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A Generic Construction of Ciphertext-Policy Attribute- Based Encryption Supporting Attribute Revocation 被引量:7
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作者 WU Qiuxin 《China Communications》 SCIE CSCD 2014年第A01期93-100,共8页
Attribute-based encryption is drawing more attention with its inherent attractive properties which are potential to be widely used in the newly developing cloud computing. However, one of the main obstacles for its ap... Attribute-based encryption is drawing more attention with its inherent attractive properties which are potential to be widely used in the newly developing cloud computing. However, one of the main obstacles for its application is how to revoke the attributes of the users, though some ABE schemes have realized revocation, they mostly focused on the user revocation that revokes the user's whole attributes, or attribute revocation under the indirect revocation model such that all the users' private keys will be affected by the revocation. In this paper, we define the model of CP-ABE supporting the attribute revocation under the direct revocation model, in which the revocation list is embed in the ciphertext and none of the users' private keys will be affected by the revocation process. Then we propose a generic construction, and prove its security with the decision q-BDHE assumption. 展开更多
关键词 attribute revocation attribute based encryption ciphertext-Policy generic construction.
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Attack on Optical Double Random Phase Encryption Based on the Principle of Ptychographical Imaging 被引量:2
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作者 李拓 史祎诗 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第1期63-66,共4页
The principle of ptychography is applied in known plain text attack on the double random phase encoding (DRPE) system. We find that with several pairs of plain texts and cipher texts, the model of attack on DRPE can... The principle of ptychography is applied in known plain text attack on the double random phase encoding (DRPE) system. We find that with several pairs of plain texts and cipher texts, the model of attack on DRPE can be converted to the model of ptyehographical imaging. Owing to the inherent merits of the ptyehographical imaging, the DRPE system can be breached totally in a fast and nearly perfect way, which is unavailable for currently existing attack methods. Further, since the decryption keys can be seen as an object to be imaged from the perspective of imaging, the ptychographical technique may be a kind of new direction to further analysis of the security of other encryption systems based on double random keys. 展开更多
关键词 of as for it Attack on Optical Double Random Phase encryption based on the Principle of Ptychographical Imaging in IS on
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Attribute-Based Re-Encryption Scheme in the Standard Model 被引量:2
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作者 GUO Shanqing ZENG Yingpei +1 位作者 WEI Juan XU Qiuliang 《Wuhan University Journal of Natural Sciences》 CAS 2008年第5期621-625,共5页
In this paper, we propose a new attribute-based proxy re-encryption scheme, where a semi-trusted proxy, with some additional information, can transform a ciphertext under a set of attributes into a new ciphertext unde... In this paper, we propose a new attribute-based proxy re-encryption scheme, where a semi-trusted proxy, with some additional information, can transform a ciphertext under a set of attributes into a new ciphertext under another set of attributes on the same message, but not vice versa, furthermore, its security was proved in the standard model based on decisional bilinear Diffie-Hellman assumption. This scheme can be used to realize fine-grained selectively sharing of encrypted data, but the general proxy rencryption scheme severely can not do it, so the proposed schemecan be thought as an improvement of general traditional proxy re-encryption scheme. 展开更多
关键词 ATTRIBUTE-based re-encryption scheme standard model network storage
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Multi-authority proxy re-encryption based on CPABE for cloud storage systems 被引量:7
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作者 Xiaolong Xu Jinglan Zhou +1 位作者 Xinheng Wang Yun Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第1期211-223,共13页
The dissociation between data management and data ownership makes it difficult to protect data security and privacy in cloud storage systems.Traditional encryption technologies are not suitable for data protection in ... The dissociation between data management and data ownership makes it difficult to protect data security and privacy in cloud storage systems.Traditional encryption technologies are not suitable for data protection in cloud storage systems.A novel multi-authority proxy re-encryption mechanism based on ciphertext-policy attribute-based encryption(MPRE-CPABE) is proposed for cloud storage systems.MPRE-CPABE requires data owner to split each file into two blocks,one big block and one small block.The small block is used to encrypt the big one as the private key,and then the encrypted big block will be uploaded to the cloud storage system.Even if the uploaded big block of file is stolen,illegal users cannot get the complete information of the file easily.Ciphertext-policy attribute-based encryption(CPABE)is always criticized for its heavy overload and insecure issues when distributing keys or revoking user's access right.MPRE-CPABE applies CPABE to the multi-authority cloud storage system,and solves the above issues.The weighted access structure(WAS) is proposed to support a variety of fine-grained threshold access control policy in multi-authority environments,and reduce the computational cost of key distribution.Meanwhile,MPRE-CPABE uses proxy re-encryption to reduce the computational cost of access revocation.Experiments are implemented on platforms of Ubuntu and CloudSim.Experimental results show that MPRE-CPABE can greatly reduce the computational cost of the generation of key components and the revocation of user's access right.MPRE-CPABE is also proved secure under the security model of decisional bilinear Diffie-Hellman(DBDH). 展开更多
关键词 cloud storage data partition multi-authority security proxy re-encryption attribute-based encryption(ABE).
