Let A be a commutative unital C^(*)-algebra with the unit element e and M be a full Hilbert A-module.Denote by End_(A)(M)the algebra of all bounded A-linear mappings on M and by M′the set of all bounded A-linear mapp...Let A be a commutative unital C^(*)-algebra with the unit element e and M be a full Hilbert A-module.Denote by End_(A)(M)the algebra of all bounded A-linear mappings on M and by M′the set of all bounded A-linear mappings from M into A.In this paper,we prove that if there exists x_(0) in M and f_(0) in M′such that f_(0)(x_(0))=e,then every A-linear Lie triple derivation on End_(A)(M)is standard.展开更多
Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, ...Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.展开更多
Digital twin is a novel technology that has achieved significant progress in industrial manufactur-ing systems in recent years.In the digital twin envi-ronment,entities in the virtual space collect data from devices i...Digital twin is a novel technology that has achieved significant progress in industrial manufactur-ing systems in recent years.In the digital twin envi-ronment,entities in the virtual space collect data from devices in the physical space to analyze their states.However,since a lot of devices exist in the physical space,the digital twin system needs to aggregate data from multiple devices at the edge gateway.Homomor-phic integrity and confidentiality protections are two important requirements for this data aggregation pro-cess.Unfortunately,existing homomorphic encryp-tion algorithms do not support integrity protection,and existing homomorphic signing algorithms require all signers to use the same signing key,which is not feasible in the digital twin environment.Moreover,for both integrity and confidentiality protections,the homomorphic signing algorithm must be compatible with the aggregation manner of the homomorphic en-cryption algorithm.To address these issues,this paper designs a novel homomorphic aggregation scheme,which allows multiple devices in the physical space to sign different data using different keys and support in-tegrity and confidentiality protections.Finally,the security of the newly designed scheme is analyzed,and its efficiency is evaluated.Experimental results show that our scheme is feasible for real world applications.展开更多
As data analysis often incurs significant communication and computational costs,these tasks are increasingly outsourced to cloud computing platforms.However,this introduces privacy concerns,as sensitive data must be t...As data analysis often incurs significant communication and computational costs,these tasks are increasingly outsourced to cloud computing platforms.However,this introduces privacy concerns,as sensitive data must be transmitted to and processed by untrusted parties.To address this,fully homomorphic encryption(FHE)has emerged as a promising solution for privacy-preserving Machine-Learning-as-a-Service(MLaaS),enabling computation on encrypted data without revealing the plaintext.Nevertheless,FHE remains computationally expensive.As a result,approximate homomorphic encryption(AHE)schemes,such as CKKS,have attracted attention due to their efficiency.In our previous work,we proposed RP-OKC,a CKKS-based clustering scheme implemented via TenSEAL.However,errors inherent to CKKS operations—termed CKKS-errors—can affect the accuracy of the result after decryption.Since these errors can be mitigated through post-decryption rounding,we propose a data pre-scaling technique to increase the number of significant digits and reduce CKKS-errors.Furthermore,we introduce an Operation-Error-Estimation(OEE)table that quantifies upper-bound error estimates for various CKKS operations.This table enables error-aware decryption correction,ensuring alignment between encrypted and plaintext results.We validate our method on K-means clustering using the Kaggle Customer Segmentation dataset.Experimental results confirm that the proposed scheme enhances the accuracy and reliability of privacy-preserving data analysis in cloud environments.展开更多
