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

Pseudo-free families of finite computational elementary abelian p -groups 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 G d {G_{d}} such that for every index d , each element of G d {G_{d}} 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

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

Groups Complexity Cryptology , Volume 9 (1) – May 1, 2017

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Publisher
de Gruyter
Copyright
Copyright © 2017 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2017-0001
Publisher site
See Article on Publisher Site

Abstract

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 G d {G_{d}} such that for every index d , each element of G d {G_{d}} 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.

Journal

Groups Complexity Cryptologyde Gruyter

Published: May 1, 2017

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