Non-malleable encryption of quantum information
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.
Cite
@article{arxiv.0808.0353,
title = {Non-malleable encryption of quantum information},
author = {Andris Ambainis and Jan Bouda and Andreas Winter},
journal= {arXiv preprint arXiv:0808.0353},
year = {2017}
}
Comments
8 pages. Title changed in v2, a couple of mistakes corrected, the results are essentially unchanged; accepted for publication at J Math Phys