Due to the rapid advancement of information technology,data has emerged as the core resource driving decision-making and innovation across all industries.As the foundation of artificial intelligence,machine learning(M...Due to the rapid advancement of information technology,data has emerged as the core resource driving decision-making and innovation across all industries.As the foundation of artificial intelligence,machine learning(ML)has expanded its applications into intelligent recommendation systems,autonomous driving,medical diagnosis,and financial risk assessment.However,it relies on massive datasets,which contain sensitive personal information.Consequently,Privacy-Preserving Machine Learning(PPML)has become a critical research direction.To address the challenges of efficiency and accuracy in encrypted data computation within PPML,Homomorphic Encryption(HE)technology is a crucial solution,owing to its capability to facilitate computations on encrypted data.However,the integration of machine learning and homomorphic encryption technologies faces multiple challenges.Against this backdrop,this paper reviews homomorphic encryption technologies,with a focus on the advantages of the Cheon-Kim-Kim-Song(CKKS)algorithm in supporting approximate floating-point computations.This paper reviews the development of three machine learning techniques:K-nearest neighbors(KNN),K-means clustering,and face recognition-in integration with homomorphic encryption.It proposes feasible schemes for typical scenarios,summarizes limitations and future optimization directions.Additionally,it presents a systematic exploration of the integration of homomorphic encryption and machine learning from the essence of the technology,application implementation,performance trade-offs,technological convergence and future pathways to advance technological development.展开更多
Ciphertext data retrieval in cloud databases suffers from some critical limitations,such as inadequate security measures,disorganized key management practices,and insufficient retrieval access control capabilities.To ...Ciphertext data retrieval in cloud databases suffers from some critical limitations,such as inadequate security measures,disorganized key management practices,and insufficient retrieval access control capabilities.To address these problems,this paper proposes an enhanced Fully Homomorphic Encryption(FHE)algorithm based on an improved DGHV algorithm,coupled with an optimized ciphertext retrieval scheme.Our specific contributions are outlined as follows:First,we employ an authorization code to verify the user’s retrieval authority and perform hierarchical access control on cloud storage data.Second,a triple-key encryption mechanism,which separates the data encryption key,retrieval authorization key,and retrieval key,is designed.Different keys are provided to different entities to run corresponding system functions.The key separation architecture proves particularly advantageous in multi-verifier coexistence scenarios,environments involving untrusted third-party retrieval services.Finally,the enhanced DGHV-based retrieval mechanism extends conventional functionality by enabling multi-keyword queries with similarity-ranked results,thereby significantly improving both the functionality and usability of the FHE system.展开更多
In this study,we investigated privacy-preserving ID3 Decision Tree(PPID3)training and inference based on fully homomorphic encryption(FHE),which has not been actively explored due to the high computational cost associ...In this study,we investigated privacy-preserving ID3 Decision Tree(PPID3)training and inference based on fully homomorphic encryption(FHE),which has not been actively explored due to the high computational cost associated with managing numerous child nodes in an ID3 tree.We propose HEaaN-ID3,a novel approach to realize PPID3 using the Cheon-Kim-Kim-Song(CKKS)scheme.HEaaN-ID3 is the first FHE-based ID3 framework that completes both training and inference without any intermediate decryption,which is especially valuable when decryption keys are inaccessible or a single-cloud security domain is assumed.To enhance computational efficiency,we adopt a modified Gini impurity(MGI)score instead of entropy to evaluate information gain,thereby avoiding costly inverse operations.In addition,we fully leverage the Single Instruction Multiple Data(SIMD)property of CKKS to parallelize computations at multiple tree nodes.Unlike previous approaches that require decryption at each node or rely on two-party secure computation,our method enables a fully non-interactive training and inference pipeline in the encrypted domain.We validated the proposed scheme using UCI datasets with both numerical and nominal features,demonstrating inference accuracy comparable to plaintext implementations in Scikit-Learn.Moreover,experiments show that HEaaN-ID3 significantly reduces training and inference time per node relative to earlier FHE-based approaches.展开更多
