In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtai...In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).展开更多
Commitment scheme is a basic component of many cryptographic protocols, such as coin-tossing, identification schemes, zero-knowledge and multi-party computation. In order to prevent man-in-middle attacks, non-malleabi...Commitment scheme is a basic component of many cryptographic protocols, such as coin-tossing, identification schemes, zero-knowledge and multi-party computation. In order to prevent man-in-middle attacks, non-malleability is taken into account. Many forming works focus on designing non-malleable commitments schemes based on number theory assumptions. In this paper we give a general framework to construct non- interactive and non-malleable commitment scheme with respect to opening based on more general assumptions called q-one way group homomorphisms (q-OWGH). Our scheme is more general since many existing commitment schemes can be deduced from our scheme.展开更多
For a graph G, let b(G)=max﹛|D|: Dis an edge cut of G﹜ . For graphs G and H, a map Ψ: V(G)→V(H) is a graph homomorphism if for each e=uv∈E(G), Ψ(u)Ψ(v)∈E(H). In 1979, Erd?s proved by probabilistic methods that...For a graph G, let b(G)=max﹛|D|: Dis an edge cut of G﹜ . For graphs G and H, a map Ψ: V(G)→V(H) is a graph homomorphism if for each e=uv∈E(G), Ψ(u)Ψ(v)∈E(H). In 1979, Erd?s proved by probabilistic methods that for p ≥ 2 with if there is a graph homomorphism from G onto Kp then b(G)≥f(p)|E(G)| In this paper, we obtained the best possible lower bounds of b(G) for graphs G with a graph homomorphism onto a Kneser graph or a circulant graph and we characterized the graphs G reaching the lower bounds when G is an edge maximal graph with a graph homomorphism onto a complete graph, or onto an odd cycle.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
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 paper, the induced group homomorphism was studied. It is proved that for any ideal I of a ring R contained in J(R), K 0(π):K 0(R)→K 0(R/I) is isomorphic if and only if K 0(π) + is a sem...In this paper, the induced group homomorphism was studied. It is proved that for any ideal I of a ring R contained in J(R), K 0(π):K 0(R)→K 0(R/I) is isomorphic if and only if K 0(π) + is a semigroup isomorphism; characterizations are given for the semilocal rings being semiperfect.展开更多
Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（F） be its subsemigroup consisting of all matrices with rank p...Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（F） be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn（F） such that F M^Pn（F）. A map f ： F→R is called a homomorphism if f（AB） = f（A）f（B） for any A, B ∈F. In particular, f is called an endomorphism if F = R. The structure of all homomorphisms from F to R （respectively, all endomorphisms of Mn（F）） is described.展开更多
Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-...Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-algebras） for the generalized Jensen–type functional equationwhere r is a fixed positive real number in （1, ∞）.展开更多
We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result...We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.展开更多
In this paper,linear maps preserving Lie products at zero points on nest algebras are studied.It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism....In this paper,linear maps preserving Lie products at zero points on nest algebras are studied.It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism.As an application,the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.展开更多
Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homo...Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.展开更多
We introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology.Accordingly,we use this cohomology to characteriz...We introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology.Accordingly,we use this cohomology to characterize linear deformations of crossed homomorphisms between Lie-Yamaguti algebras.If two linear or formal deformations of a crossed homomorphism are equivalent,then we show that their infinitesimals are in the same cohomology class.Moreover,we show that an order n deformation of a crossed homomorphism can be extended to an order n+1 deformation if and only if the obstruction class is trivial.展开更多
We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to a problem of Kaplansky for all vo...We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to a problem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simple complex Banach algebra onto another,we also show that the following statements are equivalent:(1) Φ is an homomorphism;(2)Φ is completely invertibility preserving;(3)Φ is 2-invertibility preserving.展开更多
In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is st...In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.展开更多
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is...In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.展开更多
Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g（x） = x for all x ∈ R, or char（R） = 2, R satisfies the sta...Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g（x） = x for all x ∈ R, or char（R） = 2, R satisfies the standard identity s4（x1, x2, x3, x4）, L is commutative and u2 ∈ Z（R）, for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R.展开更多
