基于混沌公钥密码的身份认证研究
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摘要
混沌系统因其对初值的敏感性和良好的伪随机性,在密码学方面有着巨大的应用价值。近年来,对混沌系统的研究逐渐成为热点。但是大量的研究成果局限于混沌对称加密范畴,利用混沌来构造公钥密码系统的研究还比较少。目前最具代表性的基于混沌的公钥密码算法是由L.Kocarev提出的基于Chebyshev多项式的公钥密码算法。这种公钥算法思想的提出带动了整个混沌领域对公钥密码体系包括加密算法、数字签名、密钥协商、身份认证等方面的研究热潮。但是该项研究仍然处于初级阶段,存在很多不完善的地方。因此本文针对基于Chebyshev多项式的公钥密码体系的研究是有意义的。
在通信技术飞速发展、电子商务日渐广泛应用的今天,身份认证已成为网络中信息安全最重要的一道防线。本文选取了基于有限域的Chebyshev多项式作为研究对象,其所具有的良好的混沌特性、半群特性和单向性可以很好的应用到公钥加密算法、密钥协商及身份认证中去。本文在深入研究基于有限域Chebyshev多项式的类ElGamal算法的基础上,将Chebyshev多项式与身份认证相结合,分析目前已提出的基于Chebyshev多项式的身份认证方案所存在的安全漏洞,并提出新的方案。通过安全性分析和编程实现,证明新方案是安全可行的。
Chaotic system has great application value in cryptography because of its sensitive dependence on initial conditions and pseudo-randomness. In recent years, a lot of chaotic cryptosystems have been proposed; however, most of them focus on encryption algorithm of secret key cryptography. Compared with chaotic secret key cryptography, there is much less research on public-key cryptography based on chaos. The most representative public-key cryptography based on chaos is public-key cryptography algorithms based on Chebyshev polynomials, which is proposed by L.Kocarev. The idea lead to the development of public-key cryptosystems based on chaos, which includes encryption algorithms, digital signatures, key agreement, identity authentication and other aspects. But the research is still elementary, many problems still exist. So, research of public-key cryptosystem based on Chebyshev polynomials is meaningful.
With the development of communication technology and the widely use of ecommerce, identity authentication has become the most important line of defense in information security of network. Chebyshev polynomials based on finite fields can be used in public-key encryption algorithms, key agreement and identity authentication for its good semi-group property and one-way trapped characteristic. In this paper, an ElGamal-like algorithm using Chebyshev polynomials based on finite fields is deeply researched and the security of the proposed identity authentication scheme based on chebyshev polynomials is also analyzed. According to the above research, the new identity authentication schemes based on chebyshev polynomials are proposed. The program results of the new identity authentication schemes analysis prove the schemes are secure and practical.
在通信技术飞速发展、电子商务日渐广泛应用的今天,身份认证已成为网络中信息安全最重要的一道防线。本文选取了基于有限域的Chebyshev多项式作为研究对象,其所具有的良好的混沌特性、半群特性和单向性可以很好的应用到公钥加密算法、密钥协商及身份认证中去。本文在深入研究基于有限域Chebyshev多项式的类ElGamal算法的基础上,将Chebyshev多项式与身份认证相结合,分析目前已提出的基于Chebyshev多项式的身份认证方案所存在的安全漏洞,并提出新的方案。通过安全性分析和编程实现,证明新方案是安全可行的。
Chaotic system has great application value in cryptography because of its sensitive dependence on initial conditions and pseudo-randomness. In recent years, a lot of chaotic cryptosystems have been proposed; however, most of them focus on encryption algorithm of secret key cryptography. Compared with chaotic secret key cryptography, there is much less research on public-key cryptography based on chaos. The most representative public-key cryptography based on chaos is public-key cryptography algorithms based on Chebyshev polynomials, which is proposed by L.Kocarev. The idea lead to the development of public-key cryptosystems based on chaos, which includes encryption algorithms, digital signatures, key agreement, identity authentication and other aspects. But the research is still elementary, many problems still exist. So, research of public-key cryptosystem based on Chebyshev polynomials is meaningful.