With increasing demand for data circulation,ensuring data security and privacy is paramount,specifically protecting privacy while maximizing utility.Blockchain,while decentralized and transparent,faces challenges in p...With increasing demand for data circulation,ensuring data security and privacy is paramount,specifically protecting privacy while maximizing utility.Blockchain,while decentralized and transparent,faces challenges in privacy protection and data verification,especially for sensitive data.Existing schemes often suffer from inefficiency and high overhead.We propose a privacy protection scheme using BGV homomorphic encryption and Pedersen Secret Sharing.This scheme enables secure computation on encrypted data,with Pedersen sharding and verifying the private key,ensuring data consistency and immutability.The blockchain framework manages key shards,verifies secrets,and aids security auditing.This approach allows for trusted computation without revealing the underlying data.Preliminary results demonstrate the scheme's feasibility in ensuring data privacy and security,making data available but not visible.This study provides an effective solution for data sharing and privacy protection in blockchain applications.展开更多
Compared with Zn^(2+),the current mainly reported charge carrier for zinc hybrid capacitors,small-hydrated-sized and light-weight NH_(4)^(+)is expected as a better one to mediate cathodic interfacial electrochemical b...Compared with Zn^(2+),the current mainly reported charge carrier for zinc hybrid capacitors,small-hydrated-sized and light-weight NH_(4)^(+)is expected as a better one to mediate cathodic interfacial electrochemical behaviors,yet has not been unraveled.Here we propose an NH_(4)^(+)-modulated cationic solvation strategy to optimize cathodic spatial charge distribution and achieve dynamic Zn^(2+)/NH_(4)^(+)co-storage for boosting Zinc hybrid capacitors.Owing to the hierarchical cationic solvated structure in hybrid Zn(CF_(3)SO_(3))_(2)–NH_4CF_(3)SO_(3)electrolyte,high-reactive Zn^(2+)and small-hydrate-sized NH_4(H_(2)O))(4)^(+)induce cathodic interfacial Helmholtz plane reconfiguration,thus effectively enhancing the spatial charge density to activate 20%capacity enhancement.Furthermore,cathodic interfacial adsorbed hydrated NH_(4)^(+)ions afford high-kinetics and ultrastable C···H(NH_(4)^(+))charge storage process due to a much lower desolvation energy barrier compared with heavy and rigid Zn(H_(2)O)_6^(2+)(5.81 vs.14.90 eV).Consequently,physical uptake and multielectron redox of Zn^(2+)/NH_(4)^(+)in carbon cathode enable the zinc capacitor to deliver high capacity(240 mAh g^(-1)at 0.5 A g^(-1)),large-current tolerance(130 mAh g^(-1)at 50 A g^(-1))and ultralong lifespan(400,000cycles).This study gives new insights into the design of cathode–electrolyte interfaces toward advanced zinc-based energy storage.展开更多
This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. ...This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.展开更多
Wireless transmission method in wireless sensor networks has put forward higher requirements for private protection technology. According to the packet loss problem of private protection algorithm based on slice techn...Wireless transmission method in wireless sensor networks has put forward higher requirements for private protection technology. According to the packet loss problem of private protection algorithm based on slice technology, this paper proposes the data private protection algorithm with redundancy mechanism, which ensures privacy by privacy homomorphism mechanism and guarantees redundancy by carrying hidden data. Moreover,it selects the routing tree generated by CTP(Collection Tree Protocol) as routing path for data transmission. By dividing at the source node, it adds the hidden information and also the privacy homomorphism. At the same time,the information feedback tree is established between the destination node and the source node. In addition, the destination node immediately sends the packet loss information and the encryption key via the information feedback tree to the source node. As a result,it improves the reliability and privacy of data transmission and ensures the data redundancy.展开更多
