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Blockchain and signcryption enabled asynchronous federated learning framework in fog computing
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作者 Zhou Zhou Youliang Tian +3 位作者 Jinbo Xiong Changgen Peng Jing Li Nan Yang 《Digital Communications and Networks》 2025年第2期442-454,共13页
Federated learning combines with fog computing to transform data sharing into model sharing,which solves the issues of data isolation and privacy disclosure in fog computing.However,existing studies focus on centraliz... Federated learning combines with fog computing to transform data sharing into model sharing,which solves the issues of data isolation and privacy disclosure in fog computing.However,existing studies focus on centralized single-layer aggregation federated learning architecture,which lack the consideration of cross-domain and asynchronous robustness of federated learning,and rarely integrate verification mechanisms from the perspective of incentives.To address the above challenges,we propose a Blockchain and Signcryption enabled Asynchronous Federated Learning(BSAFL)framework based on dual aggregation for cross-domain scenarios.In particular,we first design two types of signcryption schemes to secure the interaction and access control of collaborative learning between domains.Second,we construct a differential privacy approach that adaptively adjusts privacy budgets to ensure data privacy and local models'availability of intra-domain user.Furthermore,we propose an asynchronous aggregation solution that incorporates consensus verification and elastic participation using blockchain.Finally,security analysis demonstrates the security and privacy effectiveness of BSAFL,and the evaluation on real datasets further validates the high model accuracy and performance of BSAFL. 展开更多
关键词 Blockchain signcryption Federated learning ASYNCHRONOUS Fog computing
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Certificateless Proxy Identity-Based Signcryption Scheme Without Bilinear Pairings 被引量:8
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作者 亓延峰 唐春明 +2 位作者 娄裕 徐茂智 郭宝安 《China Communications》 SCIE CSCD 2013年第11期37-41,共5页
Signcryption, which was introduced by ZHEN~ is a cryptographic primitive that fulfils the functions of both digital signature and encryption and guarantees confidentiality, integrity and non-repudiation in a more effi... Signcryption, which was introduced by ZHEN~ is a cryptographic primitive that fulfils the functions of both digital signature and encryption and guarantees confidentiality, integrity and non-repudiation in a more effi- cient way. Certificateless signcryption and pro- xy signcryption in identity-based cryptography were proposed for different applications. Most of these schemes are constructed by bilinear pairings from elliptic curves. However, some schemes were recently presented without pai- rings. In this paper, we present a certificateless proxy identity-based signcryption scheme with- out bilinear pairings, which is efficient and secure. 展开更多
关键词 certificateless signcryption iden-tity-based cryptography proxy signcryption elliptic curve discrete logarithm problem
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Efficient and Provably Secure Multi-Recipient Signcryption from Bilinear Pairings 被引量:5
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作者 LI Fagen HU Yupu LIU Shuanggen 《Wuhan University Journal of Natural Sciences》 CAS 2007年第1期17-20,共4页
Signcryption is a cryptographic primitive that performs signature and encryption simultaneously, at lower computational costs and communication overheads than the signature-then- encryption approach. In this paper, we... Signcryption is a cryptographic primitive that performs signature and encryption simultaneously, at lower computational costs and communication overheads than the signature-then- encryption approach. In this paper, we propose an efficient multi-recipient signcryption scheme based on the bilinear pairings, which broadcasts a message to multiple users in a secure and authenticated manner. We prove its semantic security and unforgeability under the Gap Diffie-Hellman problem assumption in the random oracle model. The proposed scheme is more efficient than re-signcrypting a message n times using a signcryption scheme in terms of computational costs and communication overheads. 展开更多
关键词 signcryption multi-recipient signcryption bilinear pairings provable security
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Concurrent Signcryption Using Bilinear Pairings for E-commerce
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作者 罗铭 邹春华 +1 位作者 胡军 闻英友 《China Communications》 SCIE CSCD 2011年第2期1-11,共11页