With the development of communication technology and the widely use of ecommerce, identity authentication has become the most important line of defense in information security of network. Chebyshev polynomials based on finite fields can be used in public-key encryption algorithms, key agreement and identity authentication for its good semi-group property and one-way trapped characteristic. In this paper, an ElGamal-like algorithm using Chebyshev polynomials based on finite fields is deeply researched and the security of the proposed identity authentication scheme based on chebyshev polynomials is also analyzed. According to the above research, the new identity authentication schemes based on chebyshev polynomials are proposed. The program results of the new identity authentication schemes analysis prove the schemes are secure and practical.
引文
[1]陈鲁生,沈世镒.现代密码学(第一版)[M].北京:科学出版社,2002.2.
[2] Shannon C E. Communication theory of secrecy system. Bell System Technical Journal.1949, 10, 28(4).656-715.
[3] Diffie W,Hellman M E. New direction in cryptography. IEEE Transaction on Information Theory, 1976, 11, 22(6).644-654.
[4]廖晓峰等.混沌密码学原理及其应用.北京:科学出版社,2009.3-10.
[5]郝柏林.从抛物线谈起—混沌动力学引论.上海:上海科技教育出版社,1993.93-96.
[6] Tien-Yien Li, Iames A.Yorke.Period three implies chaos.American Mathematical Monthly.1975,12,82(10).985-992.
[7]陈式刚.映像与混沌.北京:北京国防工业出版社,1992.
[8]赵耿,方锦清.现代信息安全与混沌保密通信应用研究的进展. 2003,6. 23(2). 212-255.
[9]陆启韶.分岔与奇异性.上海:上海科技教育出版社,1995.
[10]郑德玲,赵耿,徐国保. Logistic映射数字流混沌奇怪吸引子及参数.北京科技大学学报. 2002,6. 24(3). 350-352.
[11]陈士华等.混沌动力学初步.武汉:武汉水利电力大学出版社,1998.76-92.
[12]刘式达等.自然科学中的混沌和分形.北京:北京大学出版社,2003.
[13]王育民,刘建伟.通信网的安全—理论与技术.西安:西安电子科技大学出版社,1999.
[14] Geng Zhao, GuanrongChen, Fangfang Lu.Analysis of some recently proposed chaos-based public key encryption algorithms.2006 International Conference on Communications, Circuits and Systems Proceedings . IEEE press , 2006 ,6.1573-1576.
[15]杨波.现代密码学(第一版) [M] .北京:清华大学出版社,2003.91-95,109,179-180.
[16]刘木生.基于PKI和指纹识别技术的身份认证技术研究和设计[D].硕士学位论文.中国科学技术大学. 2003.
[17]胡志远.口令破解与加密技术[M].北京:机械工业出版社,2003.
[18]周福才,朱伟勇.基于混沌理论身份认证的研究[J].东北大学学报(自然科学版),2002,8, 23(8).730-732.
[19] Xiaoyun Wang, Hongbo Yu. How to Break MD5 and Other Hash Functions[C]. Advances in Cryptology-EUROCRYPT 2005. 2005. 19-35.
[20] Xiaoyun Wang, Yiqun Lisa Yin, Hongbo Yu. Finding Collisions in the Full SHA1[C]. Advances in Cryptology-CRYPTO 2005. 2005. 17-36.
[21] PUHUA GUAN.Cellular automaton public—key cryptosystem[J].Complex System,1987,1.5l-57.
[22] FEIGN HWU . The Interpolating Random Spline Cryptosystem and the Chaotic-Map Public-key Cryptosystem[D].PhD thesis,Faculty of the Graduate School,University of Missouri—Rolla, 1993.
[23] R.Tenny, L.S.Tsimring, L.Larson, etc.Using distributed nonlinear dynamics for public key encryption.Physical review letters.2003,1,90(4).479-482.
[24] R.Tenny, L.S.Tsimring.Additive mixing modulation for public key encryption based on distributed dynamics.IEEE Transactions on Circuits and Systems.2005,3. 52(3).672-679.
[25] Goce Jakimoski, Ljupco Kocarev.Analysis of some recently proposed chaos-based encryption algorithms.Physics Letters A.2001,12. 291(6).381-384.
[26]石熙,廖晓峰。基于环面自同构的公钥加密算法。重庆大学学报(自然科学版)。2006,3. 29(3).62-64.
[27] BLEICHENBACHER D . On the Security of the KMOV public key cryptosystem[M].Advances in Cryptology-CRPTO’97(LNCSl294),1997.235—248.
[28] Ruanjan B. Novel public key encryption technique based on multiple chaotic systems. Phys. Rev. Lett, 2005, 8. 26:098702.