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Fully Secure Identity-based Broadcast Encryption in the Subgroups 被引量:1
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作者 张乐友 胡予濮 吴青 《China Communications》 SCIE CSCD 2011年第2期152-158,共7页
In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive se... In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security. 展开更多
关键词 identity-based broadcast encryption dual system encryption full security static assumption SUBGROUP provable security
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Hybrid Cloud Security by Revocable KUNodes-Storage with Identity-Based Encryption
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作者 S.Saravanakumar S.Chitra 《Computer Systems Science & Engineering》 SCIE EI 2022年第12期985-996,共12页
Cloud storage is a service involving cloud service providers providingstorage space to customers. Cloud storage services have numerous advantages,including convenience, high computation, and capacity, thereby attracti... Cloud storage is a service involving cloud service providers providingstorage space to customers. Cloud storage services have numerous advantages,including convenience, high computation, and capacity, thereby attracting usersto outsource data in the cloud. However, users outsource data directly via cloudstage services that are unsafe when outsourcing data is sensitive for users. Therefore, cipher text-policy attribute-based encryption is a promising cryptographicsolution in a cloud environment, and can be drawn up for access control by dataowners (DO) to define access policy. Unfortunately, an outsourced architectureapplied with attribute-based encryption introduces numerous challenges, including revocation. This issue is a threat to the data security of DO. Furthermore,highly secure and flexible cipher text-based attribute access control with role hierarchy user grouping in cloud storage is implemented by extending the KUNodes(revocation) storage identity-based encryption. Result is evaluated using Cloudsim, and our algorithm outperforms in terms of computational cost by consuming32 MB for 150-MB files. 展开更多
关键词 Cloud computing storage identification based revocation attribute based access control encryption DECRYPTION
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An Efficient Identity-Based Homomorphic Broadcast Encryption
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作者 Mei Cai 《Journal of Computer and Communications》 2019年第2期23-30,共8页
Broadcast encryption (BE) allows a sender to broadcast its message to a set of receivers in a single ciphertext. However, in broadcast encryption scheme, ciphertext length is always related to the size of the receiver... Broadcast encryption (BE) allows a sender to broadcast its message to a set of receivers in a single ciphertext. However, in broadcast encryption scheme, ciphertext length is always related to the size of the receiver set. Thus, how to improve the communication of broadcast encryption is a big issue. In this paper, we proposed an identity-based homomorphic broadcast encryption scheme which supports an external entity to directly calculate ciphertexts and get a new ciphertext which is the corresponding result of the operation on plaintexts without decrypting them. The correctness and security proofs of our scheme were formally proved. Finally, we implemented our scheme in a simulation environment and the experiment results showed that our scheme is efficient for practical applications. 展开更多
关键词 IDENTITY-based BROADCAST encryption Homomorphic COMMUNICATION
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OBLIVIOUS TRANSFER WITH ACCESS CONTROL AND IDENTITY-BASED ENCRYPTION WITH ANONYMOUS KEY ISSUING
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作者 Xu Lingling Zhang Fangguo Wen Yamin 《Journal of Electronics(China)》 2011年第4期571-579,共9页
In ACM'CCS 2009,Camenisch,et al.proposed the Oblivious Transfer with Access Control(AC-OT) in which each item is associated with an attribute set and can only be available,on request,to the users who have all the ... In ACM'CCS 2009,Camenisch,et al.proposed the Oblivious Transfer with Access Control(AC-OT) in which each item is associated with an attribute set and can only be available,on request,to the users who have all the attributes in the associated set.Namely,AC-OT achieves access control policy for conjunction of attributes.Essentially,the functionality of AC-OT is equivalent to the sim-plified version that we call AC-OT-SV:for each item,one attribute is associated with it,and it is requested that only the users who possess the associated attribute can obtain the item by queries.On one hand,AC-OT-SV is a special case of AC-OT when there is just one associated attribute with each item.On the other hand,any AC-OT can be realized by an AC-OT-SV.In this paper,we first present a concrete AC-OT-SV protocol which is proved to be secure in the model defined by Camenisch,et al..Then from the protocol,interestingly,a concrete Identity-Based Encryption(IBE) with Anonymous Key Issuing(AKI) is given which is just a direct application to AC-OT-SV.By comparison,we show that the AKI protocol we present is more efficient in communications than that proposed by Chow. 展开更多
