Research Of Public Key Cryptography Based On Chebyshev Polynomials And The Related Work

With the rapid development of informationization, the application of new technologies such as cloud computing and big data will face more information security threats, cryptography becomes the key point to guarantee security. Since the communication environment has become increasingly complex and cryptanalysis ability is constantly improved, the security of some traditional cryptographic algorithms is threatened. Chaos is a certain system which can produce seemingly random behavior, with extreme sensitivity to initial conditions and system parameters, and good features such as pseudorandomness. satisfying the confusion and diffusion principle in the cryptosystem design. Thus chaos theory can inject new vitality into the research of new form cryptography technology.At present, the research of chaos-based cryptography mainly focuses on the chaotic stream and block cipher, etc., but chaos-based public key cryptography is relatively weak. This thesis concentrates on the research of chaotic public-key cryptography based on Chebyshev polynomials, involving the chaotic Hash function, the secure construction of public key cryptography, the design of the digital signature and key exchange protocol, and the application of public key cryptography in chaotic image encryption. The main results are as follows:(1) This thesis puts forward a novel one-way Hash function scheme (HFGCS) based on the globally coupled spatiotemporal chaotic system with paralleled structure. The length of plaintext block and final Hash value can be flexibly adjusted according to the actual demand. Experimental analysis indicates that HFGCS scheme has strong sensitivity to the plaintext and diffusion ability. The related comparison also shows its good performance. The research of chaotic Hash function provides the tool for public key cryptography based on Chebyshev polynomials and its related research.(2) Aiming at the disability to resist chosen-ciphertext attack of Chebyshev-Elgamal public key cryptography scheme (CEPKC) in finite field, this thesis puts forward two kinds of secure public key cryptography scheme based on Chebyshev polynomials:CEPKC-I and CEPKC-II, which can resist chosen-ciphertext attack and ensure the information integrity verification. Compared with CEPKC-â…  scheme, CEPKC-â…¡ scheme can break the limitation of encrypted plaintext length and has smaller ciphertext expansion rate. Furthermore, CEPKC-â…¡ is provably secure under the standard model against Indistinguishability under Adaptive Chosen Ciphertext Attack (IND-CCA2).An identity-based forward-secure digital signature scheme (IBFSS) is proposed, which takes advantage of public key cryptography by Chebyshev polynomials. IBFSS can make use of the identity information to verify the signature and prevent the forgery of previous signing messages even through the current secret key is leaked. The security of IBFSS scheme relies on the large integer factorization and Cheyshev discrete logarithm problem (CDLP). It also has advantages of simple structure and low computation cost.This thesis points out security and performance defects of a existing three-party key exchange protocol based on Chebyshev polynomial (3PKAC-â… ), then puts forward an improved scheme (3PKAC-â…¡), which can ensure the user identity information confidentiality and mutual authentication, and decrease the key distribution and management cost. In order to reduce the network communication burden of key exchange protocol, a novel two-party key exchange protocol scheme based on Chebyshev polynomials (2PKAC) is proposed, which has efficient key distribution and management strategy. Security analysis shows that 2PKAC scheme can resist different attacks.(3) Based on DNA encoding and chaotic systems, this thesis proposes a new selective image encryption scheme (SIE). The extreme sensitivity of Logistic and spatiotemporal chaotic system as well as the structural complexity can increase the complexity. The DNA encoding and algebraic operations can speed up the image confusion and diffusion ability. By selecting the first four high effective bit in each pixel, SIE scheme can reduce half of the encrypted data. This image information entropy is modulated as the parameters of spatiotemporal chaotic system, which makes it effective to resist chosen-plaintext attack. In order to solve the problem of key distribution and the information entropy transmission, SIE scheme and the proposed CEPKC-â…¡ scheme are combined to form a mixed encryption system. Experimental simulation and security analysis show that SIE scheme can guarantee security and high efficiency.