Research Of Public Key Ciyptosystems And Key Agreement Based On Chebyshev Polynomial

Nowadays, the security of information draws more and more attentions, and it has become into a worldwide issue. Cryptography is the core of information security which is the purpose of Cryptography. Chaotic system has great application value in cryptography because of its broadband spectrum, sensitive dependence on initial conditions, pseudo-randomness and so on.Up to now, a lot of researches focused on symmetric-key cryptosystems, but less applied to public-key cryptosystems. The most representative public-key cryptography based on chaos is the public-key cryptography algorithms based on Chebyshev polynomials which was proposed by L.Kocarev. But the algorithm was proved not safe, even extended to finite fields. So, this paper proposed an improved ElGamal-like algorithm using the semi-group property of Chebyshev polynomials based on finite fields. The key point of this algorithm was the appointment of "the alternative multiply coefficient ki" which can forge the ciphertext tactfully and make the chosen-ciphertext attack out of work. Besides, the digital signature of the ciphertext can prevent the result from faking and tampering attack and make it have the function of identity authentication. Experimental results and performance analyses showed that the improved algorithm has much higher security and practical value.In addition, an improved key agreement scheme based on Chebyshev polynomials was proposed, which utilized RSA algorithm to encrypt and decrypt the value of Chebyshev polynomial, and ensured the security of the secret key. Besides, this key agreement protocol scheme has the funtion of identity authentication. The correctness, effectiveness and security of the new scheme were proved by theory analysis and experimental results.