The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptos...The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptosystems use substitution-boxes.Nowadays,data privacy has become a key concern for consumers who transfer sensitive data from one place to another.To address these problems,many companies rely on cryptographic techniques to secure data from illegal activities and assaults.Among these cryptographic approaches,AES is a well-known algorithm that transforms plain text into cipher text by employing substitution box(S-box).The S-box disguises the relationship between cipher text and the key to guard against cipher attacks.The security of a cipher using an S-box depends on the cryptographic strength of the respective S-box.Therefore,various researchers have employed different techniques to construct high order non-linear S-box.This paper provides a novel approach for evolving S-boxes using coset graphs for the action of the alternating group A5 over the finite field and the symmetric group S256.The motivation for this work is to study the symmetric group and coset graphs.The authors have performed various analyses against conventional security criteria such as nonlinearity,differential uniformity,linear probability,the bit independence criterion,and the strict avalanche criterion to determine its high cryptographic strength.To evaluate its image application performance,the proposed S-box is also used to encrypt digital images.The performance and comparison analyses show that the suggested S-box can secure data against cyber-attacks.展开更多
设 G 为有限群,那么 G 的 FF—模的研究在研究包含 G 的抛物系(G,P_1,P_2,B)中起很重要的作用,而 G 的 FF—模的研究又主要归结于抛物系中关于有限群阶的不等式的证明.本文先证明了抛物系中有限群的阶不等式的一个结果,并由此得到了关...设 G 为有限群,那么 G 的 FF—模的研究在研究包含 G 的抛物系(G,P_1,P_2,B)中起很重要的作用,而 G 的 FF—模的研究又主要归结于抛物系中关于有限群阶的不等式的证明.本文先证明了抛物系中有限群的阶不等式的一个结果,并由此得到了关于弱李型单群结果的一个简化证明.展开更多
A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vert...A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms,then either G is normal in Aut(Γ),or Aut(Γ)contains a non-abelian simple normal subgroup T such that G≤T and(G,T)is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups.If G is arc-transitive,then G is always normal in Aut(Γ),and if G is regular on the vertices of Γ,then the number of possible exceptional pairs(G,T)is reduced to 5.展开更多
In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and th...In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.展开更多
文摘The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptosystems use substitution-boxes.Nowadays,data privacy has become a key concern for consumers who transfer sensitive data from one place to another.To address these problems,many companies rely on cryptographic techniques to secure data from illegal activities and assaults.Among these cryptographic approaches,AES is a well-known algorithm that transforms plain text into cipher text by employing substitution box(S-box).The S-box disguises the relationship between cipher text and the key to guard against cipher attacks.The security of a cipher using an S-box depends on the cryptographic strength of the respective S-box.Therefore,various researchers have employed different techniques to construct high order non-linear S-box.This paper provides a novel approach for evolving S-boxes using coset graphs for the action of the alternating group A5 over the finite field and the symmetric group S256.The motivation for this work is to study the symmetric group and coset graphs.The authors have performed various analyses against conventional security criteria such as nonlinearity,differential uniformity,linear probability,the bit independence criterion,and the strict avalanche criterion to determine its high cryptographic strength.To evaluate its image application performance,the proposed S-box is also used to encrypt digital images.The performance and comparison analyses show that the suggested S-box can secure data against cyber-attacks.
基金supported by the National Natural Science Foundation of China(11571035,11731002)the 111 Project of China(B16002).
文摘A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms,then either G is normal in Aut(Γ),or Aut(Γ)contains a non-abelian simple normal subgroup T such that G≤T and(G,T)is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups.If G is arc-transitive,then G is always normal in Aut(Γ),and if G is regular on the vertices of Γ,then the number of possible exceptional pairs(G,T)is reduced to 5.
基金supported by the National Natural Science Foundation of China(11731002,11701503,11971248,12061089)and the Fundamental Research Funds for the Central Universities.
文摘In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency 11.The list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the graphs associated with the simple group J1 and PSL(2,p),where p is a prime.
