External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in...External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in the quantum computing epoch. Three hard problems on this new platform, Subgroup Root Problem, Multi-variant Subgroup Root Problem and Subgroup Action Problem are presented and well analyzed, which all have no relations with conjugacy. New secure public key encryption system and key agreement protocol are designed based on these hard problems. The new cryptosystems can be implemented in a general group environment other than in braid or Artin groups.展开更多
Let G be a finite group generated by S and C(G,S) the Cayley digraphs of G with connection set S.In this paper,we give some sufficient conditions for the existence of hamiltonian circuit in C(G,S),where G=Zm×H is...Let G be a finite group generated by S and C(G,S) the Cayley digraphs of G with connection set S.In this paper,we give some sufficient conditions for the existence of hamiltonian circuit in C(G,S),where G=Zm×H is a semiproduct of Zmby a subgroup H of G.In particular,if m is a prime,then the Cayley digraph of G has a hamiltonian circuit unless G=Zm×H.In addition,we introduce a new digraph operation,called φ-semiproduct of Γ1by Γ2and denoted by Γ1×Γ_φΓ2,in terms of mapping φ:V(Γ2)→{1,-1}.Furthermore we prove that C(Zm,{a})×_φ C(H,S) is also a Cayley digraph if φ is a homomorphism from H to{1,-1} ≤ Zm~*,which produces some classes of Cayley digraphs that have hamiltonian circuits.展开更多
基金Supported by the National Natural Science Funda-tion of China (60403027)
文摘External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in the quantum computing epoch. Three hard problems on this new platform, Subgroup Root Problem, Multi-variant Subgroup Root Problem and Subgroup Action Problem are presented and well analyzed, which all have no relations with conjugacy. New secure public key encryption system and key agreement protocol are designed based on these hard problems. The new cryptosystems can be implemented in a general group environment other than in braid or Artin groups.
基金sponsored by the National Natural Science Foundation of China (No. 11671344)Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2022D01A218)the Scientific Research Projects of Universities in Xinjiang Province (No. XJEDU2019Y030)
文摘Let G be a finite group generated by S and C(G,S) the Cayley digraphs of G with connection set S.In this paper,we give some sufficient conditions for the existence of hamiltonian circuit in C(G,S),where G=Zm×H is a semiproduct of Zmby a subgroup H of G.In particular,if m is a prime,then the Cayley digraph of G has a hamiltonian circuit unless G=Zm×H.In addition,we introduce a new digraph operation,called φ-semiproduct of Γ1by Γ2and denoted by Γ1×Γ_φΓ2,in terms of mapping φ:V(Γ2)→{1,-1}.Furthermore we prove that C(Zm,{a})×_φ C(H,S) is also a Cayley digraph if φ is a homomorphism from H to{1,-1} ≤ Zm~*,which produces some classes of Cayley digraphs that have hamiltonian circuits.
