# Equivalence of F - algebras and cubic forms

Agrawal, Manindra ; Saxena, Nitin (2006) Equivalence of F - algebras and cubic forms Lecture Notes in Computer Science, 3884 . pp. 115-126. ISSN 0302-9743

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Related URL: http://dx.doi.org/10.1007/11672142_8

## Abstract

We study the isomorphism problem of two "natural" algebraic structures - \mathbbFF -algebras and cubic forms. We prove that the F -algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form 3Λ(#F - 1), this result implies that the two problems are infact equivalent. This result also has the following interesting consequence: Graph Isomorphism ≤ Pm F -algebra Isomorphism ≤ PmCubic Form Equivalence.

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