Concurrent signature was introduced as an efficient approach to solving the problem of fair exchange of signatures. Almost all fair exchange e-commerce protocols based on concurrent signature that have been proposed u... Concurrent signature was introduced as an efficient approach to solving the problem of fair exchange of signatures. Almost all fair exchange e-commerce protocols based on concurrent signature that have been proposed until now either do not provide message privacy protection or adopt the sign-then-encrypt scheme to provide confidentiality. However,confidentiality is an important requirement of fair exchange e-commerce protocol. In this paper,a new concept called concurrent signcryption which combines the concepts of concurrent signature and signcryption together to resolve the confidentiality problem in e-commerce systems based on concurrent signature. We also propose a concurrent signcryption scheme using bilinear pairings and prove its security in the random oracle model. Compared with the sign-then-encrypt scheme using bilinear pairings,our scheme enjoys shorter message length and less operation cost. Moreover,in our scheme the two ambiguous signcryptions can be published in any order. 展开更多
关键词 concurrent signature signcryption concurrent signcryption random oracle
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An Efficient Proxy Blind Signcryption Scheme for IoT
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作者 Aamer Khan Insaf Ullah +3 位作者 Fahad Algarni Muhammad Naeem M.Irfan Uddin Muhammad Asghar Khan 《Computers, Materials & Continua》 SCIE EI 2022年第3期4293-4306,共14页
Recent years have witnessed growing scientific research interest in the Internet of Things(IoT)technologies,which supports the development of a variety of applications such as health care,Industry 4.0,agriculture,ecol... Recent years have witnessed growing scientific research interest in the Internet of Things(IoT)technologies,which supports the development of a variety of applications such as health care,Industry 4.0,agriculture,ecological data management,and other various domains.IoT utilizes the Internet as a prime medium of communication for both single documents as well as multi-digital messages.However,due to the wide-open nature of the Internet,it is important to ensure the anonymity,untraceably,confidentiality,and unforgeability of communication with efficient computational complexity and low bandwidth.We designed a light weight and secure proxy blind signcryption for multi-digital messages based on a hyperelliptic curve(HEC).Our results outperform the available schemes in terms of computational cost and communication bandwidth.The designed scheme also has the desired authentication,unforgeability of warrants and/or plaintext,confidentiality,integrity,and blindness,respectively.Further,our scheme is more suitable for devices with low computation power such as mobiles and tablets. 展开更多
关键词 Proxy signcryption multi-digital-documents proxy blind signcryption hyperelliptic curve IOT
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Provably Secure General Aggregate Signcryption Scheme in the Random Oracle Model 被引量:14
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作者 Qi Zhenghua Ren Xunyi Yang Geng 《China Communications》 SCIE CSCD 2012年第11期107-116,共10页
To reduce the size of certificate chains and the ciphertext size in secure routing protocols, a General Aggregate Signcryption Scheme (GASC) is presented. In GASC, an identity-based signcryption algorithm and an aggre... To reduce the size of certificate chains and the ciphertext size in secure routing protocols, a General Aggregate Signcryption Scheme (GASC) is presented. In GASC, an identity-based signcryption algorithm and an aggregate signature algorithm are combined in a practical and secure manner to form the general aggregate signcryption scheme's schema and concept, and a new secure, efficiently general aggregate signcryption scheme, which allows the aggregation of n distinct signcryptions by n distinct users on n distinct messages, is proposed. First, the correction of the GASC scheme is analyzed. Then, we formally prove the security of GASC in the random oracle models IND-CCA2 and EUF-CMA under the DBDHP assumption and the DLP assumption, respectively. The results show that the GASC scheme is not only secure against any probabilistic polynomial-time IND-GASC-CCA2 and EUF-GASC-CMA adversary in the random oracle models but also efficient in pairing ê computations. In addition, the GASC scheme gives an effective remedy to the key escrow problem, which is an inherent issue in IBC by splitting the private key into two parts, and reduces the communication complexity by eliminating the interaction among the senders (signers) before the signcryption generation. 展开更多
关键词 identity-based cryptography signcryption aggregate signature bilinear pairing
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Provably Secure Certificateless Ring Signcryption Scheme 被引量:11
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作者 祁正华 杨庚 任勋益 《China Communications》 SCIE CSCD 2011年第3期99-106,共8页
Ring signcryption enables a user to send a message confidentially and authentically to a specific receiver in an anonymous way.One of the main reasons for the slow adoption of identity-based cryptography is the inhere... Ring signcryption enables a user to send a message confidentially and authentically to a specific receiver in an anonymous way.One of the main reasons for the slow adoption of identity-based cryptography is the inherent key escrow problem.In this paper a new certificateless ring signcryption scheme from pairings is presented.It is escrow free in that no KGC is able to decrypt ciphertexts itself.We then formally prove the security of the new scheme in the random oracle model IND-CCA2 and EUF-CMA. 展开更多