关键词 Oblivious Transfer(OT) Access Control(AC) Identity-based encryption(IBE) Anonymous Key Issuing(AKI)
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Construction and Implementation of a Privacy-Preserving Identity-Based Encryption Architecture
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作者 David Bissessar Carlisle Adams 《Journal of Information Security》 2023年第4期304-329,共26页
A recent proposal by Adams integrates the digital credentials (DC) technology of Brands with the identity-based encryption (IBE) technology of Boneh and Franklin to create an IBE scheme that demonstrably enhances priv... A recent proposal by Adams integrates the digital credentials (DC) technology of Brands with the identity-based encryption (IBE) technology of Boneh and Franklin to create an IBE scheme that demonstrably enhances privacy for users. We refer to this scheme as a privacy-preserving identity-based encryption (PP-IBE) construction. In this paper, we discuss the concrete implementation considerations for PP-IBE and provide a detailed instantiation (based on q-torsion groups in supersingular elliptic curves) that may be useful both for proof-of-concept purposes and for pedagogical purposes. 展开更多
关键词 Identity-based encryption (IBE) Digital Credentials (DC) PRIVACY Pairing-based Cryptography Supersingular Elliptic Curve q-Torsion Group
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Security Analysis of a Privacy-Preserving Identity-Based Encryption Architecture
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作者 Carlisle Adams 《Journal of Information Security》 2022年第4期323-336,共14页
Identity-Based Encryption (IBE) has seen limited adoption, largely due to the absolute trust that must be placed in the private key generator (PKG)—an authority that computes the private keys for all the users in the... Identity-Based Encryption (IBE) has seen limited adoption, largely due to the absolute trust that must be placed in the private key generator (PKG)—an authority that computes the private keys for all the users in the environment. Several constructions have been proposed to reduce the trust required in the PKG (and thus preserve the privacy of users), but these have generally relied on unrealistic assumptions regarding non-collusion between various entities in the system. Unfortunately, these constructions have not significantly improved IBE adoption rates in real-world environments. In this paper, we present a construction that reduces trust in the PKG without unrealistic non-collusion assumptions. We achieve this by incorporating a novel combination of digital credential technology and bilinear maps, and making use of multiple randomly-chosen entities to complete certain tasks. The main result and primary contribution of this paper are a thorough security analysis of this proposed construction, examining the various entity types, attacker models, and collusion opportunities in this environment. We show that this construction can prevent, or at least mitigate, all considered attacks. We conclude that our construction appears to be effective in preserving user privacy and we hope that this construction and its security analysis will encourage greater use of IBE in real-world environments. 展开更多
关键词 Security Analysis Identity-based encryption (IBE) Reducing Trust Preserving Privacy Honest-but-Curious Attacker Malicious Attacker
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Privacy Preserving Scheme for Location-Based Services 被引量:1
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作者 Youssef Gahi Mouhcine Guennoun +1 位作者 Zouhair Guennoun Khalil El-Khatib 《Journal of Information Security》 2012年第2期105-112,共8页