A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copre...A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copres∞（U）. A module U is a co-＊∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞（U） and I is a set, N∈Copres∞（U） is equivalent to Ext1R（N,U）→Ext1R（UI,U） is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞（U）, N∈Copres∞（U） is equivalent to the induced sequence 0→Δ（N）→Δ（M）→Δ（L）→0 which is exact if and only if U induces a duality ΔUS：⊥USCopres∞（U）：ΔRU. Moreover, U is a co-＊n-module if and only if U is a co-＊∞-module and Copres∞（U）=Copresn（U）.展开更多
Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true...Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true.(2) It proved that the isomorphous relationship of the bottomgroups which guid to the hypergroup can still keep such relationship.(3) It proved that the basic isomorphous Theorem and the homogenous Theorem of the bottomgroup which raise to the hypergroup are still true.(4) It point out that when the isomorphous bottomgroups have been raised to the hypergroup,the conditions which form the isomorphism should be lessened.展开更多
Schuster introduced the notion of Blaschke-Minkowski homomorphisms and first considered Busemann-Petty type problems. In this paper, we study the Busemann-Petty type problems for the geominimal surface area with respe...Schuster introduced the notion of Blaschke-Minkowski homomorphisms and first considered Busemann-Petty type problems. In this paper, we study the Busemann-Petty type problems for the geominimal surface area with respect to Blaschke-Minkowski homomorphisms.展开更多
In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.展开更多
The Blaschke-Minkowski homomorphisms was defined by Schuster.Recently,Wang extended its concept to Lp version.In this paper,we obtain affirmative and negative forms of the Shephard type problems for Lp geominimal surf...The Blaschke-Minkowski homomorphisms was defined by Schuster.Recently,Wang extended its concept to Lp version.In this paper,we obtain affirmative and negative forms of the Shephard type problems for Lp geominimal surface areas with respect to the Lp Blaschke-Minkowski homomorphisms.展开更多
In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some pr...In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).展开更多
In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes...In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.展开更多
In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the con...In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.展开更多
基金Supported by the Shaanxi College Students Innovation and Entrepreneurship Training Program(Grant No.S202110708069)。
文摘Let A be a commutative unital C^(*)-algebra with the unit element e and M be a full Hilbert A-module.Denote by End_(A)(M)the algebra of all bounded A-linear mappings on M and by M′the set of all bounded A-linear mappings from M into A.In this paper,we prove that if there exists x_(0) in M and f_(0) in M′such that f_(0)(x_(0))=e,then every A-linear Lie triple derivation on End_(A)(M)is standard.
文摘Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.
基金supported by ZTE Industry-University-Institute Cooperation Funds under Grant No.IA20230628015the State Key Laboratory of Particle Detection and Electronics under Grant No.SKLPDE-KF-202314.
文摘Digital twin is a novel technology that has achieved significant progress in industrial manufactur-ing systems in recent years.In the digital twin envi-ronment,entities in the virtual space collect data from devices in the physical space to analyze their states.However,since a lot of devices exist in the physical space,the digital twin system needs to aggregate data from multiple devices at the edge gateway.Homomor-phic integrity and confidentiality protections are two important requirements for this data aggregation pro-cess.Unfortunately,existing homomorphic encryp-tion algorithms do not support integrity protection,and existing homomorphic signing algorithms require all signers to use the same signing key,which is not feasible in the digital twin environment.Moreover,for both integrity and confidentiality protections,the homomorphic signing algorithm must be compatible with the aggregation manner of the homomorphic en-cryption algorithm.To address these issues,this paper designs a novel homomorphic aggregation scheme,which allows multiple devices in the physical space to sign different data using different keys and support in-tegrity and confidentiality protections.Finally,the security of the newly designed scheme is analyzed,and its efficiency is evaluated.Experimental results show that our scheme is feasible for real world applications.
基金funded by National Science and Technology Council,Taiwan,grant numbers are 110-2401-H-002-094-MY2 and 112-2221-E-130-001.