关键词 ring signcryption certificateless cryptography bilinear pairing
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Analysis and Improvement of Authenticatable Ring Signcryption Scheme 被引量:9
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作者 李发根 Shirase Masaaki Takagi Tsuyoshi 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第6期679-683,共5页
We show that the Zhang-Yang-Zhu-Zhang identity-based authenticatable ring signcryption scheme is not secure against chosen plaintext attacks.Furthermore, we propose an improved scheme that remedies the weakness of the... We show that the Zhang-Yang-Zhu-Zhang identity-based authenticatable ring signcryption scheme is not secure against chosen plaintext attacks.Furthermore, we propose an improved scheme that remedies the weakness of the Zhang-Yang-Zhu-Zhang scheme.The improved scheme has shorter ciphertext size than the Zhang-Yang-Zhu-Zhang scheme.We then prove that the improved scheme satisfies confidentiality, unforgeability, anonymity and authenticatability. 展开更多
关键词 identity-based cryptography bilinear pairings ring signcryption ring signature
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Multi-Receiver Signcryption Scheme with Multiple Key Generation Centers through Public Channel in Edge Computing 被引量:5
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作者 Lipeng Wang Zhi Guan +1 位作者 Zhong Chen Mingsheng Hu 《China Communications》 SCIE CSCD 2022年第4期177-198,共22页
The emerging edge computing technology for the Internet of Things has been playing an important role in our daily life. It is promising to utilize a multi-receiver signcryption scheme to protect the transmission data ... The emerging edge computing technology for the Internet of Things has been playing an important role in our daily life. It is promising to utilize a multi-receiver signcryption scheme to protect the transmission data when an edge device broadcasts its sensing data to many different end devices at a time.There are several things to consider when we design a signcryption scheme. First existing schemes need to maintain a secure channel to generate the user private key, which may increase economic costs. Second the system private key of those schemes is kept secret by a single key generation center(KGC), and the single point of failure of KGC may compromise the whole system. For this, we propose a multi-receiver multimessage signcryption scheme without the secure channel. Firstly the scheme allows KGC to send secrets through the public channel, which reduces maintenance costs. Secondly, to eliminate the single point of failure, the scheme utilizes multiple KGCs to manage the system private key, and updates the secret of each KGC periodically to resist advanced persistent threat attacks. We demonstrate that the proposed scheme can achieve expected security properties. Performance analysis shows that it is with shorter ciphertext length and higher efficiency. 展开更多
关键词 internet of things signcryption edge computing UNFORGEABILITY CONFIDENTIALITY
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Secure and efficient multi-message and multi-receiver ID-based signcryption for rekeying in ad hoc networks 被引量:5
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作者 邱婧 BAI Jun +1 位作者 SONG Xin-chuan HOU Su-mei 《Journal of Chongqing University》 CAS 2013年第2期91-96,共6页
In this paper, the security technology of ad hoc networks is studied.To improve the previous multi-receiver signcryption schemes, an ID-based multi-message and multi-receiver signcryption scheme for rekeying in ad hoc... In this paper, the security technology of ad hoc networks is studied.To improve the previous multi-receiver signcryption schemes, an ID-based multi-message and multi-receiver signcryption scheme for rekeying in ad hoc networks is proposed.In this scheme, a sender can simultaneously signcrypt n messeges for n receivers, and a receiver can unsigncrypt the ciphertext to get his message with his own private key.An analysis of this scheme indicates that it achieves authenticity and confidentiality in the random oracle model while being of lower computation and communication overhead.Finally, for the application of our scheme in ad hoc, a threshold key updating protocol for ad hoc networks is given. 展开更多
关键词 signcryption multi-receiver multi-message bilinear pairings provable security ad hoc networks introduction
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An Efficient Identity-Based Anonymous Signcryption Scheme 被引量:4
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作者 YU Yong LI Fagen XU Chunxiang SUN Ying 《Wuhan University Journal of Natural Sciences》 CAS 2008年第6期670-674,共5页
