Interpolation of functions related to the integer factoring problem

Abstract

The security of the RSA public key cryptosystem depends on the intractability of the integer factoring problem. This paper shall give some theoretical support to the assumption of hardness of this number theoretic problem. We obtain lower bounds on degree, weight, and additive complexity of polynomials interpolating functions related to the integer factoring problem, including Euler's totient function, the divisor sum functions, Carmichael's function, and the RSA-function. These investigations are motivated by earlier results of the same flavour on the interpolation of discrete logarithm and Diffie-Hellman mapping. © Springer-Verlag Berlin Heidelberg 2006.