Research Of Public Key Cryptosystems Based On Chaos

Public-key Cryptosystems is one of the most important academic researches in the modern cryptography. Chaotic systems are indeed characterized by sensitive dependence on initial conditions and similarity to random behavior, properties which seem pretty much the required by several cryptographic primitives. At present, a lot of applications remain within the confines of chaotic symmetric-key cryptosystems, but less applies to chaotic public-key cryptosystems. So, research of chaotic public-key cryptosystems is propitious to the development of public-key cryptosystems.In this paper, a modified ElGamal-like algorithm using Chebyshev polynomials based on finite fields is proposed with using a semi-group property, which makes possible implementing a trapdoor mechanism. Theory analysis indicates that security of the modified ElGamal-like algorithm is based on the intractability of the integer factorization problem and conventional discrete log problem. The program results of modified ElGamal-like algorithm analysis prove the feasibility of this scheme.The result analysis illustrate that this ElGamal-like algorithm can resist ciphertext only attack, if a few parameters are limited to choose, which enhances the security of the whole cryptographic algorithms. So, the modified ElGamal-like algorithm using Chebyshev polynomials based on finite fields has potential developments.