Applications of two-faced processes to random number generation

Boris Ryabko, Nadezhda Savina

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

Random and pseudorandom number generators (RNG and PRNG) are used for many purposes including cryptographic, modeling and simulation applications. For such applications a generated bit sequence should mimic true random, i.e., by definition, such a sequence could be interpreted as the result of the flips of a fair coin with sides that are labeled 0 and 1 (i.e., it is the Bernoulli process with p(0) = p(1) = 1/2). It is known that the Shannon entropy of this process is 1 per letter, whereas for any other stationary process with binary alphabet the Shannon entopy is stricly less than 1. On the other hand, the entropy of the PRNG output should be much less than 1 bit (per letter), but the output sequence should look like truly random. We describe random processes for which these, contradictory at first glance, properties, are valid. More precisely, it is shown that there exist binary-alphabet random processes whose entropy is less than 1 bit (per letter), but the frequency of occurrence of any word u goes to 2-u, where u is the length of u. In turn, it gives a possibility to construct RNG and PRNG which possess theoretical guarantees. This possibility is important for applications such as those in cryptography. We performed some experiments in which low-entropy sequences are transformed into two-faced sequences.

Original languageEnglish
Title of host publication2016 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages132-136
Number of pages5
ISBN (Electronic)9781509042319
DOIs
Publication statusPublished - 9 Dec 2016
Event15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016 - Saint-Petersburg, Russian Federation
Duration: 26 Sep 201629 Sep 2016

Publication series

Name2016 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016

Conference

Conference15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016
CountryRussian Federation
CitySaint-Petersburg
Period26.09.201629.09.2016

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