title: A quantum approach to homomorphic encryption.
abstract: 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. The quantum data is encoded on bosons of distinct species in distinct spatial modes, and the quantum computations are manipulations of these bosons in a manner independent of their species. 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.
authors.affiliation: Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372.
authors.forename: Si-Hui
authors.initials: SH
authors.lastname: Tan
authors.affiliation: Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372.
authors.forename: Joshua A
authors.initials: JA
authors.lastname: Kettlewell
authors.affiliation: Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372.
authors.forename: Yingkai
authors.initials: Y
authors.lastname: Ouyang
authors.affiliation: School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.|International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China.
authors.forename: Lin
authors.initials: L
authors.lastname: Chen
authors.affiliation: Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372.|Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, Singapore 117543.
authors.forename: Joseph F
authors.initials: JF
authors.lastname: Fitzsimons