Paper 2018/659

On the Menezes-Teske-Weng’s conjecture

Sihem Mesnager and Kwang Ho Kim and Junyop Choe and Chunming Tang

Abstract

In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conjecture on properties of the solutions of a type of quadratic equation over the binary extension fields, which had been convinced by extensive experiments but the proof was unknown until now. We prove that this conjecture is correct. Furthermore, using this proved conjecture, we have completely determined the null space of a class of linear polynomials.