  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.
