RSA型加密系统(RSA加密系统及其改进系统的统称)至今仍然被广泛应用于许多注重电子数据安全的电子商务系统中.然而对现有的RSA型加密方案分析发现:(1)只有在随机谕言机模型下抗CCA2攻击的RSA型加密方案,还没有在标准模型下实现IND-CCA2安全的RSA型概率加密方案;(2)没有在标准模型下实现抗CPA且保持乘法同态性的RSA型同态加密方案,而同态性是实现安全多方计算和云计算安全服务的重要性质之一;(3)在实现密文不可区分方面,这些方案除HD-RSA外都是通过一个带hash的Feistel网络引入随机因子的,从而导致这些方案只能在随机谕言机模型下实现IND-CCA2安全.针对以上问题,本文在RSA加密系统的基础上,通过增加少量的有限域上的模指数运算,设计了一个标准模型下具有IND-CPA安全的RSA型概率同态加密方案和一个具有IND-CCA2安全的RSA型概率加密方案.这两个方案在实现密文不可区分时,都不再通过明文填充引入随机因子.此外,本文还提出一个RSA问题的变形问题(称作RSA判定性问题).
Abstract
RSA and its modified schemes (which are called by a joint name,RSA-type encryption schemes) are still deployed in many commercial systems where data security is very important.Analyzing RSA-type encryption schemes,we find that:(1) to the best of our knowledge,all these schemes are merely secure against adaptive chosen-ciphertext attack(CCA2) in the random oracle(RO) model,and there is no RSA-type schemes yet that is indistinguishable under adaptive chosen-ciphertext attack in the standard model;(2) there is no RSA-type scheme that is secure against chosen plaintext attack(CPA) but keeping multiplicative homomorphism,whereas encryption schemes with homomorphism are important for secure multi-party computations and secure cloud services;(3) except for the Hybrid Dependent RSA(HD-RSA),all the schemes introduce randomness into ciphertext by a Feistel network with hash functions;hence,this brings all the schemes to achieve IND-CCA2 security merely in RO model.In this paper,we propose two RSA-type encryption schemes that only need a few more modular arithmetic operations.One is indistinguishable against chosen plaintext attack with homomorphism,while another is indistinguishable against adaptive chosen ciphertext attack in standard model.Both schemes are probabilistic without plaintext padding.Furthermore,we propose a new variant RSA problem,which is called RSA decisional problem(denote by DRSA).
关键词
RSA密码系统 /
IND-CCA2安全 /
标准模型 /
同态性 /
概率加密
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Key words
RSA cryptosystem /
IND-CCA2 security /
standard model /
homomorphism /
probabilistic encryption
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中图分类号:
TP309
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参考文献
[1] 杨波.密码学中的可证明安全[M].北京:清华大学出版社,2017.
[2] Goldwasser S,et al.Probabilistic encryption[J].Journal of Computer and System Sciences,1984,28(2):270-299.
[3] Naor M,et al.Public-key cryptosystems provably secure against chosen ciphertext attacks[A].C Koutsougeras.Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing[C].New York:ACM,1990.427-437.
[4] Gentry C,et al.Using fully homomorphic hybrid encryption to minimize non-interative zero-knowledge proofs[J].Journal of Cryptology,2015,28(4):820-843.
[5] Koblitz N,et al.The random oracle model:a twenty-year retrospective[J].Designs,Codes and Cryptography,2015,77(2-3):587-610.
[6] Gu K,et al.Secure and efficient multi-proxy signature scheme in the standard model[J].Chinese Journal of Electronics,2016,25(1):93-99.
[7] 陈明.标准模型下可托管的基于身份认证密钥协商[J].电子学报,2015,43(10):1954-1962. Chen ming.Escrowable identity-based authenticated key agreement in the standard model[J].ACTA Electronia Sinica,2015,43(10):1954-1962.(in Chinese)
[8] Rivest R L,et al.A method for obtaining digital signatures and public-key cryptosystems[J].Communications of the ACM,1983,26(1):96-99.
[9] Jonsson J,et al.PKCS# 1:RSA Cryptography Specifications Version 2.2[R].https://www.rfc-editor.org/rfc/pdfrfc/rfc8017.txt.pdf,2016-11-6/2017-11-26.
[10] Pointcheval D.HD-RSA:Hybrid dependent RSA-a new public-key encryption scheme[J].Submission to IEEE P1363a,1999.
[11] Shoup V.OAEP reconsidered[J].Journal of Cryptology,2002,15(4):223-249.
[12] Boneh D.Simplified OAEP for the RSA and Rabin functions[A].Advances in Cryptology-CRYPTO 2001[C].Berlin Heidelberg:Springer,2001.275-291.
[13] Phan D H,Pointcheval D.OAEP 3-round:A generic and secure asymmetric encryption padding[A].Pil Joong Lee.Advances in Cryptology-ASIACRYPT 2004[C].Berlin Heidelberg:Springer,2004.63-77.
[14] Cui Y,et al.On achieving chosen ciphertext security with decryption errors[A].Hideki Imai.Proceedings of the Applied Algebra,Algebraic Algorithms and Error-Correcting Codes-16th International Symposium[C].Las Vegas:Springer,2006.173-182.
[15] 胡予濮,牟宁波,等.一种改进的三轮OAEP明文填充方案[J].计算机学报,2009,32(4):611-617. Hu Yu-Pu,Mu Ning-Bo,et al.An improved OAEP3-round padding scheme[J].Chinese Journal of Computers,2009,32(4):611-617.(in Chinese)
[16] 刘英莎,余文秋,等.一种增强的OAEP方案EAEP3+[J].计算机学报,2014,37(5):1052-1057. Liu Ying-Sha,Yu Wen-Qiu,et al.An enhanced OAEP scheme EAEP3+[J].Chinese Journal of Computers,2014,37(5):1052-1057.(in Chinese)
[17] Kiltz E,et al.Instantiability of RSA-OAEP under chosen-plaintext attack[J].Journal of Cryptology,2017,30(3):889-919.
[18] Kiltz E,Pietrzak K.On the security of padding-based encryption schemes-or-why we cannot prove OAEP secure in the standard model[A].Antoine Joux.Advances in Cryptology-EUROCRYPT 2009[C].Berlin Heidelberg:Springer,2009.389-406.
[19] Cramer R,Shoup V.A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack[A].Hugo Krawczyk.Advances in Cryptology-CRYPTO'98[C].Berlin Heidelberg:Springer,1998.13-25.
[20] Bellare M,et al.Hash-function based PRFs:AMAC and its multi-user security[A].Marc Fischlin.Annual International Conference on the Theory and Applications of Cryptographic Techniques[C].Berlin,Heidelberg:Springer,2016.566-595.
[21] Katz J,Lindell Y.Introduction to Modern Cryptography[M].Boca Raton:CRC Press,2014.
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脚注
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基金
国家自然科学基金 (No.61272435,61373020); 西安工程大学博士科研启动基金 (No.107020331)
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