A quantum approach to homomorphic encryption
This addresses the challenge of secure quantum computation for cryptography applications, representing a novel theoretical advancement rather than an incremental improvement.
The paper tackles the problem of enabling quantum computation on encrypted data by presenting a private-key quantum homomorphic encryption scheme based on group theory, achieving the ability to hide up to a constant fraction of encrypted information with polynomial overhead scaling.
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 a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data. A particular instance of our encoding hides up to a constant fraction of the information encrypted. This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length. 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.