The Number Theoretic Hilbert Transform
This work addresses a specific mathematical problem in number theory and cryptography, offering a new transform for scrambling applications, but it appears incremental as it builds on existing discrete Hilbert transform concepts.
The paper introduces a number-theoretic Hilbert transform (NHT) that preserves circulant and alternating zero/non-zero row properties of the discrete Hilbert transform, with examples for 4-, 6-, and 8-point cases, and shows it can serve as a primitive for cryptographic scrambling transformations.
This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being zero and non-zero. Specific examples for 4-point, 6-point, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cryptographically useful scrambling transformations.