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I'm in the middle of planning a 5000ish word essay on fully homomorphic cryptography, the current practical implementations and their limitations.

Which areas of CS as a subject have been (or will be) most affected or will utilise fully homomorphic cryptography the most in the coming years and developments?

PS. I did several searches and couldn't find a repeated iteration of this question, hope the fact this isn't a specific theory questions gets me in hot water!

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Before turning to your actual question, let me mention that there aren't any practical implementations of fully homomorphic encryption. There are some implementations that are far from being practical, and it's hard to guess whether that will change in the foreseeable future.

Fully homomorphic encryption is a goal in itself, as it enables outsourcing computation resources without sacrificing privacy. As such, its applications are mainly outside computer science, in the same way that the word processor Microsoft Word doesn't have any applications inside computer science (other than writing papers; though you should do that in LaTeX).

That said, fully homomorphic encryption could be used as a building block for other cryptographic applications. Vaikuntanathan's technical survey article contains some pointers in Section 6.4: verifiably outsourcing computation; and constructing short non-interactive zero-knowledge proofs. The latter has other applications and is not an end in itself, see Groth's technical survey article.

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