抗量子攻击的高效盲签名方案
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摘要
盲签名方案已在电子现金、电子选举、不经意传输等领域得到广泛应用。基于数论假设(大整数分解问题和离散对数问题)的盲签名方案存在不能抵抗量子攻击和亚指数攻击问题,基于传统证书的格上盲签名方案存在需要耗费巨大存储开销和通信代价的问题。针对上述问题,文章结合基于格的密码体制和基于身份的密码体制的优势,提出了一种高效、可抵抗量子算法攻击的盲签名方案,并在随机喻示模型下,基于格上小整数解(SIS)问题的困难性假设,证明了新方案的安全性。新方案使用固定维数的格基委托算法生成用户的私钥,实现了短私钥和短签名的目标。
Blind signature schemes have been widely used in areas such as e-cash, e-voting, oblivious transfer, etc. Blind signature schemes based on the number theory assumptions, such as big integer factorization problem(IFP) and discrete logarithm problem(DLP), could not resist the cryptanalysis by quantum attacksand sub-exponent algorithms, and lattice-based blind signature schemes based on traditional certificate had the problems of huge storage overhead and communication cost. Aiming at above problems, based on the advantages of lattice-based cryptosystem and identity-based cryptosystem, this paper proposes a blind signature scheme with high efficiency and quantum-resistant attacks. The scheme is proven secure with the hardness of the Small Integer Solution(SIS) problem in the random oracle model. The scheme extracts users' secret-key by using lattice basis delegation with fixed-dimension technique, and hence achieves short secret-keys and short signatures.
Blind signature schemes have been widely used in areas such as e-cash, e-voting, oblivious transfer, etc. Blind signature schemes based on the number theory assumptions, such as big integer factorization problem(IFP) and discrete logarithm problem(DLP), could not resist the cryptanalysis by quantum attacksand sub-exponent algorithms, and lattice-based blind signature schemes based on traditional certificate had the problems of huge storage overhead and communication cost. Aiming at above problems, based on the advantages of lattice-based cryptosystem and identity-based cryptosystem, this paper proposes a blind signature scheme with high efficiency and quantum-resistant attacks. The scheme is proven secure with the hardness of the Small Integer Solution(SIS) problem in the random oracle model. The scheme extracts users' secret-key by using lattice basis delegation with fixed-dimension technique, and hence achieves short secret-keys and short signatures.
引文
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[15]崔巍,辛阳,胡程瑜,等.高效的基于身份的(受限)部分盲签名[J].北京邮电大学学报,2008,31(4):53-57.
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[22]MICCIANCIO D,REGEV O.Worst-case to Averagecase Reductions Based on Gaussian Measures[J].SIAM Journal on Computing,2007,37(1):267-302.
[23]AGRAWAL S,DAN B,BOYEN X..Lattice Basis Delegation in Fixed Dimension and Shorter-Ciphertext Hierarchical IBE[C]//Springer.Advances in Cryptology-CRYPTO 2010,Cryptology Conference,August 15-19,2010,Santa Barbara,Ca,USA.Heidelberg:Springer,2010:98-115.
[24]CHA J C,CHEON J H.An Identity-Based Signature from Gap Diffie-Hellman Groups[C]//Springer.International Workshop on Theory and Practice in Public Key Cryptography:Public Key Cryptography.January 6-8,2003,London,UK.Heidelberg:Springer,2003:18-30.
[2]SHOR P W.Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer[EB/OL].https://arxiv.org/abs/quant-ph/9508027,2017-6-15.
[3]张焕国,韩文报,来学嘉,等.网络空间安全综述[J].中国科学:信息科学,2016,46(2):125-164.
[4]BENJAMIN P G,MCLAREN M,GOYAL S K,et al.Quantum Computation with Classical Light:Implementation of the Deutsch–Jozsa Algorithm[J].Physics Letters A,2016,380:1925-1931.
[5]BERNSTEIN D J,BUCHMANN J,DAHMEN E.Postquantum Cryptography[J].Lecture Notes in Computer Science,2008,6061:729-748.
[6]CHAUM D.Blind Signatures for Untraceable Payments[C]//Springer.Advances in Cryptology:Proceedings of CRYPTO'82,August 23-25,1982.Santa Barbara,California,USA.Berlin:Springer-Verlag,1983:199-203.
