A quantum approach to fully homomorphic encryption

Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of the group of unitary operations to present a private-key quantum homomorphic encryption scheme that hides arbitrary quantum computations. A particular instance of our encoding hides information at least proportional to m/ logm bits when m bits are encrypted. This highlights the potential of our protocol to hide a non-trivial amount of information, and is suggestive of a large class of encodings that might yield better security.