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Journal articles on the topic 'Proxy signature'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Xin, Xiangjun, Qinglan Yang, and Fagen Li. "Quantum proxy signature with provable security." Modern Physics Letters A 35, no. 24 (2020): 2050197. http://dx.doi.org/10.1142/s0217732320501977.

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A quantum proxy signature scheme makes the proxy signer can generate a quantum signature on behalf of the original signer. Although many quantum proxy signature schemes have been proposed, none of them can be formally proved to be secure. There is not even security model for the quantum proxy signatures. Some quantum proxy signature schemes have been proved to be insecure against forgery attacks. In this paper, first, the formal definition and the corresponding security model for the quantum proxy signatures are proposed. Second, based on the Hadamard operator and the controlled NOT operation,

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2

Wu, Jian. "Identity-Based Proxy Signcryption Schemes." Applied Mechanics and Materials 380-384 (August 2013): 2605–8. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.2605.

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Identity-based encryption and signature schemes that allow any pair of users to communicate securely and to verify each other's signatures without verifying certificate. A signcryption is a primitive that provides the properties of both digital signatures and encryption schemes in a way that is more efficient than signing and encrypting separately. Proxy signature schemes are a variation of ordinary digital signature scheme that allow a proxy signer to sign messages on behalf of the original singer which proxy signcryption simultaneously fulfill both the functions of signature and encryption i

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3

Wei, Lulu, Daofeng Li, and Zhiqiang Liu. "Provable Secure Attribute-Based Proxy Signature Over Lattice Small Integer Solution Problem in Random Oracle Model." Electronics 12, no. 7 (2023): 1619. http://dx.doi.org/10.3390/electronics12071619.

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Current proxy signature schemes are mostly identity-based proxy signatures that distinguish users by identity. This signature method faces some problems, such as identity information leakage and single access control. Attribute-based proxy signature (ABPS) divides the signer’s identity information into a collection of attributes; thus, users’ identity information can be protected and access control can become fine-grained. With the development of quantum computers, the security of signature schemes based on traditional number theory problems is under threat. Therefore, we construct a new attri

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4

Deng, Yu Qiao. "A Blind Proxy Re-Signatures Scheme Based on Random Oracle." Advanced Materials Research 204-210 (February 2011): 1062–65. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.1062.

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Digital signature schemes allow a signer to transform any message into a signed message, such that anyone can verify the validity of the signed message using the signer’s public key, but only the signer can generate signed messages. A proxy re-signature, which is a type of digital signatures, has significant applications in many areas. Proxy signature scheme was first introduced by Blaze, Bleumer, and Strauss, but that scheme is inefficient and with limited features. After that, some Proxy re-signature schemes were proposed by researchers. This paper constructs a blind proxy re-signatures sche

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5

TZENG, SHIANG-FENG, CHENG-CHI LEE, and MIN-SHIANG HWANG. "A BATCH VERIFICATION FOR MULTIPLE PROXY SIGNATURE." Parallel Processing Letters 21, no. 01 (2011): 77–84. http://dx.doi.org/10.1142/s0129626411000084.

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In this article, we proposed a batch verification scheme for multiple proxy signatures to reduce the proxy signature verification time. The proposed scheme is not only efficient because it does not verify each individual proxy signature separately, but also secure because it can detect forged multiple proxy signatures without failure.

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6

Luo, Jiaoyan, Liming Zuo, and Hao Liu. "Quantum-Resistant Lattice-Based Proxy Signature." Symmetry 17, no. 2 (2025): 261. https://doi.org/10.3390/sym17020261.

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With the advancement of quantum computing, the utilization of quantum algorithms such as Shor’s algorithm enables the efficient resolution of problems that are intractable in classical computing paradigms, posing a significant threat to traditional signature schemes. Lattice-based cryptography is considered one of the most promising post-quantum cryptographic algorithms due to its computational advantages and potential resistance to quantum attacks. Proxy signature is an authorization mechanism that allows the original signer to delegate the signing power to a proxy. The security of existing p

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7

Feng, Yanyan, Qian Zhang, Jinjing Shi, Shuhui Chen, and Ronghua Shi. "Quantum Proxy Signature Scheme with Discrete Time Quantum Walks and Quantum One-Time Pad CNOT Operation." Applied Sciences 10, no. 17 (2020): 5770. http://dx.doi.org/10.3390/app10175770.

