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Yes, you can do that. Start by generating a random key and encrypting the data under that key. Now, you in turn encrypt that key with your password-derived key. The twist is that you include the already encrypted file in your PBKDF. So you generate a random key $k$ and then encapsulate it as $\mathcal{E}_{k'}(k)$, where $k' = H(PBKDF(\text{password}) \| ...


In distributed systems it is often bad practice to have "Shared Master Key". If a bad guy breaks in one of your devices he has the most important crypto piece of the system, and you're pretty much done. Rather have one key per device, and these keys are signed by an Authority I would say.


Your teacher is right, and here's why: What happens if you encrypt A with G and B with G? You can't decipher it, because you have no idea if the G in the ciphertext was an A or a B. So for the plaintext letter A you can use the ciphertext letter A, B, C, D, ..., Y or Z. (26 possible letters.) For B you can use A, B, C, D, ..., Y or Z, but not the letter ...


Based on the additional details in the comments, it seems like your question is: given $c_1=a\oplus d$ and $c_2=b\oplus d$, can we get $(a+b)\oplus d$. Where $a,b,d\in\mathbb{Z}_p$, $+$ is addition modulo $p$, and $\oplus$ is a bitwise XOR of the values, then taken modulo $p$. Or put another way, is there an operation $\boxplus$, such that $(a\oplus ...

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