New results on quasi-subfield polynomials

TL;DR

This paper introduces new quasi-subfield polynomial families and a theorem limiting their existence, showing they do not improve the efficiency of solving the ECDLP over small characteristic finite fields.

Contribution

It provides novel quasi-subfield polynomial families and a theoretical limit on their existence, impacting their applicability to ECDLP algorithms.

Findings

New quasi-subfield polynomial families discovered

A theorem limits the existence of such polynomials

No speedup achieved for ECDLP algorithms using these polynomials

Abstract

Quasi-subfield polynomials were introduced by Huang et al. together with a new algorithm to solve the Elliptic Curve Discrete Logarithm Problem (ECDLP) over finite fields of small characteristic. In this paper we provide both new quasi-subfield polynomial families and a new theorem limiting their existence. Our results do not allow to derive any speedup for the new ECDLP algorithm compared to previous approaches.