[29]李树均。数字化混沌密码的分析与设计。博士学位论文。西安交通大学,2003.
[30]王开,裴文江,邹留华,何振亚.一种多混沌系统公钥密码算法的安全性分析.物理学报[J].2006, 12. 55(12).6243-6247.
[31] L.Kocarev, J.Makraduli, and P.Amato.Public-Key Encryption Based on Chebyshev Maps . Proceedings of the 2003 International Symposium on Circuits and Systems.2003, 5. 3.28-31.
[32] Pina Bergamo, Paolo D’Aroc, Alfredo De Santis, etc.Security of Public Key Cryptosystems based on Chebyshev Polynomials.IEEE Transactions on Circuits and Systems.2005,7.52(7).1382-1393.
[33] Kocarev L, Sterjev M, Amato P. RSA encryption algorithm based on torus automorphisms. ISCA’04, 2004, 4.Ⅳ.577-580.
[34]王大虎,杨维,李庆九.基于混沌理论的公钥加密方案的研究[C].通信理论与信号处理新进展——2005年通信理论与信号处理年会论文集,2005.
[35]王大虎,魏学业,李庆九等.基于Chebshecv多项式的公钥加密和密钥交换方案的改进[A].铁道学报.2006, 10. 28(5).95-98.
[36]宁红宙,刘云,何德全.一种新的会话密钥协商算法[A].高技术通讯.2005, 11. 15(11).13-16.
[37] XU Bang-hai, JIANG Li, XU Qun-san.A Novel Public Key Cryptography Using Chebyshev Polynomials . Journal of Shaanxi University of Science & Technology.2005,12.23(6).48-52.
[38] Wang Dahu, Hu Zhiguo, Tong Zaojing, Zha Xiaofei. An Identity Authentication System Based on Chebyshev Polynomials, The 1st International Conference on Information Science and Engineering (ICISE 2009), Nanjing, 2009[C]. 2009,12.1648-1650
[39]刘亮,刘云,宁红宙.公钥体系中Chebyshev多项式的改进[A].北京交通大学学报.2005,10.29(5).56-60.
[40] Lima J.B, Campello de Souza R.M, Panario D. Security of Public-key Cryptosystems Based on Chebyshev Polynomials over Prime Finite Fields. IEEE International Symposium (ISIT 2008). 2008,7.1843– 1847.
[41] Xian D, Liao X, Wong K.An Efficient Entire Chaos-Based Scheme for Deniable Authentication[A].Chaos, Solitons and Fractals.2005,2.23(4).1327-1331.
[42] Alvarez, G , Security problems with a chaos-based deniable authentication scheme[J]. Chaos, Solitons and Fractals , 2005,10.26(1).7-11.
[43] Xiao D, Liao X, Deng S.A novel key agreement protocol based on chaotic maps[J]. Inform Sci 2007, 2 .177(4).1136-1142.
[44] Han S. Security of a key agreement protocol based on chaotic maps. Chaos Solitons Fract 2008,11.38(3).764–768.
[45] Tao Xianga, Kwok-Wo Wongb, Xiaofeng Liao.On the security of a novel key agreement protocol based on chaotic maps[J]. Chaos, Solitons & Fractals, 2009, 4.40(2).672-675.
[46] Xingyuan Wang, Jianfeng Zhao. An improved key agreement protocol based on chaos[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 12. 15(12).4052-4057.
[47] E. J. Yoon and K. Y. Yoo, A New Key Agreement Protocol Based on Chaotic Maps, In Proceedings of The Second KES International Symposium on Agent and Multi-Agent Systems: Technologies and Applications(KES-AMSTA’08), 2008.4953.897-906.
[48] Huei-Ru Tseng, Rong-Hong Jan, Wuu Yang, A Chaotic Maps-based Key Agreement Protocol that Preserves User Anonymity, IEEE International Conference on Communications (ICC 2009), Dresden, Germany, 2009, 6. 1-6.
[49] Yoshimura T, Kohda T. Resonance Properties of Chebyshev Chaotic Sequences [A] . Proceedings of the 2004 International Symposium on Circuits and Systems Volume 4[C]. New York: IEEE, 2004, 5. 4.573-576.
[50]赵耿,闫慧,童宗科.基于Chebyshev多项式的公钥密码算法的研究[J],计算机工程.2008,34.137-139.
