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Problem 1 in Stanford's crypto class [1]:

Data compression is often used in data storage or transmission. Suppose you want to use data compression in conjunction with encryption. Does it make more sense to

A. Compress the data and then encrypt the result, or

B. Encrypt the data and then compress the result.

Now we know the correct answer is Neither.

[1] http://crypto.stanford.edu/~dabo/cs255/hw_and_proj/hw1.pdf

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If you're encrypting and storing files, the answer is (A). The question is, in light of this result, frustratingly imprecise.

Well, B makes no sense. A makes sense, but might have leaks, that depending on use case (and in particular, whether the attacker can execute chosen plaintext attacks like in SSL) may or may not weaken the system, but it still makes sense.

For a confusing example of a fairly leaky cryptosystem involving compression that works well in practice and has a proof of security that is aware of the leak, see Douceur et al.'s "convergent encryption".

http://research.microsoft.com/apps/mobile/publication.aspx?i...

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