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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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CiteScore 2017: 0.32

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1869-6104
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Pseudo-free families of finite computational elementary abelian p-groups

Mikhail Anokhin
Published Online: 2017-04-19 | DOI: https://doi.org/10.1515/gcc-2017-0001

Abstract

We initiate the study of (weakly) pseudo-free families of computational elementary abelian p-groups, where p is an arbitrary fixed prime. We restrict ourselves to families of computational elementary abelian p-groups Gd such that for every index d, each element of Gd is represented by a single bit string of length polynomial in the length of d. First, we prove that pseudo-freeness and weak pseudo-freeness for families of computational elementary abelian p-groups are equivalent. Second, we give some necessary and sufficient conditions for a family of computational elementary abelian p-groups to be pseudo-free (provided that at least one of two additional conditions holds). Third, we establish some necessary and sufficient conditions for the existence of pseudo-free families of computational elementary abelian p-groups.

Keywords: Family of computational groups; pseudo-free family of computational groups; weakly pseudo-free family of computational groups; collision-intractable family of functions; one-way family of functions

MSC 2010: 68Q17; 94A60

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About the article

Received: 2015-11-29

Published Online: 2017-04-19

Published in Print: 2017-05-01


Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 13-01-00183

This research was supported in part by the Russian Foundation for Basic Research (13-01-00183).


Citation Information: Groups Complexity Cryptology, Volume 9, Issue 1, Pages 1–18, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2017-0001.

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