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I wonder how this compares to homomorphic encryption? If I understand correctly, I could give someone a computation with an embedded key that operates over encrypted data, and they wouldn't be able to decrypt the data other than for the computation I gave them, right?

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I think it compares more to a One Time Program or Functional Encryption.

Homomorphic Encryption won't prevent you from decrypting other outputs (if you have a decryption key), and with Functional Encryption it's assumed both parties know the function being evaluated, so OTP is really the closest.

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