The Improved Public-key Encryption Algorithm Based On Finite Field Chebyshev Polynomial And RSA Cryptosystem

According to a public key cryptography algorithm based on the chaotic characteristics of the finite field Chebyshev polynomial and RSA, by defining the initial generation of key values and conditions, intermediate values of limited in encryption algorithm, this thesis provides an improved method, the improved algorithm is still based on large integer factorization and crack of finite fields Chebyshev polynomial iteration problem, through the analysis of the algorithm and examples, prove the validity of the algorithm. The module p in improved algorithm is as a private key, so it can very good resistance to ciphertext-only attack. Through exhaustive attack on traditional RSA algorithm and the improved algorithm module, and the algorithm structure analysis, explained in terms of safety improvement algorithm and big integer factorization or discrete Chebyshev problem solving over finite fields is quite. The algorithm even if the modulus p is cracked, but it is very difficult to obtain the private key d. In efficiency, under the condition of the same amount.of information, we give the analysis and comparison of the improved algorithm and the original algorithm, the traditional RSA and EIGamal algorithm based on the finite field Chebyshev polynomials. Then use program to realize the fast matrix iterative calculation of finite fields Chebyshev polynomial and its application to the improved algorithm, which greatly saves the computing time. At the same time to ensure safe and fast calculation of the improved algorithm, the selection parameters requirements are proposed.