[7]LI F,ZHANG M,TAKAGI T.Identity-based Partially Blind Signature in the Standard Model for Electronic Cash[J].Mathematical&Computer Modelling,2013,58:196-203.
[8]López-García L,Perez L J D,Rodríguez-Henríquez F.A Pairing-Based Blind Signature E-Voting Scheme[J].Computer Journal,2014,57(10):1460-1471.
[9]张利利,马艳琴,卜春霞,等.一种安全高效的匿名电子选举方案[J].数学的实践与认识,2015,45(11):156-160.
[10]CHANG C C,CHENG T F.A Provably Secure t-out-of-n Oblivious Transfer Mechanism Based on Blind Signature[J].Journal of Information Hiding&Multimedia Signal Processing,2014,5(1):1-12.
[11]WU L C,YEH Y S,FAN C I.Fail-stop Blind Signature Scheme Based on the Integer Factorization[J].Journal of Discrete Mathematical Sciences&Cryptography,2004,7(3):281-290.
[12]MALA H,NEZHADANSARI N.New Blind Signature Schemes Based on the(elliptic curve)Discrete Logarithm Problem[C]//IEEE.International Conference on Computer and Knowledge Engineering,October 31-November 1,2013,Mashhad,Iran.New York:IEEE,2013:196-201.
[13]CHAKRABORTY K,MEHTA J.A Stamped Blind Signature Scheme Based on Elliptic Curve Discrete Logarithm Problem[J].International Journal of Network Security,2012,14(6):316-319.
[14]HUANG Z,CHEN K,WANG Y.Efficient Identity-Based Signatures and Blind Signatures.[C]//Springer.Cryptology and network security:4th International Conference,CANS 2005,December 14-16,2005,Xiamen,China,Heidelberg:Springer,2005:120-133.
[15]崔巍,辛阳,胡程瑜,等.高效的基于身份的(受限)部分盲签名[J].北京邮电大学学报,2008,31(4):53-57.
[16]张晓敏.一种新的基于身份的盲签名[J].信息网络安全.2012(2):55-57.
[17]MAYKVS R.Lattice-based Blind Signatures[EB/OL].http://xueshu.baidu.com/s?wd=paperuri%3A%28934eab09eb0fb47a63f6ed5169a900b3%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F6682844%2F&ie=utf-8&sc_us=7620202453667423086,2017-6-15.
[18]王凤和,胡予濮,王春晓.基于格的盲签名方案[J].武汉大学学报(信息科学版).2010.5(35):550-553.
[19]SHAMIR A.Identity-Based Cryptosystems and Signature Schemes[C]//Springer.The Workshop on the Theory and Application of Cryptographic Techniques.April 1984,Paris,France.Heidelberg:Springer,1984:47-53.
[20]AJTAI M.Generating Hard Instances of Lattice Problems[C]//ACM.Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing.22-24 May 1996,Philadelphia.New York:ACM,1996:99-108.
[21]BOYEN X.Lattice Mixing and Vanishing Trapdoors:A Framework for Fully Secure Short Signatures and More[EB/OL].http://xueshu.baidu.com/s?wd=paperuri%3A%28e4dffc966d1d34071910a1a5bdd0e7d4%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fwww.springerlink.com%2Fcontent%2Fd51k4w52910807n2%2F&ie=utf-8&sc_us=11547643294592337504,2017-6-15.
[22]MICCIANCIO D,REGEV O.Worst-case to Averagecase Reductions Based on Gaussian Measures[J].SIAM Journal on Computing,2007,37(1):267-302.
[23]AGRAWAL S,DAN B,BOYEN X..Lattice Basis Delegation in Fixed Dimension and Shorter-Ciphertext Hierarchical IBE[C]//Springer.Advances in Cryptology-CRYPTO 2010,Cryptology Conference,August 15-19,2010,Santa Barbara,Ca,USA.Heidelberg:Springer,2010:98-115.
[24]CHA J C,CHEON J H.An Identity-Based Signature from Gap Diffie-Hellman Groups[C]//Springer.International Workshop on Theory and Practice in Public Key Cryptography:Public Key Cryptography.January 6-8,2003,London,UK.Heidelberg:Springer,2003:18-30.