The order components of a finite group are introduced in [12]. In [9], it is proved that the group PSL(3, q), where q is an odd prime power, is uniquely determined by its order components. In this paper, we show that ...The order components of a finite group are introduced in [12]. In [9], it is proved that the group PSL(3, q), where q is an odd prime power, is uniquely determined by its order components. In this paper, we show that the group PSL(3, q), where q=2~m, is also uniquely determined by its order components.展开更多
The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we...The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we will prove OC（G） = OC（^2Dp（3）） if and only if G is isomorphic to ^2Dp（3）. A main consequence of our result is the validity of Thompson＇s conjecture for the groups under consideration.展开更多
Attribute-based encryption with keyword search(ABEKS)is a novel cryptographic paradigm that can be used to implementfine-grained access control and retrieve ciphertexts without disclosing the sensitive information.It i...Attribute-based encryption with keyword search(ABEKS)is a novel cryptographic paradigm that can be used to implementfine-grained access control and retrieve ciphertexts without disclosing the sensitive information.It is a perfect combination of attribute-based encryption(ABE)and public key encryption with keyword search(PEKS).Nevertheless,most of the existing ABEKS schemes have limited search capabilities and only support single or simple conjunctive keyword search.Due to the weak search capability and inaccurate search results,it is difficult to apply these schemes to practical applications.In this paper,an effi-cient expressive ABEKS(EABEKS)scheme supporting unbounded keyword uni-verse over prime-order groups is designed,which supplies the expressive keyword search function supporting the logical connectives of“AND”and“OR”.The proposed scheme not only leads to low computation and communica-tion costs,but also supports unbounded keyword universe.In the standard model,the scheme is proven to be secure under the chosen keyword attack and the cho-sen plaintext attack.The comparison analysis and experimental results show that it has better performance than the existing EABEKS schemes in the storage,com-putation and communication costs.展开更多
For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G i...For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.展开更多
文摘The order components of a finite group are introduced in [12]. In [9], it is proved that the group PSL(3, q), where q is an odd prime power, is uniquely determined by its order components. In this paper, we show that the group PSL(3, q), where q=2~m, is also uniquely determined by its order components.
文摘The author will prove that the group ^2Dp（3） can be uniquely determined by its order components, where p ≠ 2^m ＋ 1 is a prime number, p ≥ 5. More precisely, if OC（G） denotes the set of order components of G, we will prove OC（G） = OC（^2Dp（3）） if and only if G is isomorphic to ^2Dp（3）. A main consequence of our result is the validity of Thompson＇s conjecture for the groups under consideration.
基金supported in part by the National Natural Science Foundation of China under Grant No.61772009the Natural Science Foundation of Jiangsu Province under Grant No.BK20181304.
文摘Attribute-based encryption with keyword search(ABEKS)is a novel cryptographic paradigm that can be used to implementfine-grained access control and retrieve ciphertexts without disclosing the sensitive information.It is a perfect combination of attribute-based encryption(ABE)and public key encryption with keyword search(PEKS).Nevertheless,most of the existing ABEKS schemes have limited search capabilities and only support single or simple conjunctive keyword search.Due to the weak search capability and inaccurate search results,it is difficult to apply these schemes to practical applications.In this paper,an effi-cient expressive ABEKS(EABEKS)scheme supporting unbounded keyword uni-verse over prime-order groups is designed,which supplies the expressive keyword search function supporting the logical connectives of“AND”and“OR”.The proposed scheme not only leads to low computation and communica-tion costs,but also supports unbounded keyword universe.In the standard model,the scheme is proven to be secure under the chosen keyword attack and the cho-sen plaintext attack.The comparison analysis and experimental results show that it has better performance than the existing EABEKS schemes in the storage,com-putation and communication costs.
基金This work has been supported by the Research Institute for Fundamental Sciences Tabriz,Iran.
文摘For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.