Homomorphic encryption schemes make it possible to perform arithmetic operations, like additions and multiplications, over encrypted values. This capability provides enhanced protection for data and offers new researc... Homomorphic encryption schemes make it possible to perform arithmetic operations, like additions and multiplications, over encrypted values. This capability provides enhanced protection for data and offers new research directions, including blind data processing. Using homomorphic encryption schemes, a Location-Based Service (LBS) can process encrypted inputs to retrieve encrypted location-related information. The retrieved encrypted data can only be decrypted by the user who requested the data. The technology still faces two main challenges: the encountered processing time and the upper limit imposed on the allowed number of operations. However, the protection of users’ privacy achieved through this technology makes it attractive for more research and enhancing. In this paper we use homomorphic encryption schemes to build a fully secure system that allows users to benefit from location-based services while preserving the confidentiality and integrity of their data. Our novel system consists of search circuits that allow an executor (i.e. LBS server) to receive encrypted inputs/requests and then perform a blind search to retrieve encrypted records that match the selection criterion. A querier can send the user’s position and the service type he/she is looking for, in encrypted form, to a server and then the server would respond to the request without any knowledge of the contents of the request and the retrieved records. We further propose a prototype that improves the practicality of our system. 展开更多
关键词 PRIVACY LOCATION based SERVICES Homomorphic encryption
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Fog-Based Secure Framework for Personal Health Records Systems
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作者 Lewis Nkenyereye S.M.Riazul Islam +2 位作者 Mahmud Hossain MAbdullah-Al-Wadud Atif Alamri 《Computers, Materials & Continua》 SCIE EI 2021年第2期1937-1948,共12页
The rapid development of personal health records(PHR)systems enables an individual to collect,create,store and share his PHR to authorized entities.Health care systems within the smart city environment require a patie... The rapid development of personal health records(PHR)systems enables an individual to collect,create,store and share his PHR to authorized entities.Health care systems within the smart city environment require a patient to share his PRH data with a multitude of institutions’repositories located in the cloud.The cloud computing paradigm cannot meet such a massive transformative healthcare systems due to drawbacks including network latency,scalability and bandwidth.Fog computing relieves the load of conventional cloud computing by availing intermediate fog nodes between the end users and the remote servers.Assuming a massive demand of PHR data within a ubiquitous smart city,we propose a secure and fog assisted framework for PHR systems to address security,access control and privacy concerns.Built under a fog-based architecture,the proposed framework makes use of efficient key exchange protocol coupled with ciphertext attribute based encryption(CP-ABE)to guarantee confidentiality and fine-grained access control within the system respectively.We also make use of digital signature combined with CP-ABE to ensure the system authentication and users privacy.We provide the analysis of the proposed framework in terms of security and performance. 展开更多
关键词 Fog computing personal health records ciphertext attribute based encryption secure communications
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VANET Security through Group Broadcast Encryption
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作者 Eric Eduardo Bunese Eduardo Todt Luiz Carlos Pessoa Albini 《Journal of Computer and Communications》 2020年第8期22-35,共14页
VANET security is an evolving topic in mobile networks, as providing a secure layer of communications in such a dynamic and fast network is a challenge. The work presented in this article was conducted in order to ver... VANET security is an evolving topic in mobile networks, as providing a secure layer of communications in such a dynamic and fast network is a challenge. The work presented in this article was conducted in order to verify and evaluate the feasibility of applying group broadcast cryptography to the VANET environment, as an attempt to gain performance by decreasing the number of messages in the wireless network. Group broadcast is a symmetric/asymmetric hybrid cryptography method, aiming to merge the best of the two approaches without their major drawbacks. Simulations were set-up and run using the ONE simulator, comparing the usage of the three different cryptography approaches for VANETs. Results consider the number of connections, the number messages and the number of revocation messages per day. The resulting data promises that group broadcast encryption can be used to simplify the encrypting phase, reduce required storage and significantly decrease the number of messages in the network. 展开更多
