Chebyshev Approximation by Rational Expression Functions of Two Variables

Abstract

The method for constructing of Chebyshev approximation by rational expression for function of two variables is proposed. Idea of the method is based on constructing the boundary power-average approximation in p L norm with p   . Least square method with two weight functions is used to construct of this approximation. One weight function ensures the con-struction of power-average approximation, and another refines parameters of rational expression by linearization scheme. Iterative refinement of weight functions values is proposed. Results of test examples solving con-firm the effectivity of and to prove correctly the conditions that ensure the CPA-security of the NTRUCipher encryption scheme. A certain result is analytical bounds of decryption failure probability in NTRUCipher encryption scheme. This result is important for the proper parameters’ choice of the encryption scheme in its practical implementa-tion. It is shown that the decryption failure probability in the NTRUCipher varies from 357 2  to 157 2  while the value of this probability for the NTRUEncrypt encryption scheme 160 2  to 74 2  . In addition, the obtained bounds are not based