Signcryption is a cryptographic primitive that performs encryption and signature in a single logical step more efficiently than sign-then-encrypt approach. Till now, various kinds of signcryption schemes have been pro... Signcryption is a cryptographic primitive that performs encryption and signature in a single logical step more efficiently than sign-then-encrypt approach. Till now, various kinds of signcryption schemes have been proposed. Among them, the requirement of signcrypter's privacy protection is needful in some practical applications. In this paper, a new identity-based anonymous signcryption scheme from hilinear pairings, which is the organic combination of identity-based ring signature and encryption scheme, is proposed. The proposed scheme is indistinguishable against the chosen ciphertext attack under the Decisional Bilinear Diffie-Hellman assumption in the random oracle model. Its unforgeability relies on the computational Diffieellman problem. Compared with the previous schemes, the new scheme is more efficient in computation. 展开更多
关键词 IDENTITY-BASED ring signature anonynaous signcryption bilinear pairing
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Efficient Identity Based Signcryption Scheme with Public Verifiability and Forward Security 被引量:2
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作者 FEIFei-yu CHENWen CHENKe-fei MAChang-she 《Wuhan University Journal of Natural Sciences》 CAS 2005年第1期248-250,共3页
In this paper, we point out that Libert and Quisquater’s signcryption scheme cannot provide public verifiability. Then we present a new identity based signcryption scheme using quadratic residue and pairings over ell... In this paper, we point out that Libert and Quisquater’s signcryption scheme cannot provide public verifiability. Then we present a new identity based signcryption scheme using quadratic residue and pairings over elliptic curves. It combines the functionalities of both public verifiability and forward security at the same time. Under the Bilinear Diffie-Hellman and quadratic residue assumption, we describe the new scheme that is more secure and can be some-what more efficient than Libert and Quisquater’s one. 展开更多
关键词 signcryption identity based public verifiability forward security
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New Multivariate-Based Certificateless Hybrid Signcryption Scheme for Multi-Recipient 被引量:2
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作者 HAN Yiliang YUE Zelun +1 位作者 FANG Dingyi YANG Xiaoyuan 《Wuhan University Journal of Natural Sciences》 CAS 2014年第5期433-440,共8页
With the development of quantum computer, multivariate public key cryptography withstanding quantum attack has became one of the research focus. The existed signcryption schemes from discrete logarithm and bilinear pa... With the development of quantum computer, multivariate public key cryptography withstanding quantum attack has became one of the research focus. The existed signcryption schemes from discrete logarithm and bilinear paring are facing the serious threats. Based on multivariate public key cryptography, a new certificateless multi-receiver hybrid signcryption scheme has been proposed. The proposal reduced the cipher text and could handle arbitrary length messages by employing randomness reusing and hybrid encryption, as well as keeping security. In the random oracle model, the scheme's confidentiality could withstand the IND-CCA2 adversary and its unforgeability could withstand the UF-CMA adversary under the hardness of multivariat quadratic (MQ) problem and isomorphism of polynomials (IP) assumption. It has less computation overhead and higher transmission efficiency than others. It reduced 33% cipher data compared with the existed similar scheme. 展开更多
关键词 multivariate public key cryptography certificateless hybrid signcryption multi-receiver post-quantum cryptography
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Cryptanalysis and Improvement of Signcryption Schemes on Elliptic Curves 被引量:2
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作者 LIXiang-xue CHENKe-fei LIShi-qun 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第1期231-234,共4页
In this paper, we analyze two signcryption schemes on elliptic curves proposed by Zheng Yu-liang and Hideki Imai. We point out a serious problem with the schemes that the elliptic curve based signcryption schemes lose... In this paper, we analyze two signcryption schemes on elliptic curves proposed by Zheng Yu-liang and Hideki Imai. We point out a serious problem with the schemes that the elliptic curve based signcryption schemes lose confidentiality to gain non-repudiation. We also propose two improvement versions that not only overcome the security leak inherent in the schemes but also provide public verifiability or forward security. Our improvement versions require smaller computing cost than that required by signature-then-encryption methods. 展开更多
关键词 signcryption elliptic curve CRYPTANALYSIS
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A New Efficient Blind Signcryption 被引量:2
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作者 YU Xiuying HE Dake 《Wuhan University Journal of Natural Sciences》 CAS 2008年第6期662-664,共3页