文摘As data analysis often incurs significant communication and computational costs,these tasks are increasingly outsourced to cloud computing platforms.However,this introduces privacy concerns,as sensitive data must be transmitted to and processed by untrusted parties.To address this,fully homomorphic encryption(FHE)has emerged as a promising solution for privacy-preserving Machine-Learning-as-a-Service(MLaaS),enabling computation on encrypted data without revealing the plaintext.Nevertheless,FHE remains computationally expensive.As a result,approximate homomorphic encryption(AHE)schemes,such as CKKS,have attracted attention due to their efficiency.In our previous work,we proposed RP-OKC,a CKKS-based clustering scheme implemented via TenSEAL.However,errors inherent to CKKS operations—termed CKKS-errors—can affect the accuracy of the result after decryption.Since these errors can be mitigated through post-decryption rounding,we propose a data pre-scaling technique to increase the number of significant digits and reduce CKKS-errors.Furthermore,we introduce an Operation-Error-Estimation(OEE)table that quantifies upper-bound error estimates for various CKKS operations.This table enables error-aware decryption correction,ensuring alignment between encrypted and plaintext results.We validate our method on K-means clustering using the Kaggle Customer Segmentation dataset.Experimental results confirm that the proposed scheme enhances the accuracy and reliability of privacy-preserving data analysis in cloud environments.
基金supported by the fllowing projects:Natural Science Foundation of China under Grant 62172436Self-Initiated Scientific Research Project of the Chinese People's Armed Police Force under Grant ZZKY20243129Basic Frontier Innovation Project of the Engineering University of the Chinese People's Armed Police Force under Grant WJY202421.
文摘Due to the rapid advancement of information technology,data has emerged as the core resource driving decision-making and innovation across all industries.As the foundation of artificial intelligence,machine learning(ML)has expanded its applications into intelligent recommendation systems,autonomous driving,medical diagnosis,and financial risk assessment.However,it relies on massive datasets,which contain sensitive personal information.Consequently,Privacy-Preserving Machine Learning(PPML)has become a critical research direction.To address the challenges of efficiency and accuracy in encrypted data computation within PPML,Homomorphic Encryption(HE)technology is a crucial solution,owing to its capability to facilitate computations on encrypted data.However,the integration of machine learning and homomorphic encryption technologies faces multiple challenges.Against this backdrop,this paper reviews homomorphic encryption technologies,with a focus on the advantages of the Cheon-Kim-Kim-Song(CKKS)algorithm in supporting approximate floating-point computations.This paper reviews the development of three machine learning techniques:K-nearest neighbors(KNN),K-means clustering,and face recognition-in integration with homomorphic encryption.It proposes feasible schemes for typical scenarios,summarizes limitations and future optimization directions.Additionally,it presents a systematic exploration of the integration of homomorphic encryption and machine learning from the essence of the technology,application implementation,performance trade-offs,technological convergence and future pathways to advance technological development.
基金supported by the Innovation Program for Quantum Science and technology(2021ZD0301300)supported by the Fundamental Research Funds for the Central Universities(Nos.3282024046,3282024052,3282024058,3282023017).
文摘Ciphertext data retrieval in cloud databases suffers from some critical limitations,such as inadequate security measures,disorganized key management practices,and insufficient retrieval access control capabilities.To address these problems,this paper proposes an enhanced Fully Homomorphic Encryption(FHE)algorithm based on an improved DGHV algorithm,coupled with an optimized ciphertext retrieval scheme.Our specific contributions are outlined as follows:First,we employ an authorization code to verify the user’s retrieval authority and perform hierarchical access control on cloud storage data.Second,a triple-key encryption mechanism,which separates the data encryption key,retrieval authorization key,and retrieval key,is designed.Different keys are provided to different entities to run corresponding system functions.The key separation architecture proves particularly advantageous in multi-verifier coexistence scenarios,environments involving untrusted third-party retrieval services.Finally,the enhanced DGHV-based retrieval mechanism extends conventional functionality by enabling multi-keyword queries with similarity-ranked results,thereby significantly improving both the functionality and usability of the FHE system.
基金supported by Institute of Information communications Technology Planning Evaluation(IITP)grant funded by theKorea government(MSIT)[No.2022-0-01047,Development of statistical analysis algorithm and module using homomorphic encryption based on real number operation,100%].