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The quantum proxy signature is one of the most significant formalisms in quantum signatures. We put forward a quantum proxy signature scheme using quantum walk-based teleportation and quantum one-time pad CNOT (QOTP-CNOT) operation, which includes four phases, i.e., initializing phase, authorizing phase, signing phase and verifying phase. The QOTP-CNOT is achieved by attaching the CNOT operation upon the QOTP and it is applied to produce the proxy signature state. The quantum walk-based teleportation is employed to transfer the encrypted message copy derived from the binary random sequence fro

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8

James, Salome, Gowri Thumbur, and Vasudeva Reddy P. "Pairing-Free Identity-Based Proxy Signature Scheme With Message Recovery." International Journal of Information Security and Privacy 15, no. 1 (2021): 117–37. http://dx.doi.org/10.4018/ijisp.2021010106.

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In many real-world situations, signature schemes with message recovery plays a very important role to minimize the bandwidth for efficient communications. A proxy signature scheme is a kind of digital signature scheme that allows an original signer to designate his/her signing capacity to a proxy signer. The proxy signer generates a signature on a message on behalf of the original signer. Such signatures are very useful in various applications where the delegation rights is quite common, especially in distributed systems and grid computing. This paper presents a pairing-free proxy signature wi

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9

Zhang, Jian Hong, Min Xu, and Xiu Na Su. "An Efficient and Provably Secure Proxy Signature Scheme." Advanced Materials Research 211-212 (February 2011): 876–80. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.876.

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As a concept of delegating signing rights for digital signatures, proxy signature is a well studied subject in cryptography. Proxy signature is an important delegation technique. It plays an important role in auto-office system. In this paper, we give a secure and efficient proxy signature scheme. The security of the scheme is base on the fixed inversion problem of bilinear map. It has the following advantages: simple construction, short size and low computation.

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10

Liu, Yu-Chuan, Hsiang-An Wen, Chun-Li Lin, and Tzonelih Hwang. "Proxy-protected signature secure against the undelegated proxy signature attack." Computers & Electrical Engineering 33, no. 3 (2007): 177–85. http://dx.doi.org/10.1016/j.compeleceng.2006.11.004.

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11

Li, Xiangxue, and Kefei Chen. "ID-based multi-proxy signature, proxy multi-signature and multi-proxy multi-signature schemes from bilinear pairings." Applied Mathematics and Computation 169, no. 1 (2005): 437–50. http://dx.doi.org/10.1016/j.amc.2004.10.046.

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12

Liao, Da Jian, and Yuan Sheng Tang. "Comment on Lee J-s et al.'s Identity-Based Designated Verifer Proxy Signature Scheme and its Improvement." Advanced Materials Research 143-144 (October 2010): 753–57. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.753.

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In a designated verifier proxy signature scheme, one can delegate his or her signing capability to another user in such a way that the latter can sign messages on behalf of the former, but the validity of the resulting signatures can only be verified by the designated verifier. Recently, Lee J-s et al. proposed a new ID-Based designated verifier proxy signature scheme. They didn't analysis the security of their scheme. We found out that anyone can generate a valid signature on any message m and mw he choose. To overcome this flaw in Lee J-s et al.'s scheme, we formalized the notion of designat

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13

Xie, Qi. "Attacks on Self-Certified Multi-Proxy Signature Schemes with Message Recovery." Applied Mechanics and Materials 135-136 (October 2011): 316–20. http://dx.doi.org/10.4028/www.scientific.net/amm.135-136.316.

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Signature schemes with message recovery based on self-certified public keys can reduce the amount of communications and computations, since the signature verification, the public key authentication and the message recovery are simultaneously carried out in a single logical step. Integrating self-certified public-key systems and the message recovery signature schemes, in 2009, Wu et al. proposed two multi-proxy signatures based on the discrete logarithms over a finite field and the elliptic curve discrete logarithms. The proxy warrant revision attacks are proposed, and it will show that Wu et a

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14

Chande, Manoj Kumar, and Balwant Singh Thakur. "Proxy-Protected Proxy Multi-Signature Based on Elliptic Curve." International Journal of Informatics and Communication Technology (IJ-ICT) 3, no. 1 (2014): 67. http://dx.doi.org/10.11591/ijict.v3i1.pp67-72.

