“I’m in. #hackerman”

Fourier Transform can be used in image encryption and decryption. The method in which images are encrypted and decrypted use random phase masking.

Two random matrices are instantiated, and these will be treated as our keys. To encrypt, image is multiplied by the first random matrix then Discrete Fractional Fourier Transform (DFRFT) of order alpha is applied (this is phase masking). The result is then multiplied with the second random matrix, then DFRFT of order beta is applied. To decrypt, one simply works in reverse. You first apply DFRFT of order beta-prime on the encrypted image then  multiply the encrypted image with the inverse of the second random matrix. Then, DFRFT of order alpha-prime is applied, after which, the result is multiplied with the inverse of the first random matrix. Basically, to encrypt, you apply some procedures, then to decrypt, you apply the inverse, cancelling out the encryption.

This works because without the proper parameters/keys, decryption result returns noise, which an image may not be inferred from.fourier

(image is a screenshot from the work of Mr. Ashutosh; mentioned in the sources)

Ashutosh, D.S. (2013). Robust Technique for Image Encryption and Decryption Using Discrete Fractional Fourier Transform with Random Phase Masking. Retrieved from http://www.sciencedirect.com/science/article/pii/S2212017313005756

Hennelly, B.M. & Sheridan, J.T. (2003). Image encryption and the fractional Fourier transform. Retrieved from http://eprints.maynoothuniversity.ie/5809/1/BH-Image-Encryption.pdf

Sharma, P. (2013). Efficient Image Encryption and Decryption Using Discrete Wavelet Transform and Fractional Fourier Transform. Retrieved from https://arxiv.org/ftp/arxiv/papers/1401/1401.6087.pdf