Abstract
In this paper, we propose a novel method for increasing the entropy of a sequence of independent, discrete random variables with arbitrary distributions. The method uses an auxiliary table and a novel theorem that concerns the entropy of a sequence in which the elements are a bitwise exclusive-or sum of independent discrete random variables.
Highlights
Sequences of random variables play an important role in many fields of science
If we have a sequence of k random variables, a natural and important question is as follows: what is the entropy of the sequence, and how does it grow with k? Examples include dynamical systems, cryptography, simulations, and statistics
Theorem 1 indicates that the simplest method for increasing the entropy of a sequence is to group its elements into blocks with R + 1 elements and compute the bitwise exclusive-or sum of all of the elements for each block
Summary
Sequences of random variables play an important role in many fields of science. If we have a sequence of k random variables, a natural and important question is as follows: what is the entropy of the sequence, and how does it grow with k? Examples include dynamical systems, cryptography, simulations, and statistics. Because high entropy of a random sequence is a necessary condition of its use in cryptography, several general methods that increase the sequence entropy have been proposed [2,3,4,5,6,7,8,9,10,11] These methods include both very simple correctors and complicated hash functions or ciphers.
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