Public-Key Encryption Based on Extending Discrete Chebyshev Polynomials' Definition Domain to the Real Number

摘要

By combining Chebyshev polynomials with modulus compute, extending Chebyshev polynomials' definition domain to real number, some conclusions have been drawn by theoretic verification and data analyses. Making use of the framework of the traditional public-key algorithm RSA and ElGamal, this chapter proposes a chaotic public-key encryption algorithm 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 is easy to be implemented.