Suppose A is a unital C＊-algebra and r 1.In this paper,we define a unital C＊-algebra C（cb）＊（A,r） and a completely bounded unital homomorphism αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C...Suppose A is a unital C＊-algebra and r 1.In this paper,we define a unital C＊-algebra C（cb）＊（A,r） and a completely bounded unital homomorphism αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C＊（αr（A））and,for every unital C＊-algebra B and every unital completely bounded homomorphism φ：A→ B,there is a（unique）unital ＊-homomorphism π：C（cb）＊（A,r）→B such thatφ=πoαr.We prove that,if A is generated by a normal set {tλ：λ∈Λ},then C（cb）＊（A,r）is generated by the set {αr（tλ）：λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C（cb）＊（A,r）we obtain that,if Β is a unital C＊-algebra that can be embedded into A,then C（cb）＊（B,r）can be naturally embedded into C（cb）＊（A,r）.We give characterizations of C（cb）＊（A,r）for some special situations and we conclude that C（cb）＊（A,r）will be ＂nice＂ when dim（A）≤ 2 and ＂quite complicated＂ when dim（A）≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C（cb）＊（A,r）.We also define and study some analogous of C（cb）＊（A,r）.展开更多
As deep learning(DL)models are increasingly deployed in sensitive domains(e.g.,healthcare),concerns over privacy and security have intensified.Conventional penetration testing frameworks,such asOWASP and NIST,are effe...As deep learning(DL)models are increasingly deployed in sensitive domains(e.g.,healthcare),concerns over privacy and security have intensified.Conventional penetration testing frameworks,such asOWASP and NIST,are effective for traditional networks and applications but lack the capabilities to address DL-specific threats,such asmodel inversion,membership inference,and adversarial attacks.This review provides a comprehensive analysis of penetration testing for the privacy of DL models,examining the shortfalls of existing frameworks,tools,and testing methodologies.Through systematic evaluation of existing literature and empirical analysis,we identify three major contributions:(i)a critical assessment of traditional penetration testing frameworks’inadequacies when applied to DL-specific privacy vulnerabilities,(ii)a comprehensive evaluation of state-of-the-art privacy-preserving methods and their integration with penetration testing workflows,and(iii)the development of a structured framework that combines reconnaissance,threat modeling,exploitation,and post-exploitation phases specifically tailored for DL privacy assessment.Moreover,this review evaluates popular solutions such as IBMAdversarial Robustness Toolbox and TensorFlowPrivacy,alongside privacy-preserving techniques(e.g.,Differential Privacy,Homomorphic Encryption,and Federated Learning),which we systematically analyze through comparative studies of their effectiveness,computational overhead,and practical deployment constraints.While these techniques offer promising safeguards,their adoption is hindered by accuracy loss,performance overheads,and the rapid evolution of attack strategies.Our findings reveal that no single existing solution provides comprehensive protection,which leads us to propose a hybrid approach that strategically combines multiple privacy-preserving mechanisms.The findings of this survey underscore an urgent need for automated,regulationcompliant penetration testing frameworks specifically tailored to DL systems.We argue for hybrid privacy solutions that combinemultiple protectivemechanisms to ensure bothmodel accuracy and privacy.Building on our analysis,we present actionable recommendations for developing adaptive penetration testing strategies that incorporate automated vulnerability assessment,continuous monitoring,and regulatory compliance verification.展开更多
ABSTRACT:Federated Learning(FL)enables collaborative medical model training without sharing sensitive patient data.However,existing FL systems face increasing security risks from post quantum adversaries and often inc...ABSTRACT:Federated Learning(FL)enables collaborative medical model training without sharing sensitive patient data.However,existing FL systems face increasing security risks from post quantum adversaries and often incur nonnegligible computational and communication overhead when encryption is applied.At the same time,training high performance AI models requires large volumes of high quality data,while medical data such as patient information,clinical records,and diagnostic reports are highly sensitive and subject to strict privacy regulations,including HIPAA and GDPR.Traditional centralized machine learning approaches therefore pose significant challenges for cross institutional collaboration in healthcare.To address these limitations,Federated Learning was introduced to allow multiple institutions to jointly train a global model while keeping local data private.Nevertheless,conventional cryptographicmechanisms,such as RSA,are increasingly inadequate for privacy sensitive FL deployments,particularly in the presence of emerging quantum computing threats.Homomorphic encryption,which enables computations to be performed directly on encrypted data,provides an effective solution for preserving data privacy in federated learning systems.This capability allows healthcare institutions to securely perform collaborative model training while remaining compliant with regulatory requirements.Among homomorphic encryption techniques,NTRU,a lattice based cryptographic scheme defined over polynomial rings,offers strong