
For bipartite graphs , the bipartite Ramsey number is the least positive integer p so that any coloring of the edges of with k colors will result in a copy of in the ith color for some i. In this paper, we investigate the appearance of simpler monochromatic graphs such as paths under a 3-colouring of the edges of a bipartite graph. we obtain the exact value of , and for , and for by a new method of proof.
{"title":"Note on the three-coloured bipartite Ramsey numbers for paths","authors":"Ke Wang, Jiannan Zhou, Dong He, Qin Tong","doi":"10.1080/23799927.2021.1934900","DOIUrl":"https://doi.org/10.1080/23799927.2021.1934900","url":null,"abstract":"For bipartite graphs , the bipartite Ramsey number is the least positive integer p so that any coloring of the edges of with k colors will result in a copy of in the ith color for some i. In this paper, we investigate the appearance of simpler monochromatic graphs such as paths under a 3-colouring of the edges of a bipartite graph. we obtain the exact value of , and for , and for by a new method of proof.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77622663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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