Niho Bent Functions and Subiaco/Adelaide Hyperovals
arXiv:1210.4732v17 citations
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This work addresses a theoretical problem in finite geometry and cryptography by linking bent functions to hyperovals, but it is incremental as it builds on known classes.
The paper established a connection between binomial Niho bent functions and o-polynomials generating Subiaco and Adelaide hyperovals, enabling an expansion of the bent function class for Subiaco hyperovals when m ≡ 2 (mod 4).
In this paper, the relation between binomial Niho bent functions discovered by Dobbertin et al. and o-polynomials that give rise to the Subiaco and Adelaide classes of hyperovals is found. This allows to expand the class of bent functions that corresponds to Subiaco hyperovals, in the case when $m\equiv 2 (\bmod 4)$.