关键词 VANET Security Group Broadcast encryption Group based VANET
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Hyper-chaos encryption using convolutional masking and model free unmasking
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作者 齐国元 Sandra Bazebo Matondo 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第5期161-166,共6页
In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos a... In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative. 展开更多
关键词 Qi hyper-chaos MASKING high-order differentiator chaos-based encryption
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Enabling Privacy Preservation and Decentralization for Attribute-Based Task Assignment in Crowdsourcing
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作者 Tianqing Liang 《Journal of Computer and Communications》 2020年第4期81-100,共20页
Crowdsourcing allows people who are endowed with certain skills to accomplish special tasks with incentive. Despite the state-of-art crowdsourcing schemes have guaranteed low overhead and considerable quality, most of... Crowdsourcing allows people who are endowed with certain skills to accomplish special tasks with incentive. Despite the state-of-art crowdsourcing schemes have guaranteed low overhead and considerable quality, most of them expose task content and user’s attribute information to a centralized server. These servers are vulnerable to single points of failure, the leakage of user’s privacy information, and lacking of transparency. We therefore explored an alternative design for task assignment based on the emerging decentralized blockchain technology. While enabling the advantages of the public blockchain, changing to open operations requires some additional technology and design to preserve the privacy of user’s information. To mitigate this issue, we proposed a secure task assignment scheme, which enables task content preservation and anonymous attribute requirement checking. Specifically, by adopting the cryptographic techniques, the proposed scheme enables task requester to safely place his task in a transparent blockchain. Furthermore, the proposed scheme divides the attribute verification process into public pre-verification and requester verification, so that the requester can check only the identity of the worker, instead of verifying the attributes one by one, thereby preserving the identity of worker while significantly reducing the requester’s calculation burden. Additionally, security analysis demonstrated unrelated entities cannot learn about the task content and identity information from all data uploaded by requester and worker. Performance evaluation showed the low computational overhead of our scheme. 展开更多
关键词 Crowdsourcing TASK ASSIGNMENT ATTRIBUTE-based encryption Blockchain Smart CONTRACT
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Identity-Based Steganography in Spatial Domain
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作者 Xuba Xu Qiankai Nie 《Journal of Computer and Communications》 2018年第3期68-77,共10页
This paper proposed an identity-based steganographic scheme, where a receiver with certain authority can recover the secret message ready for him, but cannot detect the existence of other secret messages. The proposed... This paper proposed an identity-based steganographic scheme, where a receiver with certain authority can recover the secret message ready for him, but cannot detect the existence of other secret messages. The proposed scheme created several separate covert communication channels tagged by the Fuzzy Identity-Based Encryption (FIBE) in one grayscale image. Then each channel is used to embed one secret message by using any content-aware steganographic scheme. Receivers with different attributes can extract different messages corresponded. The Experiments illustrated the feasibility of this identity-based secret message extraction. Further, the proposed scheme presents high undetectability against steganalytic attack launched by receivers without corresponded attributes. 展开更多
关键词 STEGANOGRAPHY MULTIPLE EMBEDDING FUZZY IDENTITY-based encryption
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Attribute-Based Secure Data Sharing with Efficient Revocation in Fog Computing
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作者 Asma Alotaibi Ahmed Barnawi Mohammed Buhari 《Journal of Information Security》 2017年第3期203-222,共20页