resistance against quantum attacks by relying on the hardness of the Shortest Vector Problem(SVP).Moreover,NTRU supports limited homomorphic operations that are sufficient for secure aggregation in federated learning.In this work,we propose an NTRU enhanced federated learning framework specifically designed for medical and healthcare applications.Experimental results demonstrate that the proposed approach achieves classification performance comparable to standard federated learning,with final accuracy consistently exceeding 0.93.The framework introduces predictable encryption latency on the order of hundreds of milliseconds per training round and a fixed ciphertext communication overhead per client under practical deployment settings.In addition,the proposed systemeffectivelymitigatesmultiple security threats,including quantum computing attacks,by ensuring robust encryption throughout the training process.By integrating the security and homomorphic properties of NTRU,this study establishes a privacy preserving and quantumresistant federated learning framework that supports the secure,legal,and efficient deployment of AI technologies in healthcare,thereby laying a solid foundation for future intelligent healthcare systems.展开更多
As cyberattacks become increasingly sophisticated and intelligent,demand for machine-learning-based anomaly detection systems is growing.However,conventional systems generally assume a trusted server environment,where...As cyberattacks become increasingly sophisticated and intelligent,demand for machine-learning-based anomaly detection systems is growing.However,conventional systems generally assume a trusted server environment,where traffic data is collected and analyzed in plaintext.This assumption introduces inherent privacy risks,as privacy-sensitive information may be exposed if the server is compromised or misused.To address this limitation,privacy-preserving anomaly detection approaches have been actively studied,enabling anomaly detection to be performed directly on encrypted traffic without revealing privacy-sensitive data.While these approaches offer strong confidentiality guarantees,they suffer from significant drawbacks,including substantial computational overhead,high latency,and degraded detection accuracy.To overcome these limitations,we propose a privacy-aware anomaly detection(PAAD)model that adaptively applies homomorphic encryption based on the privacy sensitivity of incoming traffic.Instead of encrypting all data indiscriminately,PAAD dynamically determines whether traffic should be processed in plaintext or ciphertext and performs homomorphic inference only for privacy-sensitive data.This selective encryption strategy effectively balances privacy protection and system efficiency.Extensive experiments conducted under diverse network environments demonstrate that the proposed PAAD model significantly outperforms conventional anomaly detection models.In particular,PAAD improves detection accuracy by up to 73%,reduces latency by up to 8.6 times,and achieves negligible information leakage,highlighting its practicality for real-world privacy-sensitive network monitoring scenarios.展开更多
文摘In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).
基金the National Natural Science Foundations of China (Nos. 60673079 and 60572155)
文摘Commitment scheme is a basic component of many cryptographic protocols, such as coin-tossing, identification schemes, zero-knowledge and multi-party computation. In order to prevent man-in-middle attacks, non-malleability is taken into account. Many forming works focus on designing non-malleable commitments schemes based on number theory assumptions. In this paper we give a general framework to construct non- interactive and non-malleable commitment scheme with respect to opening based on more general assumptions called q-one way group homomorphisms (q-OWGH). Our scheme is more general since many existing commitment schemes can be deduced from our scheme.
文摘For a graph G, let b(G)=max﹛|D|: Dis an edge cut of G﹜ . For graphs G and H, a map Ψ: V(G)→V(H) is a graph homomorphism if for each e=uv∈E(G), Ψ(u)Ψ(v)∈E(H). In 1979, Erd?s proved by probabilistic methods that for p ≥ 2 with if there is a graph homomorphism from G onto Kp then b(G)≥f(p)|E(G)| In this paper, we obtained the best possible lower bounds of b(G) for graphs G with a graph homomorphism onto a Kneser graph or a circulant graph and we characterized the graphs G reaching the lower bounds when G is an edge maximal graph with a graph homomorphism onto a complete graph, or onto an odd cycle.
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 paper, the induced group homomorphism was studied. It is proved that for any ideal I of a ring R contained in J(R), K 0(π):K 0(R)→K 0(R/I) is isomorphic if and only if K 0(π) + is a semigroup isomorphism; characterizations are given for the semilocal rings being semiperfect.
基金the Chinese NSF under Grant No.10271021the Younth Fund of Heilongjiang Provincethe Fund of Heilongjiang Education Committee for Oversea Scholars under Grant No.1054HQ004
文摘Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（F） be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn（F） such that F M^Pn（F）. A map f ： F→R is called a homomorphism if f（AB） = f（A）f（B） for any A, B ∈F. In particular, f is called an endomorphism if F = R. The structure of all homomorphisms from F to R （respectively, all endomorphisms of Mn（F）） is described.
