I am working on the design of an image encryption algorithm. The algorithm has a sound score of entropy, low correlation, resistance to anti-cropping attacks, and resistance to salt and pepper noise. The only issue with the algorithm is its resistance to counter gaussian noise.
IYH Dear Rashad Ali
Have a look at Double Random Phase Encoding (DPRE).
Full discloure: While DRPE provides a level of resistance to Gaussian noise, it's not immune to noise. The effectiveness of DRPE against Gaussian noise depend on factors such as the amplitude of the noise, the characteristics of the phase masks, and the specific implementation of the DRPE algo. You will need to test your encryption system under various noise conditions to ensure its robustness for your use cases.
Here's how it works and why it's resistant to such noise:
a) DRPE involves applying two random phase masks to the image—one in the spatial domain and one in the Fourier domain. The process typically includes the following steps:
- The original image is multiplied by a random phase mask in the spatial domain.
- The result is then transformed into the Fourier domain using a Fast Fourier Transform (FFT).
- A second random phase mask is applied in the Fourier domain.
- An inverse FFT is performed to obtain the encrypted image.
b) Resistance to Gaussian Noise
- Random Phase Masks: The use of random phase masks in DRPE means that the important information of the image is diffused throughout the entire encrypted image. This diffusion makes the encrypted data less susceptible to localized noise, such as Gaussian noise, because the critical information is not concentrated in any specific area.
- Fourier Domain Operations: Since Gaussian noise primarily affects the high-frequency components of an image, the encryption in the Fourier domain allows for the manipulation of these components. By carefully designing the phase masks, the algorithm can make the encrypted image less sensitive to the frequency range where Gaussian noise has the most impact.
- Noise Distribution: When Gaussian noise is added to an encrypted image created with DRPE, the noise tends to spread out across the entire image upon decryption. This is due to the random phase masks redistributing the noise throughout the image, which can make it easier to filter out or correct.
- Error Tolerance: DRPE can be inherently error-tolerant. Small perturbations caused by noise do not significantly alter the phase information. When the decryption process is applied, the image can often be reconstructed without substantial degradation, even in the presence of noise.
IYH Dear Rashad Ali
Generally, no. Double Random Phase Encoding is generally considered an irreversible image encryption technique due to its underlying mathematical nature. Why? The main reason behind this lies in the convolution process applied during encoding, which blends the original img with a pseudorandom reference function generated via two separate random phases. Upon decryption, the inverse operation requires precise knowledge of both random phases employed initially—otherwise, perfect recovery of the original image becomes impossible.
Certain variations of the DRPE algo are explored for potentially reversible scenarios. Extensions incorporate auxiliary channels or side info alongside the encrypted imgs themselves, enabling partial restoration even when facing missing or corrupted phase terms.
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