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

Pseudo-free families of finite computational elementary abelian p-groups AbstractWe initiate the study of (weakly) pseudo-freefamilies of computational elementary abelian p-groups,where p is an arbitrary fixed prime. We restrict ourselvesto families of computational elementary abelian p-groupsGd${G_{d}}$such that for every index d, each element of Gd${G_{d}}$is represented by a single bit string of length polynomialin the length of d. First, we prove that pseudo-freenessand weak pseudo-freeness for families of computationalelementary abelian p-groups are equivalent. Second, wegive some necessary and sufficient conditions for a familyof computational elementary abelian p-groups to bepseudo-free (provided that at least one of two additionalconditions holds). Third, we establish some necessary andsufficient conditions for the existence of pseudo-freefamilies 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): 18 – May 1, 2017

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

Abstract

AbstractWe initiate the study of (weakly) pseudo-freefamilies of computational elementary abelian p-groups,where p is an arbitrary fixed prime. We restrict ourselvesto families of computational elementary abelian p-groupsGd${G_{d}}$such that for every index d, each element of Gd${G_{d}}$is represented by a single bit string of length polynomialin the length of d. First, we prove that pseudo-freenessand weak pseudo-freeness for families of computationalelementary abelian p-groups are equivalent. Second, wegive some necessary and sufficient conditions for a familyof computational elementary abelian p-groups to bepseudo-free (provided that at least one of two additionalconditions holds). Third, we establish some necessary andsufficient conditions for the existence of pseudo-freefamilies of computational elementary abelian p-groups.

Journal

Groups Complexity Cryptologyde Gruyter

Published: May 1, 2017

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