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In this work, we propose a proxy-protected proxy multi-signature scheme based on EllipticCurve Digital Signature Algorithm (ECDSA), which aims at providing data authenticity,integrity, and non-repudiation to satisfy the basic properties of partial delegation proxy signaturedescribed by Mambo et al. as well as strong proxy signature properties defined byLee et. al. The proposed signing/verifying scheme combines the advantages of proxyprotectedsignature and multi-signature scheme. The security of the proposed schemes isbased on the difficulty of breaking the elliptic curve discrete logarithm pro

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15

Menon, Tulasi. "An Identity Based Proxy Re-Signature Scheme." International Journal of Engineering and Technology 4, no. 3 (2012): 303–9. http://dx.doi.org/10.7763/ijet.2012.v4.370.

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16

Yi, Lijang, Guoqiang Bai, and Guozhen Xiao. "Proxy multi-signature scheme: A new type of proxy signature scheme." Electronics Letters 36, no. 6 (2000): 527. http://dx.doi.org/10.1049/el:20000422.

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17

Li, Fengyin, Mengjiao Yang, Zhihao Song, Ping Wang, and Guoping Li. "Post-Quantum Secure Identity-Based Proxy Blind Signature Scheme on a Lattice." Entropy 25, no. 8 (2023): 1157. http://dx.doi.org/10.3390/e25081157.

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Blind signatures have been widely applied when privacy preserving is required, and the delegation of blind signature rights and a proxy blind signature (Proxy-BS) become necessary when the signer cannot sign. Existing Proxy-BS schemes are based on traditional cryptographically hard problems, and they cannot resist quantum attacks. Moreover, most current Proxy-BS schemes depend on public key infrastructure (PKI), which leads to high certificate storage and management overhead. To simplify key management and resist quantum attacks, we propose a post-quantum secure identity-based proxy blind sign

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18

Heo, Jinseok, Hohyeon Jeong, and Eunseok Lee. "Proxy Signature, ID-based Partially Blind Signature and Proxy Partially Blind Signature using Bilinear-pairing." KIISE Transactions on Computing Practices 26, no. 12 (2020): 556–60. http://dx.doi.org/10.5626/ktcp.2020.26.12.556.

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19

Tolyupa, Eugene A. "Some proxy signature protocols." Prikladnaya diskretnaya matematika, no. 11 (March 1, 2011): 70–77. http://dx.doi.org/10.17223/20710410/11/5.

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20

Du, Hongzhen, and Qiaoyan Wen. "Certificateless proxy multi-signature." Information Sciences 276 (August 2014): 21–30. http://dx.doi.org/10.1016/j.ins.2014.02.043.

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21

Jin, Zhengping, and Qiaoyan Wen. "Certificateless multi-proxy signature." Computer Communications 34, no. 3 (2011): 344–52. http://dx.doi.org/10.1016/j.comcom.2010.06.013.

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22

Yang, Piyi, Zhenfu Cao, and Xiaolei Dong. "Threshold proxy re-signature." Journal of Systems Science and Complexity 24, no. 4 (2011): 816–24. http://dx.doi.org/10.1007/s11424-011-8370-3.

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23

Tang, Fei, Hongda Li, Qihua Niu, and Bei Liang. "Secure Mobile Agent from Leakage-Resilient Proxy Signatures." Mobile Information Systems 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/901418.

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A mobile agent can sign a message in a remote server on behalf of a customer without exposing its secret key; it can be used not only to search for special products or services, but also to make a contract with a remote server. Hence a mobile agent system can be used for electronic commerce as an important key technology. In order to realize such a system, Lee et al. showed that a secure mobile agent can be constructed using proxy signatures. Intuitively, a proxy signature permits an entity (delegator) to delegate its signing right to another entity (proxy) to sign some specified messages on b

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24

Zhou, Xuan Wu. "Further Study on System Optimization in Proxy Signature." Applied Mechanics and Materials 20-23 (January 2010): 518–24. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.518.