文摘In this study,we investigated privacy-preserving ID3 Decision Tree(PPID3)training and inference based on fully homomorphic encryption(FHE),which has not been actively explored due to the high computational cost associated with managing numerous child nodes in an ID3 tree.We propose HEaaN-ID3,a novel approach to realize PPID3 using the Cheon-Kim-Kim-Song(CKKS)scheme.HEaaN-ID3 is the first FHE-based ID3 framework that completes both training and inference without any intermediate decryption,which is especially valuable when decryption keys are inaccessible or a single-cloud security domain is assumed.To enhance computational efficiency,we adopt a modified Gini impurity(MGI)score instead of entropy to evaluate information gain,thereby avoiding costly inverse operations.In addition,we fully leverage the Single Instruction Multiple Data(SIMD)property of CKKS to parallelize computations at multiple tree nodes.Unlike previous approaches that require decryption at each node or rely on two-party secure computation,our method enables a fully non-interactive training and inference pipeline in the encrypted domain.We validated the proposed scheme using UCI datasets with both numerical and nominal features,demonstrating inference accuracy comparable to plaintext implementations in Scikit-Learn.Moreover,experiments show that HEaaN-ID3 significantly reduces training and inference time per node relative to earlier FHE-based approaches.
基金supported by the National Key Research and Development Plan in China(Grant No.2020YFB1005500)。
文摘With increasing demand for data circulation,ensuring data security and privacy is paramount,specifically protecting privacy while maximizing utility.Blockchain,while decentralized and transparent,faces challenges in privacy protection and data verification,especially for sensitive data.Existing schemes often suffer from inefficiency and high overhead.We propose a privacy protection scheme using BGV homomorphic encryption and Pedersen Secret Sharing.This scheme enables secure computation on encrypted data,with Pedersen sharding and verifying the private key,ensuring data consistency and immutability.The blockchain framework manages key shards,verifies secrets,and aids security auditing.This approach allows for trusted computation without revealing the underlying data.Preliminary results demonstrate the scheme's feasibility in ensuring data privacy and security,making data available but not visible.This study provides an effective solution for data sharing and privacy protection in blockchain applications.
基金financially supported by the National Natural Science Foundation of China(Nos.22272118,22172111 and 22309134)the Science and Technology Commission of Shanghai Municipality,China(Nos.22ZR1464100,20ZR1460300 and 19DZ2271500)+3 种基金China Postdoctoral Science Foundation(2022M712402)Shanghai Rising-Star Program(23YF1449200)Zhejiang Provincial Science and Technology Project(2022C01182)the Fundamental Research Funds for the Central Universities(22120210529 and 2023-3-YB-07)。
文摘Compared with Zn^(2+),the current mainly reported charge carrier for zinc hybrid capacitors,small-hydrated-sized and light-weight NH_(4)^(+)is expected as a better one to mediate cathodic interfacial electrochemical behaviors,yet has not been unraveled.Here we propose an NH_(4)^(+)-modulated cationic solvation strategy to optimize cathodic spatial charge distribution and achieve dynamic Zn^(2+)/NH_(4)^(+)co-storage for boosting Zinc hybrid capacitors.Owing to the hierarchical cationic solvated structure in hybrid Zn(CF_(3)SO_(3))_(2)–NH_4CF_(3)SO_(3)electrolyte,high-reactive Zn^(2+)and small-hydrate-sized NH_4(H_(2)O))(4)^(+)induce cathodic interfacial Helmholtz plane reconfiguration,thus effectively enhancing the spatial charge density to activate 20%capacity enhancement.Furthermore,cathodic interfacial adsorbed hydrated NH_(4)^(+)ions afford high-kinetics and ultrastable C···H(NH_(4)^(+))charge storage process due to a much lower desolvation energy barrier compared with heavy and rigid Zn(H_(2)O)_6^(2+)(5.81 vs.14.90 eV).Consequently,physical uptake and multielectron redox of Zn^(2+)/NH_(4)^(+)in carbon cathode enable the zinc capacitor to deliver high capacity(240 mAh g^(-1)at 0.5 A g^(-1)),large-current tolerance(130 mAh g^(-1)at 50 A g^(-1))and ultralong lifespan(400,000cycles).This study gives new insights into the design of cathode–electrolyte interfaces toward advanced zinc-based energy storage.
