Nonlinear image encryption using a fully phase nonzero-order joint transform correlator in the Gyrator domain

Abstract

Abstract.A novel nonlinear image encryption scheme based on a fully phase nonzeroorder joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption-decryption scheme.

Effects of using an encrypted image corrupted by noise and occlusion in a security system based on joint transform correlator and Gyrator transform

“…To generate the encrypted image [2], we substract the central orders (|t α (u, v)| 2 and |h α (u, v)| 2 ) from the JGPD and divide by the nonlinear term |h α (u, v)| 2 , thus obtaining the expression…”

“…2(d)) is retrieved, because the central orders (|t α (u, v)| 2 and |h α (u, v)| 2 ) were removed from the JGPD and the nonlinear operation given by the term |h α (u, v)| 2 was introduced in the denominator of the encrypted function, see Eq. (11) [2].…”

Image quality and security through nonlinear joint transform encryption

“…The DRPE implemented with a JTC architecture has been extended from the Fourier domain to the Fresnel domain [14], the fractional Fourier domain [15][16] and the Gyrator domain [17][18][19]. In the nonlinear approaches [14,16,19], the nonlinear operations introduced in the JTC have become essential to correctly decrypt the input signal with satisfactory quality.…”

“…In the nonlinear approaches [14,16,19], the nonlinear operations introduced in the JTC have become essential to correctly decrypt the input signal with satisfactory quality. Moreover, the extension to other domains has increased the security of the overall encryption-decryption system by introducing new parameters that must be adjusted prior to obtaining the hidden information.…”

“…A fully-phase nonzero-order JTC architecture in the Gyrator domain has been designed with an improved resistance to brute force attacks, CPA, KPA and cyphertext-only attacks [19]. In this case the combination of two nonlinearities along with the rotation angle of the Gyrator transform improve the security of the encryption scheme.…”