一种针对El-Gamal数字签名生成的安全外包计算方案
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摘要
云计算作为一种新型计算模式,满足了人们将计算能力作为一种资源的需求。云服务器可以为资源受限的用户提供计算能力、存储空间等多方面的支持。完全可信的云服务器在实际应用中非常少见,不受信任的云服务器可能会窃取用户隐私。文章提出一种针对El-Gamal数字签名生成的安全外包计算方案,在云服务器的协助下,资源受限的签名者可以高效生成El-Gamal签名,且保护签名者的隐私不被泄露。该方案还包含验证机制,使签名者可以验证云服务器返回结果的正确性。理论分析证明,该方案可以在保护签名者隐私的前提下帮助签名者提高签名生成效率。
As a new computing mode, cloud computing has realized people's requirement of computing power as a resource. Cloud servers can provide resource-constrained clients with much support, including computing power and storage space. But fully trusted servers are rare in practice. Untrusted servers may steal the privacy of the clients. This paper presents a secure outsourcing scheme for El-Gamal signature generation, which makes resourceconstrained signers could efficiently generate El-Gamal signature with the help of cloud servers. Meanwhile, our scheme also provides privacy protection of signers. Our scheme also includes verification mechanism, which allows signer to check the correctness of result returned by the cloud server. The security analysis proves that our proposed scheme can help signers to improve signature generation efficiency under the premise of protecting signers' privacy.
As a new computing mode, cloud computing has realized people's requirement of computing power as a resource. Cloud servers can provide resource-constrained clients with much support, including computing power and storage space. But fully trusted servers are rare in practice. Untrusted servers may steal the privacy of the clients. This paper presents a secure outsourcing scheme for El-Gamal signature generation, which makes resourceconstrained signers could efficiently generate El-Gamal signature with the help of cloud servers. Meanwhile, our scheme also provides privacy protection of signers. Our scheme also includes verification mechanism, which allows signer to check the correctness of result returned by the cloud server. The security analysis proves that our proposed scheme can help signers to improve signature generation efficiency under the premise of protecting signers' privacy.
引文
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[21]CHEN X,HUANG X,LI J,et al.New Algorithms for Secure Outsourcing of Large-Scale Systems of Linear Equations[J].IEEETransactions on Information Forensics&Security,2014,10(1):69-78.
[22]DENG Fuhu,LI Zhenyu,ZENG Liyao,et al.A Cloud Decryption System Based on El-Gamal Security Outsourcing Decryption[J].Netinfo Security,2017,17(12):73-79.邓伏虎,李震宇,曾莉尧,等.一种支持El-Gamal安全外包解密的云密码系统[J].信息网络安全,2017,17(12):73-79.
[2]RIVEST R L,SHAMIR A,ADLEMAN L.A Method for Obtaining Digital Signatures and Public-key Cryptosystems[J].Communications of the ACM,1978,26(2):96-99.
[3]EL GAMAL T.A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms[J].IEEE Transactions on Information Theory,1985,31(4):469-472.
[4]REN K,WANG C,WANG Q.Security Challenges for the Public Cloud[J].IEEE Internet Computing,2012,16(1):69-73.
[5]WANG C,CAO N,REN K,et al.Enabling Secure and Efficient Ranked Keyword Search over Outsourced Cloud Data[J].IEEETransactions on Parallel&Distributed Systems,2012,23(8):1467-1479.
[6]HOHENBERGER S,LYSYANSKAYA A.How to Securely Outsource Cryptographic Computations[EB/OL].http://www.cs.jhu.edu/~susan/papers/HL05.pdf,2018-7-1.
[7]CHEN X,LI J,MA J,et al.New Algorithms for Secure Outsourcing of Modular Exponentiations[EB/OL].https://www.cnsr.ictas.vt.edu/publication/06567860.pdf,2018-7-1.
[8]YE J,XU Z,DING Y.Secure Outsourcing of Modular Exponentiations in Cloud and Cluster Computing[J].Cluster Computing,2016,19(2):811-820.
