Bounds on fixed input/output length post-processing functions for biased physical random number generators

Abstract

Post-processing functions are used to reduce the imperfectness of physical random number generators. At FSE '07, Dichtl considered the case where the physical random number generator outputs independent bits that have a constant bias, and the post-processing function has fixed input and output lengths. In this paper, we first present a number of bounds on deg(n,m), which is a measure of the reduction of biases with n-bit input and m-bit output post-processing functions. We next show the exact values of deg(n,m) for a large class of (n,m) such that 1 ≤ m ≤ n ≤ 16, by using the bounds on deg(n,m) and a computer simulation. We finally discuss how we have derived these numerical values. © 2009 Springer.