Non-malleable encryption of quantum information

TL;DR

This paper introduces the concept of non-malleable quantum encryption, showing its equivalence to unitary 2-designs, and provides bounds and constructions for such designs, enhancing quantum encryption security.

Contribution

It establishes the equivalence between non-malleable encryption and unitary 2-designs and presents new bounds and constructions for approximate 2-designs.

Findings

Non-malleable encryption is equivalent to a unitary 2-design.

A new proof of the lower bound on the number of unitaries in a 2-design.

Existence of approximate 2-designs with O(ε^{-2} d^4 log d) elements.

Abstract

We introduce the notion of "non-malleability" of a quantum state encryption scheme (in dimension d): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a "unitary 2-design" [Dankert et al.], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of (d^2-1)^2+1 on the number of unitaries in a 2-design [Gross et al.], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with =< d^5 elements, we show that there are always approximate 2-designs with O(epsilon^{-2} d^4 log d) elements.