Verify that if you have an image I with all zeroes except...

Verify that if you have an image $I$ with all zeroes except for a single location with value 1, that $(f * I)(a,b) = f$. Try it for a 3x3 filter $f$ and a 5x5 image $I$ with a 1 in the middle and zeros everywhere else. Note that the result $(f * I)(a, b)$ might be a bit offset from $f(a, b)$ depending on your indexing.

We can recover the original image by XORing the noise image with the key in a certain fashion. XOR (also known as exclusive OR) is a boolean 'bitwise' operation. You can read about it here. In Python, with A&B integers, 'A^B' performs a bitwise XOR on the bits representing the integer values of A and B. Also, there is an augmented operator, '^='. 'A ^= B' XORs A & B and stores the result in A. Also, Numpy arrays define '^' and '^=' operators. We encrypt an image by XORing the image with a key. We recover the image by XORing with the key again. This works because A^B^A = B. Load the key array by doing key = np.load('key.npy'). Note that the length of the key is the same as one row of the secret image. To reveal the secret image, XOR each red, green, and blue row of the image with the key, then display the very pretty result. The 'imageshow' function may provide a better rendition than plt.imshow.

Akash M.

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