Fractional Fourier Transform Image Encryption Nonlinear Algorithm With Chaos And Random Phase

Image encryption is the effective measure to ensure the safety of the image. Mostof the image encryption is linear, compared with the nonlinear encryption system,linear encryption method is weak resistance to attack. Log-polar coordinatetransform is a kind of typical nonlinear transform. In this article, log-polarcoordinate transform is introduced into the study of the image encryption to improvethe ability against the attack of image encryption system, thus enhancing thesecurity of image encryption system.First of all, this paper introduces the fractional Fourier transform, the fractionalmellin transform, Arnold transform and its extended form in detail. Specially thefractional mellin transform and its realization method are analyzed. Setting up asimple way to achieve the fractional mellin transform, the fractional mellintransform of an image is equivalent to the log-polar coordinate transform of theimage then a certain order of the fractional Fourier transform. This laid thefoundation for the fast implementation of fractional Fourier transform imageencryption nonlinear algorithm with chaos and random phase is proposed in thispaper.Secondly, this paper establishes fractional Fourier transform image encryptionnonlinear algorithm with chaos and random phase and studied the effectiveness andsafety of the image encryption algorithm in detail, the research work mainly fromthe statistical characteristic analysis,sensitivity analysis of key, analysis ofanti-attack ability analysis of anti-interference ability and robustness analysis onfive different angles.In addition, this paper also adopts the numerical simulation method exemplarilyresearch the statistical distribution, the logarithmic mean square error，peak signalnoise ratio of the ciphertext image of this kind of image encryption algorithm andthe ciphertext image is damaged to decrypt the effect. The research results show thatfractional Fourier transform image encryption nonlinear password system withchaos and random phase is safe and effective, and can effectively resist the crackingattack of various typical password attack methods.