Fog computing is a concept that extends the paradigm of cloud computing to the network edge. The goal of fog computing is to situate resources in the vicinity of end users. As with cloud computing, fog computing provi... Fog computing is a concept that extends the paradigm of cloud computing to the network edge. The goal of fog computing is to situate resources in the vicinity of end users. As with cloud computing, fog computing provides storage services. The data owners can store their confidential data in many fog nodes, which could cause more challenges for data sharing security. In this paper, we present a novel architecture for data sharing in a fog environment. We explore the benefits of fog computing in addressing one-to-many data sharing applications. This architecture sought to outperform the cloud-based architecture and to ensure further enhancements to system performance, especially from the perspective of security. We will address the security challenges of data sharing, such as fine-grained access control, data confidentiality, collusion resistance, scalability, and the issue of user revocation. Keeping these issues in mind, we will secure data sharing in fog computing by combining attributebased encryption and proxy re-encryption techniques. Findings of this study indicate that our system has the response and processing time faster than classical cloud systems. Further, experimental results show that our system has an efficient user revocation mechanism, and that it provides high scalability and sharing of data in real time with low latency. 展开更多
关键词 ATTRIBUTE-based encryption FINE-GRAINED Access Control FOG COMPUTING PROXY Re-encryption User REVOCATION
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Parallel Key Insulated ID-Based Public Key Cryptographic Primitive with Outsourced Equality Test
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作者 Seth Alornyo Mustapha Adamu Mohammed +2 位作者 Bright Anibrika Selorm Kodzo Pious Akwasi Sarpong Michael Asante 《Journal of Computer and Communications》 2020年第12期197-213,共17页
Parallel key-insulation allows the use of multiple helper keys to protect private decryption keys during secret decryption key updates. This approach prevents decryption key leakage or exposure in insecure environment... Parallel key-insulation allows the use of multiple helper keys to protect private decryption keys during secret decryption key updates. This approach prevents decryption key leakage or exposure in insecure environment. We combined parallel key-insulated encryption (PKIE) with multiple helper keys and identity-based encryption with the equality test (IBE-ET) to obtain parallel key insulated ID-based public key encryption with outsourced equivalent test (PKI-IBPKE-ET). The scheme inherits the advantages of identity-based encryption (IBE), which simplifies certificate management for public key encryption. Furthermore, the parallel key-insulation with multiple helper mechanism was introduced in our scheme, which perfectly reduced the possibility of helper key exposure. Our scheme will enable the protection and periodic update of decryption keys in insecure environment. Our scheme achieves a weak indistinguishable identity chosen ciphertext (W-IND-ID-CCA) security in the random oracle model. Ultimately, it is observed that our scheme is feasible and practical through the experimental simulation and theoretical analysis. 展开更多
关键词 Identity-based encryption Equality Test Parallel Key-Insulated
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Research on the Security Protection Scheme for Container-Based Cloud Platform Node Based on BlockChain Technology 被引量:1
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作者 Xiaolan Xie Tao Huang Zhihong Guo 《国际计算机前沿大会会议论文集》 2018年第1期3-3,共1页
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Efficient hierarchical identity based encryption scheme in the standard model over lattices 被引量:2
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作者 Feng-he WANG Chun-xiao WANG Zhen-hua LIU 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2016年第8期781-791,共11页
Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption(HIBE) scheme in the standard model whose public key size is only(dm^2+ mn) log q b... Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption(HIBE) scheme in the standard model whose public key size is only(dm^2+ mn) log q bits and whose message-ciphertext expansion factor is only log q, where d is the maximum hierarchical depth and(n, m, q)are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is(2dm^2+ mn + m) log q. To reduce the message-ciphertext expansion factor of the proposed scheme to log q, the encryption algorithm of this scheme is built based on Gentry's encryption scheme, by which m^2 bits of plaintext are encrypted into m^2 log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks. 展开更多
关键词 Hierarchical identity based encryption scheme Lattice-based cryptography Standard model Learning with errors problem GAUSSIAN
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