Abstract: By combining Chcbyshcv polynomials with modulus compute, extending Chcbyshcv polynomials' definition domain to real number, some conclusions were drawn by theoretic verification and data analysis. Making use of the framework of the traditional publi}kcy algorithm RSA and E1Gama1, proposed a chaotic publi}key encryption algo- rithm based on extending discrete Chebyshev polynomials' definition domain to Real number. Its security is based on the intractability of the integer factorization problem as RSA，and it is able to resist the chosen cipher-text attack against RSA and easy to be implemented.

Key words: Public-key encryption, Chcbyshcv polynomials, Rcal number domain, Chaotic map