Inverting HFE systems is quasi-polynomial for all fields

Authors:
Jintai Ding;Timothy J. Hodges
Affiliations:
South China University of Technology, Guangzhou, China and Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH;South China University of Technology, Guangzhou, China and Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH
Venue:
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Year:
2011

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Abstract

In this paper, we present and prove the first closed formula bounding the degree of regularity of an HFE system over an arbitrary finite field. Though these bounds are not necessarily optimal, they can be used to deduce 1. if D, the degree of the corresponding HFE polynomial, and q, the size of the corresponding finite field, are fixed, inverting HFE system is polynomial for all fields;