[51] L.Kocarev, J.Makraduli, P.Amato. Public-Key Encryption Based on Chebyshev Polynomials[J]. Circuits, systems, and signal processing 2005. 24(5).497-517.
[2] Shannon C E. Communication theory of secrecy system. Bell System Technical Journal.1949, 10, 28(4).656-715.
[3] Diffie W,Hellman M E. New direction in cryptography. IEEE Transaction on Information Theory, 1976, 11, 22(6).644-654.
[4]廖晓峰等.混沌密码学原理及其应用.北京:科学出版社,2009.3-10.
[5]郝柏林.从抛物线谈起—混沌动力学引论.上海:上海科技教育出版社,1993.93-96.
[6] Tien-Yien Li, Iames A.Yorke.Period three implies chaos.American Mathematical Monthly.1975,12,82(10).985-992.
[7]陈式刚.映像与混沌.北京:北京国防工业出版社,1992.
[8]赵耿,方锦清.现代信息安全与混沌保密通信应用研究的进展. 2003,6. 23(2). 212-255.
[9]陆启韶.分岔与奇异性.上海:上海科技教育出版社,1995.
[10]郑德玲,赵耿,徐国保. Logistic映射数字流混沌奇怪吸引子及参数.北京科技大学学报. 2002,6. 24(3). 350-352.
[11]陈士华等.混沌动力学初步.武汉:武汉水利电力大学出版社,1998.76-92.
[12]刘式达等.自然科学中的混沌和分形.北京:北京大学出版社,2003.
[13]王育民,刘建伟.通信网的安全—理论与技术.西安:西安电子科技大学出版社,1999.
[14] Geng Zhao, GuanrongChen, Fangfang Lu.Analysis of some recently proposed chaos-based public key encryption algorithms.2006 International Conference on Communications, Circuits and Systems Proceedings . IEEE press , 2006 ,6.1573-1576.
[15]杨波.现代密码学(第一版) [M] .北京:清华大学出版社,2003.91-95,109,179-180.
[16]刘木生.基于PKI和指纹识别技术的身份认证技术研究和设计[D].硕士学位论文.中国科学技术大学. 2003.
[17]胡志远.口令破解与加密技术[M].北京:机械工业出版社,2003.
[18]周福才,朱伟勇.基于混沌理论身份认证的研究[J].东北大学学报(自然科学版),2002,8, 23(8).730-732.
[19] Xiaoyun Wang, Hongbo Yu. How to Break MD5 and Other Hash Functions[C]. Advances in Cryptology-EUROCRYPT 2005. 2005. 19-35.
[20] Xiaoyun Wang, Yiqun Lisa Yin, Hongbo Yu. Finding Collisions in the Full SHA1[C]. Advances in Cryptology-CRYPTO 2005. 2005. 17-36.
[21] PUHUA GUAN.Cellular automaton public—key cryptosystem[J].Complex System,1987,1.5l-57.
[22] FEIGN HWU . The Interpolating Random Spline Cryptosystem and the Chaotic-Map Public-key Cryptosystem[D].PhD thesis,Faculty of the Graduate School,University of Missouri—Rolla, 1993.
[23] R.Tenny, L.S.Tsimring, L.Larson, etc.Using distributed nonlinear dynamics for public key encryption.Physical review letters.2003,1,90(4).479-482.
[24] R.Tenny, L.S.Tsimring.Additive mixing modulation for public key encryption based on distributed dynamics.IEEE Transactions on Circuits and Systems.2005,3. 52(3).672-679.
[25] Goce Jakimoski, Ljupco Kocarev.Analysis of some recently proposed chaos-based encryption algorithms.Physics Letters A.2001,12. 291(6).381-384.
[26]石熙,廖晓峰。基于环面自同构的公钥加密算法。重庆大学学报(自然科学版)。2006,3. 29(3).62-64.
[27] BLEICHENBACHER D . On the Security of the KMOV public key cryptosystem[M].Advances in Cryptology-CRPTO’97(LNCSl294),1997.235—248.
[28] Ruanjan B. Novel public key encryption technique based on multiple chaotic systems. Phys. Rev. Lett, 2005, 8. 26:098702.
[29]李树均。数字化混沌密码的分析与设计。博士学位论文。西安交通大学,2003.