In a blind signcryption, besides the functions of digital signature and encryption algorithm for authentication and confidentiality, a user can delegates another user's capability with the anonymity of the participan... In a blind signcryption, besides the functions of digital signature and encryption algorithm for authentication and confidentiality, a user can delegates another user's capability with the anonymity of the participants guaranteed. Some blind signcryptions were proposed but without a blind signcryption with public public verifiability. In this paper, verifiability that is proved to be efficient and secure is proposed. Through the security analysis, we proved that the scheme can offer confidentiality, integrity, unforgeability, non-repudiation and public verifiability. The coming research direction is also summarized. 展开更多
关键词 ANONYMITY blind signcryption public verifiability
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A Secure Signcryption Scheme for Electronic Health Records Sharing in Blockchain 被引量:2
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作者 Xizi Peng Jinquan Zhang +3 位作者 Shibin Zhang Wunan Wan Hao Chen Jinyue Xia 《Computer Systems Science & Engineering》 SCIE EI 2021年第5期265-281,共17页
In the existing Electronic Health Records(EHRs),the medical information of patients is completely controlled by various medical institutions.As such,patients have no dominant power over their own EHRs.These personal d... In the existing Electronic Health Records(EHRs),the medical information of patients is completely controlled by various medical institutions.As such,patients have no dominant power over their own EHRs.These personal data are not only inconvenient to access and share,but are also prone to cause privacy disclosure.The blockchain technology provides a new development direction in the medical field.Blockchain-based EHRs are characterized by decentralization,openness and non-tampering of records,which enable patients to better manage their own EHRs.In order to better protect the privacy of patients,only designated receivers can access EHRs,and receivers can authenticate the sharer to ensure that the EHRs are real and effective.In this study,we propose an identity-based signcryption scheme with multiple authorities for multiple receivers,which can resist N-1 collusion attacks among N authorities.In addition,the identity information of receivers is anonymous,so the relationship between them and the sharer is not disclosed.Under the random oracle model,it was proved that our scheme was secure and met the unforgeability and confidentiality requirements of signcryption.Moreover,we evaluated the performance of the scheme and found that it had the moderate signcryption efficiency and excellent signcryption attributes. 展开更多
关键词 Electronic health records blockchain identity-based signcryption multiple authorities multiple receivers
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Convertible Proxy Signcryption Scheme 被引量:1
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作者 李继国 李建中 +1 位作者 曹珍富 张亦辰 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2004年第2期209-213,共5页
In 1996, Mambo et al introduced the concept of proxy signature. However, proxy signature can only provide the delegated authenticity and cannot provide confidentiality. Recently, Gamage et al and Chan and Wei proposed... In 1996, Mambo et al introduced the concept of proxy signature. However, proxy signature can only provide the delegated authenticity and cannot provide confidentiality. Recently, Gamage et al and Chan and Wei proposed different proxy signcryption schemes respectively, which extended the concept of proxy signature. However, only the specified receiver can decrypt and verify the validity of proxy signcryption in their schemes. To protect the receiver's benefit in case of a later dispute, Wu and Hsu proposed a convertible authenticated encryption scheme, which can enable the receiver to convert signature into an ordinary one that can be verified by anyone. Based on Wu and Hsu' s scheme and improved Kim's scheme, we propose a convertible proxy signcryption scheme. The security of the proposed scheme is based on the intractability of reversing the one-way hash function and solving the discrete logarithm problem. The proposed scheme can satisfy all properties of strong proxy signature and withstand the public key substitution attack and does not use secure channel. In addition, the proposed scheme can be extended to convertible threshold proxy signcryption scheme. 展开更多
关键词 proxy signcryption nonrepudiation digital signature proxy signature
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An Access Control Scheme Using Heterogeneous Signcryption for IoT Environments 被引量:1
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作者 Insaf Ullah Hira Zahid +1 位作者 Fahad Algarni Muhammad Asghar Khan 《Computers, Materials & Continua》 SCIE EI 2022年第3期4307-4321,共15页
