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Additive decompositions induced by multiplicative characters over finite fields

Type of publication Peer-reviewed
Publikationsform Contribution to book (peer-reviewed)
Author Schipani D., Elia M.,
Project New Cryprosystems based on Algebra
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Contribution to book (peer-reviewed)

Book Theory and applications of finite fields
Publisher Amer. Math. Soc., Providence RI
Volume (Issue) 579
Page(s) 179 - 186
ISBN 2157-8095
Title of proceedings Theory and applications of finite fields
DOI 10.1090/conm/579/11529

Abstract

In 1952, Perron showed that quadratic residues in a field of prime order satisfy certain ad- ditive properties. This result has been generalized in different directions, and our contribution is to provide a further generalization concerning multiplicative quadratic and cubic characters over any finite field. In particular, recalling that a character partitions the multiplicative group of the field into cosets with respect to its kernel, we will derive the number of representations of an element as a sum of two elements belonging to two given cosets. These numbers are then related to the equations satisfied by the polynomial characteristic functions of the cosets.
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