2. A few months ago, I read an article about a company (or maybe it was just a guy) who claimed that he could manipulate encrypted information in a meaningful way without destroying the integrity of the data, and without knowing the actual data. This was via an cryptological homomorphism, which, I think, simply means that certain operations can be performed on x by performing a corresponding operation on E(x). It seems to me that this is a crock. Is sufficiently encrypted information indistinguishable from random noise or what?
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Well, multiplying an RSA ciphertext by a constant and then decrypting is equivalent to decrypting and multiplying by a constant, so RSA is homomorphic with respect to multiplication. Finding a cryptosystem that's homomorphic with respect to both multiplication and addition is harder, though, and that seems to be what happened. See
ReplyDeletehttp://www.schneier.com/blog/archives/2009/07/homomorphic_enc.html
for more details.