Post-Processing Functions for a Biased Physical Random Number Generator

Abstract

Abstract.A corrector is used to reduce or eliminate statistical weakness of a physical random number generator. A description of linear corrector generalizing post-processing described by M. Dichtl at FSE'07 [5] is introduced. A general formula for non linear corrector, determining the bias and the minimal entropy of the output of a function is given. Finally, a concrete and efficient construction of post-processing function, using resilient functions and cyclic codes, is proposed.

A Comparison of Post-Processing Techniques for Biased Random Number Generators

“…In this section, we describe a technique proposed by Lacharme [6], which derives good linear compression for random number generation based on good error correcting codes. The input is a random stream where each input bit has bias e. The output will be a "more" random stream where each output bit has bias e < e.…”

“…Examples of this can be found, in [6] and [9], where BCH and extended BCH codes were used to construct linear corrector functions. We note, however, that the particular codes picked in these papers do not offer significant advantages over the Von Neumann corrector.…”

“…Each of these methods has its pros and cons. Another technique, proposed by several authors [4,6,9] recently, uses linear compression functions based on good linear codes. Since there is a large pool of linear codes to choose from, it becomes possible to trade-off different aspects of a HRNG's performance, unlike in the other methods.…”

“…We show that linear compression can lower the adversary bias by much more than Von Neumann compression. In [6,9], the authors suggested using BCH codes with parameters [255,21,111] and [256,16,113] for linear compression, which do not seem to offer any advantage over Von Neumann compression in terms of throughput and correction of random bias. However, we show that these BCH codes are many times more effective than Von Neuman compression for correcting the adversary bias.…”

High-Speed Magnetoresistive Random-Access Memory Random Number Generator Using Error-Correcting Code

“…Moreover, we could not see any specific correlation between improvement and the error-correcting capability t. This does not follow the prediction of ref. 10 in which better random numbers are obtained as t (or d) increases (d and t has a relation d > 2t). Because RNG speed decreases at rate k/n, and n − k extra redundant memory cells are required, these results show that a small t can be chosen.…”