When the Wireless Sensor Network(WSN)is combined with the Internet of Things(IoT),it can be employed in a wide range of applications,such as agriculture,industry 4.0,health care,smart homes,among others.Accessing the ... When the Wireless Sensor Network(WSN)is combined with the Internet of Things(IoT),it can be employed in a wide range of applications,such as agriculture,industry 4.0,health care,smart homes,among others.Accessing the big data generated by these applications in Cloud Servers(CSs),requires higher levels of authenticity and confidentiality during communication conducted through the Internet.Signcryption is one of the most promising approaches nowadays for overcoming such obstacles,due to its combined nature,i.e.,signature and encryption.A number of researchers have developed schemes to address issues related to access control in the IoT literature,however,the majority of these schemes are based on homogeneous nature.This will be neither adequate nor practical for heterogeneous IoT environments.In addition,these schemes are based on bilinear pairing and elliptic curve cryptography,which further requires additional processing time and more communication overheads that is inappropriate for real-time communication.Consequently,this paper aims to solve the above-discussed issues,we proposed an access control scheme for IoT environments using heterogeneous signcryption scheme with the efficiency and security hardiness of hyperelliptic curve.Besides the security services such as replay attack prevention,confidentiality,integrity,unforgeability,non-repudiations,and forward secrecy,the proposed scheme has very low computational and communication costs,when it is compared to existing schemes.This is primarily because of hyperelliptic curve lighter nature of key and other parameters.The AVISPA tool is used to simulate the security requirements of our proposed scheme and the results were under two backbends(Constraint Logic-based Attack Searcher(CL-b-AtSER)and On-the-Fly Model Checker(ON-t-FL-MCR))proved to be SAFE when the presented scheme is coded in HLPSL language.This scheme was proven to be capable of preventing a variety of attacks,including confidentiality,integrity,unforgeability,non-repudiation,forward secrecy,and replay attacks. 展开更多
关键词 Internet of Things(IoT) access control big data heterogeneous signcryption
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A NEW GROUP-ORIENTED PUBLICLY VERIABLETHRESHOLD SIGNCRYPTION SCHEME 被引量:1
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作者 Chen Shangdi Bian Guangxu 《Journal of Electronics(China)》 2013年第6期567-573,共7页
Through cryptanalysis of the improved scheme of a generalized group-oriented threshold signcryption schemes,it is found that the improved scheme can effectively resist conspiracy attack and forgery attack,but does not... Through cryptanalysis of the improved scheme of a generalized group-oriented threshold signcryption schemes,it is found that the improved scheme can effectively resist conspiracy attack and forgery attack,but does not have semantic security and public verification function,and sends threshold signcryption by the secret secure channel,which increases the communication costs and potential safety hazards of the system.A new group-oriented publicly verifiable threshold signcryption scheme is proposed on the basis of the improved scheme,the new scheme overcomes the drawbacks of the improved scheme,which not only provides with semantic security and public verification function,but also can send threshold signcryption by the public channel. 展开更多
关键词 Group-oriented Threshold signcryption Public verifiable Semantic security
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Optimal Adaptive Genetic Algorithm Based Hybrid Signcryption Algorithm for Information Security
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作者 R.Sujatha M.Ramakrishnan +1 位作者 N.Duraipandian B.Ramakrishnan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2015年第5期47-68,共22页
The functions of digital signature and public key encryption are simultaneously fulfilled by signcryption,which is a cryptographic primitive.To securely communicate very large messages,the cryptographic primitive call... The functions of digital signature and public key encryption are simultaneously fulfilled by signcryption,which is a cryptographic primitive.To securely communicate very large messages,the cryptographic primitive called signcryption efficiently implements the same and while most of the public key based systems are suitable for small messages,hybrid encryption(KEM-DEM)provides a competent and practical way.In this paper,we develop a hybrid signcryption technique.The hybrid signcryption is based on the KEM and DEM technique.The KEM algorithm utilizes the KDF technique to encapsulate the symmetric key.The DEM algorithm utilizes the Adaptive Genetic Algorithm based Elliptic curve cryptography algorithm to encrypt the original message.Here,for the security purpose,we introduce the three games and we proved the attackers fail to find the security attributes of our proposed signcryption algorithm.The proposed algorithm is analyzed with Daniel of Service(DOS),Brute Force attack and Man In Middle(MIM)attacks to ensure the secure data transaction. 展开更多
关键词 HYBRID signcryption KEM DEM Adaptive GENETIC ALGORITHM EllipticCurve CRYPTOGRAPHY
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