文摘This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.
基金sponsored by the National Key R&D Program of China(No.2018YFB1003201)the National Natural Science Foundation of China(No.61672296,No.61602261)Major Natural Science Research Projects in Colleges and Universities of Jiangsu Province(No.18KJA520008)
文摘Wireless transmission method in wireless sensor networks has put forward higher requirements for private protection technology. According to the packet loss problem of private protection algorithm based on slice technology, this paper proposes the data private protection algorithm with redundancy mechanism, which ensures privacy by privacy homomorphism mechanism and guarantees redundancy by carrying hidden data. Moreover,it selects the routing tree generated by CTP(Collection Tree Protocol) as routing path for data transmission. By dividing at the source node, it adds the hidden information and also the privacy homomorphism. At the same time,the information feedback tree is established between the destination node and the source node. In addition, the destination node immediately sends the packet loss information and the encryption key via the information feedback tree to the source node. As a result,it improves the reliability and privacy of data transmission and ensures the data redundancy.
基金The National Natural Science Foundation of China (No.10971024)Specialized Research Fund for the Doctoral Program of Higher Education (No.200802860024)
文摘A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copres∞（U）. A module U is a co-＊∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞（U） and I is a set, N∈Copres∞（U） is equivalent to Ext1R（N,U）→Ext1R（UI,U） is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞（U）, N∈Copres∞（U） is equivalent to the induced sequence 0→Δ（N）→Δ（M）→Δ（L）→0 which is exact if and only if U induces a duality ΔUS：⊥USCopres∞（U）：ΔRU. Moreover, U is a co-＊n-module if and only if U is a co-＊∞-module and Copres∞（U）=Copresn（U）.
文摘Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true.(2) It proved that the isomorphous relationship of the bottomgroups which guid to the hypergroup can still keep such relationship.(3) It proved that the basic isomorphous Theorem and the homogenous Theorem of the bottomgroup which raise to the hypergroup are still true.(4) It point out that when the isomorphous bottomgroups have been raised to the hypergroup,the conditions which form the isomorphism should be lessened.
基金Supported by the National Natural Science Foundation of China(11371224)Innovation Foundation of Graduate Student of China Three Gorges University(2018SSPY136)
文摘Schuster introduced the notion of Blaschke-Minkowski homomorphisms and first considered Busemann-Petty type problems. In this paper, we study the Busemann-Petty type problems for the geominimal surface area with respect to Blaschke-Minkowski homomorphisms.
文摘In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.
基金Supported by the National Natural Science Foundation of China(11371224)Innovation Foundation of Graduate Student of China Three Gorges University(2019SSPY144)。
文摘The Blaschke-Minkowski homomorphisms was defined by Schuster.Recently,Wang extended its concept to Lp version.In this paper,we obtain affirmative and negative forms of the Shephard type problems for Lp geominimal surface areas with respect to the Lp Blaschke-Minkowski homomorphisms.
基金The NSF(11271148,11561057)of Chinathe NSF(20151BAB201007)of Jiangxi Provincethe Science and Technology Project(GJJ151061)of Jiangxi Education Department
文摘In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).
文摘In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.
基金Supported by the National Natural Science Foundation of China (61175055)the Innovation Term of Higher Education of Hubei Province,China (T201109)+1 种基金the Natural Science Foundation of Hubei Province (2012FFB01101)the Natural Science Foundation of Education Committee of Hubei Province (D20131903)
文摘In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.
