Si-Hui Tan, Singapore University of Technology and Design
We introduce an approach to homomorphic encryption on quantum data.
Homomorphic encryption is a cryptographic scheme that allows
evaluations to be performed on ciphertext without giving the evaluator
access to the secret encryption key. Random operations from an finite
abelian unitary group chosen using an encryption key chosen
uniformly at random perform the encryption, and operations that lie
within the centralizer of the encryption group perform the
computation. Since the latter operations commute with any evaluation
in the encryption group by definition, applying the inverse of the
encryption decrypts the evaluated state, and the decryption key
depends only on the encryption key. We show that the group of
operations that can be used for computation is isomorphic to a unitary
group of a large dimension. Moreover our scheme is information
theoretically secure, that is, given orthogonal inputs to our sceme,
the evaluator can only extract some amount of classical information
that is exponentially suppressed via the Holevo quantity. For a
specific encoding, we show that our scheme is able to hide a constant
fraction of bits that can be made arbitrarily close to unity.