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In the paper, we analyzed optimization algorithms for proxy signature and presented an optimized proxy signature scheme based on discrete logarithm cryptosystem. In the scheme, the signature entrusting parameters are generated with private keys of original signer and the proxy signer; dishonest proxy signer and outer adversaries can not attack secret parameters or other proxy signature with feasible polynomial algorithm, thus the scheme provides effective protection for the secrecy of proxy signers and also renders reasonable supervision on the proxy right. By utilizing random algorithms in si

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25

Chaudhari, Shilpa, R. Aparna, and Archana Rane. "A Survey on Proxy Re-Signature Schemes for Translating One Type of Signature to Another." Cybernetics and Information Technologies 21, no. 3 (2021): 24–49. http://dx.doi.org/10.2478/cait-2021-0028.

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Abstract Proxy Re-Signature (PRS) complements well-established digital signature service. Blaze-Bleumer-Strauss discussed PRS in 1998 for translating a signature on a message from Alice into a signature from Bob on the same message at semi-trusted proxy which does not learn any signing-key and cannot produce new valid signature on new message for Alice or Bob. PRS has been largely ignored since then but it has spurred considerable research interest recently for sharing web-certificates, forming weak-group signatures, and authenticating network path. This article provides a survey summarizing a

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26

Yang, Li Guo, Fu Na Ou, and Jing Zhao. "Cryptanalysis and Improvement of a Strong Designated-Verifier Proxy Signature Scheme." Applied Mechanics and Materials 397-400 (September 2013): 1999–2003. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.1999.

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By cryptanalysis of a strong designated-verifier proxy signature scheme, it is found that this scheme has security leaks: original signer can forge the proxy signers valid proxy signature for any message; not only the designated-verifier but also proxy signer can verify the signature and proxy signer can misuse it. An improvement is given, and the security analysis shows that it can resist the spiteful forgery attacks by original signer and prevent the misuse of proxy signature by proxy signer.

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27

Meng, Hui, and Xu Qian. "An ID-Based Proxy Multi-Signature Scheme." Applied Mechanics and Materials 135-136 (October 2011): 217–21. http://dx.doi.org/10.4028/www.scientific.net/amm.135-136.217.

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Proxy multi-signature is an extension of the basic proxy signature primitive, and permits two or more entities to delegate their signing capabilities to the same other entity. Combining proxy multi-signature with identity based cryptography, in this paper, We construct a concrete identity based proxy multi-signature scheme by using bilinear pairings. Analysis shows that the scheme is capable of resisting forgery attack and can satisfy all the required security properties of a proxy signature. Furthermore, the new scheme is very simple and efficient computationally. It has the property that the

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Yang, Hai Bin, Juan Li Sun, Xu An Wang, and Jian Cui. "Proxy Re-Signature Scheme from CBS to IBS." Advanced Materials Research 304 (July 2011): 355–58. http://dx.doi.org/10.4028/www.scientific.net/amr.304.355.

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In 1998, Blaze, Bleumer and Strauss proposed a new kind of cryptographic primitive called proxy re-signature. In proxy re-signature, a proxy can transform a signature computed under Alice’s secret key into one that can be verified by Bob’s public key. In 2005, Ateniese et al proposed a few re-signature schemes and also discussed its several potential applications. In this paper, we propose the first proxy re-signature scheme from certificate based signature (CBS) to identity based signature (IBS) with the help of PKG.

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Wang, Yiting, Weiqiang Qiu, Ling Dong, et al. "Proxy Signature-Based Management Model of Sharing Energy Storage in Blockchain Environment." Applied Sciences 10, no. 21 (2020): 7502. http://dx.doi.org/10.3390/app10217502.

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Sharing energy storage (SES) is a novel business model in order to increase the profits and improve the utilization rate of idle energy storage facilities. On the other hand, blockchains can be competently applied in the transaction and operation of SES because of distributed network architecture, traceability and tamper proof. In this paper, a management model of SES based on proxy signatures in the blockchain environment is proposed. Many management models including the principal-agent model are analyzed for SES in terms of benefit, cost, resources, and so on. Moreover, a blockchain framewor

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30

Yang, Xin, Long Zhang, Chun Ming Li, and Guo Qiang Li. "A Novel Hybrid Threshold Proxy Signature Scheme." Advanced Materials Research 756-759 (September 2013): 4372–76. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.4372.

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In this paper, we propose a new type of threshold proxy signature scheme: hybrid threshold proxy signature (HTPS), in which a signature is cooperatively generated by the partial original signers themselves and the proxy signers on behalf of their own original signer in threshold proxy way. We formalize the notion of security for hybrid threshold proxy signature scheme and prove our schemes security, such as, distinguishability, verifiability, strong unforgeability, strong nonrepudiation, etc.

