Research And Design Of The Probabilistic Public-key Cryptosystem Based On Chebyshev

In1976, the public-key cryptosystem proposed as a revolution in cryptography, which opens up a new era of cryptography and makes the cryptography more security. However, with technology advances and the upgrading of the computer, the attacker cracking the encrypted information is increasingly easy; the traditional encryption methods have been unable to meet people’s needs, so there is an urgent need for a new cryptosystem, which is able to resist traditional attacks.Chaotic system has many features, good cryptographic properties of which provide a new direction for the cryptosystem designers. Therefore, chaos-based cryptography favored by cryptography experts, and achieved a lot, however, these results are mostly in symmetric cryptography research, the research results based on the chaotic public-key cryptosystem is still less.In this paper, the Chebyshev characteristics of the chaotic system were analyzed and summarized, cryptosystem based on Chebyshev polynomials are introduced. The results of this study are as follows:(1) This paper analyzes the security of public-key cryptosystem of Chebyshev polynomial based on the finite field and researches the Problems.(2) This paper uses the formal language to demonstrate the equivalence of indiscernibility and semantic security, and then using formal language and reduction prove the equivalence of IND-CCA2and NM-CCA2.(3) According to the problems of public-key cryptosystem based on Chebyshev polynomials, this paper designes two probabilistic public-key cryptosystem based on Chebyshev polynomials. The analysis results show that the proposed probabilistic cryptosystem based on Chebyshev polynomials is correct; the first probabilistic cryptosystem can achieve semantic security and the second one can resist adaptive chosen-ciphertext attack based on the demonstration.At last, this paper gives the respect of the public-key cryptosystem based on chaotic system.