[9]DING Y,XU Z,YE J,et al.Secure Outsourcing of Modular Exponentiations under Single Untrusted Programme Model[EB/OL].https://doi.org/10.1016/j.jcss.2016.11.005,2018-7-1.
[10]SU Q,YU J,TIAN C,et al.How to Securely Outsource the Inversion Modulo a Large Composite Number[EB/OL].https://doi.org/10.1016/j.jss.2017.04.015,2018-7-1.
[11]ZHOU K,REN J.Secure Outsourcing of Scalar Multiplication on Elliptic Curves[EB/OL].http://www.academia.edu/27047539/Secure_Outsourcing_of_Scalar_Multiplication_on_Elliptic_Curves,2018-7-1.
[12]LEI X,LIAO X,HUANG T,et al.Achieving Security,Robust Cheating Resistance,and High-efficiency for Outsourcing Large Matrix Multiplication Computation to a Malicious Cloud[J].Information Sciences,2014,280:205-217.
[13]HU Xing,PEI Dingyi,TANG Chunming,et al.Verifiable and Secure Outsourcing of Matrix Calculation and its Application[J].Scientia Sinica(Informationis),2013,43(7):842-852.胡杏,裴定一,唐春明,等.可验证安全外包矩阵计算及其应用[J].中国科学:信息科学,2013,43(7):842-852.
[14]ZHANG Y,BLANTON M.Efficient Secure and Verifiable Outsourcing of Matrix Multiplications[EB/OL].https://www.researchgate.net/publication/312768648_Efficient_Secure_and_Verifiable_Outsourcing_of_Matrix_Multiplications,2018-7-1.
[15]WU Duoduo,LAI Qiqi,YANG Bo.Efficient,Verifiable and Secure Outsourcing of Matrix Multiplication[J].Journal of Cryptologic Research,2017,4(4):322-332.武朵朵,来齐齐,杨波.矩阵乘积的高效可验证安全外包计算[J].密码学报,2017,4(4):322-332.
[16]LEI X,LIAO X,HUANG T,et al.Outsourcing Large Matrix Inversion Computation to a Public Cloud[J].IEEE Transactions on Cloud Computing,2013,1(1):78-87.
[17]REN X,HUANG H.Secure and Efficient Protocol for Outsourcing Large Matrix Determinant Computation to Semi-honest Cloud[J].Computer Engineering&Applications,2014,50(10):82-86.任晓霞,黄宏宇.安全高效的大矩阵行列式计算云外包协议[J].计算机工程与应用,2014,50(10):82-86.
[18]FU S,YU Y,XU M.Practical Privacy-preserving Outsourcing of Large-scale Matrix Determinant Computation in the Cloud[EB/OL].https://link.springer.com/chapter/10.1007/978-3-319-68542-7_1,2018-7-1.
[19]WU Hongfeng,REN Huanshu.An Outsourcing Computing Based on Large Matrix QR Decomposition in Cloud Environment[J].Netinfo Security,2018,18(3):86-90.吴宏锋,任桓枢.云环境下基于大规模矩阵QR分解的外包计算[J].信息网络安全,2018,18(3):86-90.
[20]WANG C,REN K,WANG J,et al.Harnessing the Cloud for Securely Outsourcing Large-Scale Systems of Linear Equations[J].IEEETransactions on Parallel&Distributed Systems,2013,24(6):1172-1181.
[21]CHEN X,HUANG X,LI J,et al.New Algorithms for Secure Outsourcing of Large-Scale Systems of Linear Equations[J].IEEETransactions on Information Forensics&Security,2014,10(1):69-78.
[22]DENG Fuhu,LI Zhenyu,ZENG Liyao,et al.A Cloud Decryption System Based on El-Gamal Security Outsourcing Decryption[J].Netinfo Security,2017,17(12):73-79.邓伏虎,李震宇,曾莉尧,等.一种支持El-Gamal安全外包解密的云密码系统[J].信息网络安全,2017,17(12):73-79.
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