New Results on the Number Theoretic Hilbert Transform
This work addresses a problem in cryptography by enhancing the applicability of number theoretic Hilbert transforms through increased solution multiplicity, though it appears incremental as it builds on existing transform theory.
The paper tackled the problem of finding new polymorphic solutions for number theoretic Hilbert transforms, specifically for 14-point and 16-point transforms, resulting in the discovery of transform pairs where the sequence and transform share the same shape, which increases solution multiplicity for the same moduli.
This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for which the sequence and the transform have the same shape. The multiplicity of solutions for the same moduli increases their applicability to cryptography.