Generalized Elias schemes for efficient harvesting of truly random bits

Abstract

The problem of generating a sequence of true random bits (suitable for cryptographic applications) from random discrete or analog sources is considered. A generalized version, including Vector Quantization, of the classical approach by Elias for the generation of truly random bits is introduced, and its performance is analyzed, both in the finite case and asymptotically. The theory allows us to provide an alternative proof of the optimality of the original Elias' scheme. We also consider the problem of deriving random bits from measurements of a Poisson process and from vectors of iid Gaussian variables. The comparison with the scheme of Elias, applied to geometric-like non binary vectors, originally based on the iso-probability property of permutations of iid variables, confirms the potential of the generalized scheme proposed in our work.

Playing Games with Bounded Entropy: Convergence Rate and Approximate Equilibria

“…Von Neumann (1951) also offered a nonuniversal exact algorithm for simulation of a desired continuous distribution from a given continuous random variable with known distribution. A generalization of the algorithm of Von Neumann (1951) for arbitrary Markov inputs can be found in Elias (1972) and Bernardini and Rinaldo (2018). There are other works that have considered non-exact simulation of a source.…”