文摘Using fixed point methods, we prove the Hyers–Ulam–Rassias stability and superstability of Jordan homomorphisms （Jordan ＊-homomorphisms）, and Jordan derivations （Jordan ＊-derivations） on Banach algebras （C＊-algebras） for the generalized Jensen–type functional equationwhere r is a fixed positive real number in （1, ∞）.
文摘We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.
基金Supported by the Specialized Research Foundation for the Doctoral Program of Universities and Colleges of China(20110202110002)
文摘In this paper,linear maps preserving Lie products at zero points on nest algebras are studied.It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism.As an application,the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.
文摘Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.
基金supported by NSFC grant 12401033Qiao was partially supported by NSFC grant 11971282+1 种基金Xu was partially supported by NSFC grant 12201253Natural Science Foundation of Jiangsu Province BK20220510.
文摘We introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology.Accordingly,we use this cohomology to characterize linear deformations of crossed homomorphisms between Lie-Yamaguti algebras.If two linear or formal deformations of a crossed homomorphism are equivalent,then we show that their infinitesimals are in the same cohomology class.Moreover,we show that an order n deformation of a crossed homomorphism can be extended to an order n+1 deformation if and only if the obstruction class is trivial.
基金supported by NNSFC (10071046)PNSFS (981009)+1 种基金PYSFS(20031009)China Postdoctoral Science Foundation
文摘We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to a problem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simple complex Banach algebra onto another,we also show that the following statements are equivalent:(1) Φ is an homomorphism;(2)Φ is completely invertibility preserving;(3)Φ is 2-invertibility preserving.
文摘In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.
文摘In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.
文摘Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g（x） = x for all x ∈ R, or char（R） = 2, R satisfies the standard identity s4（x1, x2, x3, x4）, L is commutative and u2 ∈ Z（R）, for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R.
基金partially supported by a Collaboration Grant from the Simons Foundation
文摘Suppose A is a unital C＊-algebra and r 1.In this paper,we define a unital C＊-algebra C（cb）＊（A,r） and a completely bounded unital homomorphism αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C＊（αr（A））and,for every unital C＊-algebra B and every unital completely bounded homomorphism φ：A→ B,there is a（unique）unital ＊-homomorphism π：C（cb）＊（A,r）→B such thatφ=πoαr.We prove that,if A is generated by a normal set {tλ：λ∈Λ},then C（cb）＊（A,r）is generated by the set {αr（tλ）：λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C（cb）＊（A,r）we obtain that,if Β is a unital C＊-algebra that can be embedded into A,then C（cb）＊（B,r）can be naturally embedded into C（cb）＊（A,r）.We give characterizations of C（cb）＊（A,r）for some special situations and we conclude that C（cb）＊（A,r）will be ＂nice＂ when dim（A）≤ 2 and ＂quite complicated＂ when dim（A）≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C（cb）＊（A,r）.We also define and study some analogous of C（cb）＊（A,r）.
基金supported in part by the Tianjin Natural Science Foundation Project(24JCZDJC01000)the Fundamental Research Funds for the Central Universities of China(No.3122025091).
文摘As deep learning(DL)models are increasingly deployed in sensitive domains(e.g.,healthcare),concerns over privacy and security have intensified.Conventional penetration testing frameworks,such asOWASP and NIST,are effective for traditional networks and applications but lack the capabilities to address DL-specific threats,such asmodel inversion,membership inference,and adversarial attacks.This review provides a comprehensive analysis of penetration testing for the privacy of DL models,examining the shortfalls of existing frameworks,tools,and testing methodologies.Through systematic evaluation of existing literature and empirical analysis,we identify three major contributions:(i)a critical assessment of traditional penetration testing frameworks’inadequacies when applied to DL-specific privacy vulnerabilities,(ii)a comprehensive evaluation of state-of-the-art privacy-preserving methods and their integration with penetration testing workflows,and(iii)the development of a structured framework that combines reconnaissance,threat modeling,exploitation,and post-exploitation phases specifically tailored for DL privacy assessment.Moreover,this review evaluates popular solutions such as IBMAdversarial Robustness Toolbox and TensorFlowPrivacy,alongside privacy-preserving techniques(e.g.,Differential Privacy,Homomorphic Encryption,and Federated Learning),which we systematically analyze through comparative studies of their effectiveness,computational overhead,and practical deployment constraints.While these techniques offer promising safeguards,their adoption is hindered by accuracy loss,performance overheads,and the rapid evolution of attack strategies.Our findings reveal that no single existing solution provides comprehensive protection,which leads us to propose a hybrid approach that strategically combines multiple privacy-preserving mechanisms.The findings of this survey underscore an urgent need for automated,regulationcompliant penetration testing frameworks specifically tailored to DL systems.We argue for hybrid privacy solutions that combinemultiple protectivemechanisms to ensure bothmodel accuracy and privacy.Building on our analysis,we present actionable recommendations for developing adaptive penetration testing strategies that incorporate automated vulnerability assessment,continuous monitoring,and regulatory compliance verification.
