一种基于混沌的公钥加密方案
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摘要
在传统猫映射的基础上提出一种二维超混沌映射,应用四维Qi超混沌系统产生公钥系统所需的具有良好随机性的伪随机序列,将伪随机序列和超混沌映射组成公钥生成算法并产生对应的公钥和私钥,最终将密钥序列作为AES等对称加密算法的输入密钥进行加密。该公钥加密方案结合了公钥生成算法和对称加密算法,具有良好的保密性。最后对该加密方案进行Matlab仿真验证。
Based on the traditional cat mapping, a two-dimensional hyperchaotic mapping is proposed. The pseudo-random sequence with good randomness is generated by the four-dimensional Qi hyperchaotic system. The pseudo-random sequence and the hyperchaotic map are composed into the public key generating algorithm which generates the corresponding public key and private key, and finally encrypts the key sequence as the input key of symmetric encryption algorithm such as AES. The public key encryption scheme combines the public key generation algorithm and the symmetric encryption algorithm, and has good confidentiality. Finally, the simulation scheme is verified by Matlab.
Based on the traditional cat mapping, a two-dimensional hyperchaotic mapping is proposed. The pseudo-random sequence with good randomness is generated by the four-dimensional Qi hyperchaotic system. The pseudo-random sequence and the hyperchaotic map are composed into the public key generating algorithm which generates the corresponding public key and private key, and finally encrypts the key sequence as the input key of symmetric encryption algorithm such as AES. The public key encryption scheme combines the public key generation algorithm and the symmetric encryption algorithm, and has good confidentiality. Finally, the simulation scheme is verified by Matlab.
引文
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[3]杨晓元,吴立强,张敏情.基于R-LWE的公钥加密方案[J].通信学报,2013(2):23-30
[4]Okamoto T,Wang X.Public key cryptography-pck 2007[M].Springer Berlin Heidelberg,2007
[5]Sepahi R,Pieprzyk J,Shahandashti S F,et al.New security notions and relations for public-key encryption[J].Journal of Mathematical Cryptology,2012,6(3):183-227
[6]崔永刚,刘玉军.可公开验证的短密钥公钥加密方案[J].通信学报,2010,31(3):45-50
[7]陈传波,祝中涛.RSA算法应用及实现细节[J].计算机工程与科学,2006,28(9):13-14
[8]Hinek,Jason M.On the security of multi-prime RSA[J].Journal of Mathematical Cryptology,2008,2(2):117-147
[9]卢建朱,陈火炎,林飞.ElGamal型多重数字签名算法及其安全性[J].计算机研究与发展,2000,37(11):1335-1339
[10]周绯菲,鲁士文.RSA算法的内在特性、破解与防范措施[J].天津大学学报,2006,39(s1):379-382
[11]杨云江.RSA算法缺陷分析[J].贵州大学学报(自然版),2006,23(1):35-39
[12]侯小梅.电子商务安全与混沌加密的研究[D].华南理工大学,2001
[13]Kocarev L,Tasev Z.Public-key encryption based on chebyshev maps[C]//International Symposium on Circuits and Systems.IEEE xplore,2003:III-28-III-31vol.3
[14]王大虎,魏学业,柳艳红.Chebyshev多项式的公钥加密和身份认证方案的研究[J].北京交通大学学报,2005,29(5):40-42
[15]Ranjan Bose.Novel public key encryption technique based on multiple chaotic systems[J].Physical Review Letters,2005,95(9):098702
[16]王开,裴文江,邹留华,等.一种多混沌系统公钥密码算法的安全性分析[J].物理学报,2006,55(12):6243-6247
[17]杨叶.基于混沌理论的非对称加密算法研究[D].东北大学,2009
[18]Qi G,Van Wyk M A,Van Wyk B J,et al.A new hyperchaotic system and its circuit implementation[J].Chaos Solitons&Fractals,2009,40(5):2544-2549
[19]Arnol d,V.I,Avez A.Ergodic problems of classical mechanics[J].Benjamin,1968:hard:pbk
[20]Bech C,Friedrich S.Thermodynamics of chaotic systemsan introduction[M].Cambridge University Press,1993,164(7):295-296
[21]马在光,丘水生.基于广义猫映射的一种图像加密系统[J].通信学报,2003,24(2):51-57
[22]文磊,黎明.密码分析技术[C]//全国计算机科学与技术应用学术会议.2003
[23]刘景美.现代密码算法分析与研究[D].西安电子科技大学,2006