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31

Wan, Zhong-mei, Xue-jia Lai, Jian Weng, Xuan Hong, Yu Long, and Wei-wei Jia. "On constructing certificateless proxy signature from certificateless signature." Journal of Shanghai Jiaotong University (Science) 13, no. 6 (2008): 692–94. http://dx.doi.org/10.1007/s12204-008-0692-5.

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32

Kang, Baoyuan. "Attacks on One Designated Verifier Proxy Signature Scheme." Journal of Applied Mathematics 2012 (2012): 1–6. http://dx.doi.org/10.1155/2012/508981.

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In a designated verifier proxy signature scheme, there are three participants, namely, the original signer, the proxy signer, and the designated verifier. The original signer delegates his or her signing right to the proxy signer, then the proxy signer can generate valid signature on behalf of the original signer. But only the designated verifier can verify the proxy signature. Several designated verifier proxy signature schemes have been proposed. However, most of them were proven secure in the random oracle model, which has received a lot of criticism since the security proofs in the random

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33

Liu, Guang Liang, Sheng Xian Xie, and Wei Fu. "(t,k,n) Multi-Blind Proxy Signature Scheme on Elliptic Curve." Applied Mechanics and Materials 130-134 (October 2011): 291–94. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.291.

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On the elliptic curve cryptosystem proposed a new multi-proxy signature scheme - (t, k, n) threshold blind proxy signature scheme.In new program blind proxy signature and (t,k,n) threshold secret sharing scheme will be combined, and will not over-concentration of the rights of the blind proxy signer .Computation of the program is small, security is high, the achieve efficiency and the utility is better .can prevent a malicious user's forgery attack and have the security properties of proxy signature.

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34

Li, Fagen, and Yupu Hu. "Security Analysis of the Pomykala-Barabasz Scheme." Fundamenta Informaticae 80, no. 4 (2007): 453–59. https://doi.org/10.3233/fun-2007-80406.

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In 2006, Pomykala and Barabasz [Fundamenta Informaticae 69 (2006) 411–425] proposed an elliptic curve based threshold proxy signature scheme which requires shorter cryptographic keys. They claimed that their scheme satisfies the secrecy, the proxy protected, the unforgeability, the non-repudiation, and the known signers. However, in this paper, we show that their scheme cannot achieve the proxy protected, the unforgeability and the non-repudiation by demonstrating a conspiracy attack. In this attack, any t malicious proxy signers can collusively impersonate some other proxy signers to generate

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35

Chou, Jue-Sam. "A Novel Anonymous Proxy Signature Scheme." Advances in Multimedia 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/427961.

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Recently, several studies about proxy signature schemes have been conducted. In 2009, Yu et al. proposed an anonymous proxy signature scheme attempting to protect the proxy signer's privacy from outsiders. They claimed that their scheme can make the proxy signer anonymous. However, based on our research, we determined that this was not the case and the proxy signer's privacy was not anonymous. Hence, in this paper, we propose a new anonymous proxy signature scheme that truly makes the proxy signer anonymous while making it more secure and efficient when compared with Yu et al.'s scheme. Our pr

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36

Manoj Kumar Chande. "An improved proxy blind signature scheme based on ECDLP." Malaya Journal of Matematik 2, no. 03 (2014): 228–35. http://dx.doi.org/10.26637/mjm203/007.

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In a proxy blind signature scheme, there is an integration of the properties as well as advantages of both signature schemes namely proxy signature and blind signature. The concept of this signature scheme with a salient feature that, it allows a designated person say proxy signer to sign on behalf of original signer, in such a way that he/she neither has any idea about the content of the message, nor he/she can make a linkage between the signature and the identity of the requester. Therefore, it is very suitable and easily adoptable for electronic commerce, e-cash applications. Recently, Prad

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Liu, Weiwei, Yi Mu, Guomin Yang, and Yangguang Tian. "Strong Identity-Based Proxy Signature Schemes, Revisited." Wireless Communications and Mobile Computing 2018 (August 6, 2018): 1–11. http://dx.doi.org/10.1155/2018/6925019.

