Closed-form Hermite–Gaussian-like number-theoretic transform eigenvectors

• Closed-form Hermite–Gaussian-like number-theoretic transform eigenvectors are proposed.
• Such eigenvectors are used to define a new fractional number-theoretic transform (FrNTT).
• The introduced FrNTT is used as the basis for an image encryption scheme.

In this paper, we introduce closed-form Hermite–Gaussian-like (HGL) number-theoretic transform (NTT) eigenvectors. The method for constructing such eigenvectors was inspired by a recently proposed approach, where closed-form HGL discrete Fourier transform eigenvectors are constructed. Compared with a previously developed proposal for the NTT scenario, the method described in the present work avoids some ambiguities and produces eigenvectors whose components do not lie in extension fields. The new HGL eigenvectors are used to define a fractional number-theoretic transform, whose application in the image encryption framework is illustrated.