[30]王开,裴文江,邹留华,何振亚.一种多混沌系统公钥密码算法的安全性分析.物理学报[J].2006, 12. 55(12).6243-6247.
[31] L.Kocarev, J.Makraduli, and P.Amato.Public-Key Encryption Based on Chebyshev Maps . Proceedings of the 2003 International Symposium on Circuits and Systems.2003, 5. 3.28-31.
[32] Pina Bergamo, Paolo D’Aroc, Alfredo De Santis, etc.Security of Public Key Cryptosystems based on Chebyshev Polynomials.IEEE Transactions on Circuits and Systems.2005,7.52(7).1382-1393.
[33] Kocarev L, Sterjev M, Amato P. RSA encryption algorithm based on torus automorphisms. ISCA’04, 2004, 4.Ⅳ.577-580.
[34]王大虎,杨维,李庆九.基于混沌理论的公钥加密方案的研究[C].通信理论与信号处理新进展——2005年通信理论与信号处理年会论文集,2005.
[35]王大虎,魏学业,李庆九等.基于Chebshecv多项式的公钥加密和密钥交换方案的改进[A].铁道学报.2006, 10. 28(5).95-98.
[36]宁红宙,刘云,何德全.一种新的会话密钥协商算法[A].高技术通讯.2005, 11. 15(11).13-16.
[37] XU Bang-hai, JIANG Li, XU Qun-san.A Novel Public Key Cryptography Using Chebyshev Polynomials . Journal of Shaanxi University of Science & Technology.2005,12.23(6).48-52.
[38] Wang Dahu, Hu Zhiguo, Tong Zaojing, Zha Xiaofei. An Identity Authentication System Based on Chebyshev Polynomials, The 1st International Conference on Information Science and Engineering (ICISE 2009), Nanjing, 2009[C]. 2009,12.1648-1650
[39]刘亮,刘云,宁红宙.公钥体系中Chebyshev多项式的改进[A].北京交通大学学报.2005,10.29(5).56-60.
[40] Lima J.B, Campello de Souza R.M, Panario D. Security of Public-key Cryptosystems Based on Chebyshev Polynomials over Prime Finite Fields. IEEE International Symposium (ISIT 2008). 2008,7.1843– 1847.
[41] Xian D, Liao X, Wong K.An Efficient Entire Chaos-Based Scheme for Deniable Authentication[A].Chaos, Solitons and Fractals.2005,2.23(4).1327-1331.
[42] Alvarez, G , Security problems with a chaos-based deniable authentication scheme[J]. Chaos, Solitons and Fractals , 2005,10.26(1).7-11.
[43] Xiao D, Liao X, Deng S.A novel key agreement protocol based on chaotic maps[J]. Inform Sci 2007, 2 .177(4).1136-1142.
[44] Han S. Security of a key agreement protocol based on chaotic maps. Chaos Solitons Fract 2008,11.38(3).764–768.
[45] Tao Xianga, Kwok-Wo Wongb, Xiaofeng Liao.On the security of a novel key agreement protocol based on chaotic maps[J]. Chaos, Solitons & Fractals, 2009, 4.40(2).672-675.
[46] Xingyuan Wang, Jianfeng Zhao. An improved key agreement protocol based on chaos[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 12. 15(12).4052-4057.
[47] E. J. Yoon and K. Y. Yoo, A New Key Agreement Protocol Based on Chaotic Maps, In Proceedings of The Second KES International Symposium on Agent and Multi-Agent Systems: Technologies and Applications(KES-AMSTA’08), 2008.4953.897-906.
[48] Huei-Ru Tseng, Rong-Hong Jan, Wuu Yang, A Chaotic Maps-based Key Agreement Protocol that Preserves User Anonymity, IEEE International Conference on Communications (ICC 2009), Dresden, Germany, 2009, 6. 1-6.
[49] Yoshimura T, Kohda T. Resonance Properties of Chebyshev Chaotic Sequences [A] . Proceedings of the 2004 International Symposium on Circuits and Systems Volume 4[C]. New York: IEEE, 2004, 5. 4.573-576.
[50]赵耿,闫慧,童宗科.基于Chebyshev多项式的公钥密码算法的研究[J],计算机工程.2008,34.137-139.
[51] L.Kocarev, J.Makraduli, P.Amato. Public-Key Encryption Based on Chebyshev Polynomials[J]. Circuits, systems, and signal processing 2005. 24(5).497-517.
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