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Proxy signature is a useful cryptographic primitive that has been widely used in many applications. It has attracted a lot of attention since it was introduced. There have been lots of works in constructing efficient and secure proxy signature schemes. In this paper, we identify a new attack that has been neglected by many existing proven secure proxy signature schemes. We demonstrate this attack by launching it against an identity-based proxy signature scheme which is proven secure. We then propose one method that can effectively prevent this attack. The weakness in some other proxy signature

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Zhang, Lili, and Yanqin Ma. "A Lattice-Based Identity-Based Proxy Blind Signature Scheme in the Standard Model." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/307637.

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A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice-based cryptography is enjoying great interest these days, due to implementation simplicity and

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Panda, Suryakanta, and Ramesh Kumar Mohapatra. "Stamped Proxy Blind Signature Scheme." International Journal of Computer Applications 64, no. 15 (2013): 38–41. http://dx.doi.org/10.5120/10713-5690.

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40

FAN, Rui. "A new certificateless proxy signature." Journal of Computer Applications 28, no. 4 (2008): 915–17. http://dx.doi.org/10.3724/sp.j.1087.2008.00915.

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Deng, Lunzhi, Jiwen Zeng, and Yunyun Qu. "Certificateless Proxy Signature from RSA." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/373690.

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Although some good results were achieved in speeding up the computation of pairing function in recent years, it is still interesting to design efficient cryptosystems with less bilinear pairing operation. A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer within a given context. We propose a certificateless proxy signature (CLPS) scheme from RSA and prove its security under the strongest security model where the Type I/II adversary is a super Type I/II adversary.

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Zhang, Jianhong, Cheng Ji, and Qin Geng. "Designated-Verifier Chameleon Proxy Signature." International Journal of Distributed Sensor Networks 5, no. 1 (2009): 29. http://dx.doi.org/10.1080/15501320802520639.

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XU, Jie, Hong-xiang SUN, Qiao-yan WEN, and Hua ZHANG. "Improved certificateless multi-proxy signature." Journal of China Universities of Posts and Telecommunications 19, no. 4 (2012): 94–116. http://dx.doi.org/10.1016/s1005-8885(11)60288-4.

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44

Xue, Qingshui, and Zhenfu Cao. "Factoring based proxy signature schemes." Journal of Computational and Applied Mathematics 195, no. 1-2 (2006): 229–41. http://dx.doi.org/10.1016/j.cam.2005.03.085.

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Wang, Qin, and Zhenfu Cao. "Identity based proxy multi-signature." Journal of Systems and Software 80, no. 7 (2007): 1023–29. http://dx.doi.org/10.1016/j.jss.2006.12.565.

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Deng, Lunzhi, Jiwen Zeng, and Huawei Huang. "Efficient Certificateless Proxy Signature Scheme." International Journal of Foundations of Computer Science 27, no. 01 (2016): 85–100. http://dx.doi.org/10.1142/s0129054116500064.

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A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer within a given context. We propose a certificateless proxy signature (CLPS) scheme, and prove it's security under a stronger security model. Although some good results were achieved in speeding up the computation of pairing function in recent years, it is still interesting to design cryptosystem with less pairing operations. Taken into account the computational costs, our scheme only requires 2 pairing operations in delegation and signing, respectively.

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Li, JiGuo, ZhenFu Cao, and YiChen Zhang. "Nonrepudiable proxy multi-signature scheme." Journal of Computer Science and Technology 18, no. 3 (2003): 399–402. http://dx.doi.org/10.1007/bf02948911.

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Hsu, Chien-Lung, Tzong-Sun Wu, and Wei-Hua He. "New proxy multi-signature scheme." Applied Mathematics and Computation 162, no. 3 (2005): 1201–6. http://dx.doi.org/10.1016/j.amc.2004.03.001.

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Liu, Wen-yuan, Feng Tong, Bao-wen Wang, and Ya-dong Wang. "A New Proxy Blind Signature Scheme with Proxy Revocation." Journal of Electronics & Information Technology 30, no. 10 (2011): 2468–71. http://dx.doi.org/10.3724/sp.j.1146.2007.00423.

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Kim, Young-Seol, and Jik Hyun Chang. "A proxy fail-stop signature scheme with proxy revocation." Journal of Discrete Mathematical Sciences and Cryptography 11, no. 3 (2008): 281–95. http://dx.doi.org/10.1080/09720529.2008.10698184.

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