文摘ABSTRACT:Federated Learning(FL)enables collaborative medical model training without sharing sensitive patient data.However,existing FL systems face increasing security risks from post quantum adversaries and often incur nonnegligible computational and communication overhead when encryption is applied.At the same time,training high performance AI models requires large volumes of high quality data,while medical data such as patient information,clinical records,and diagnostic reports are highly sensitive and subject to strict privacy regulations,including HIPAA and GDPR.Traditional centralized machine learning approaches therefore pose significant challenges for cross institutional collaboration in healthcare.To address these limitations,Federated Learning was introduced to allow multiple institutions to jointly train a global model while keeping local data private.Nevertheless,conventional cryptographicmechanisms,such as RSA,are increasingly inadequate for privacy sensitive FL deployments,particularly in the presence of emerging quantum computing threats.Homomorphic encryption,which enables computations to be performed directly on encrypted data,provides an effective solution for preserving data privacy in federated learning systems.This capability allows healthcare institutions to securely perform collaborative model training while remaining compliant with regulatory requirements.Among homomorphic encryption techniques,NTRU,a lattice based cryptographic scheme defined over polynomial rings,offers strong resistance against quantum attacks by relying on the hardness of the Shortest Vector Problem(SVP).Moreover,NTRU supports limited homomorphic operations that are sufficient for secure aggregation in federated learning.In this work,we propose an NTRU enhanced federated learning framework specifically designed for medical and healthcare applications.Experimental results demonstrate that the proposed approach achieves classification performance comparable to standard federated learning,with final accuracy consistently exceeding 0.93.The framework introduces predictable encryption latency on the order of hundreds of milliseconds per training round and a fixed ciphertext communication overhead per client under practical deployment settings.In addition,the proposed systemeffectivelymitigatesmultiple security threats,including quantum computing attacks,by ensuring robust encryption throughout the training process.By integrating the security and homomorphic properties of NTRU,this study establishes a privacy preserving and quantumresistant federated learning framework that supports the secure,legal,and efficient deployment of AI technologies in healthcare,thereby laying a solid foundation for future intelligent healthcare systems.
基金supported by the Ministry of Trade,Industry and Energy(MOTIE)under Training Industrial Security Specialist for High-Tech Industry[grant number RS-2024-00415520]supervised by the Korea Institute for Advancement of Technology(KIAT)Ministry of Science and ICT(MSIT)under the ICAN(ICT Challenge and Advanced Network of HRD)program[grant number IITP-2022-RS-2022-00156310]+1 种基金National Research Foundation of Korea(NRF)grant[RS-2025-00518150]the Information Security Core Technology Development program[grant number RS-2024-00437252]supervised by the Institute of Information&Communication Technology Planning&Evaluation(IITP).
文摘As cyberattacks become increasingly sophisticated and intelligent,demand for machine-learning-based anomaly detection systems is growing.However,conventional systems generally assume a trusted server environment,where traffic data is collected and analyzed in plaintext.This assumption introduces inherent privacy risks,as privacy-sensitive information may be exposed if the server is compromised or misused.To address this limitation,privacy-preserving anomaly detection approaches have been actively studied,enabling anomaly detection to be performed directly on encrypted traffic without revealing privacy-sensitive data.While these approaches offer strong confidentiality guarantees,they suffer from significant drawbacks,including substantial computational overhead,high latency,and degraded detection accuracy.To overcome these limitations,we propose a privacy-aware anomaly detection(PAAD)model that adaptively applies homomorphic encryption based on the privacy sensitivity of incoming traffic.Instead of encrypting all data indiscriminately,PAAD dynamically determines whether traffic should be processed in plaintext or ciphertext and performs homomorphic inference only for privacy-sensitive data.This selective encryption strategy effectively balances privacy protection and system efficiency.Extensive experiments conducted under diverse network environments demonstrate that the proposed PAAD model significantly outperforms conventional anomaly detection models.In particular,PAAD improves detection accuracy by up to 73%,reduces latency by up to 8.6 times,and achieves negligible information leakage,highlighting its practicality for real-world privacy-sensitive network monitoring scenarios.
