# Quantum non-malleability and authentication. (arXiv:1610.04214v2 [quant-ph] UPDATED)

In encryption, non-malleability is a highly desirable property: it ensures

that adversaries cannot manipulate the plaintext by acting on the ciphertext.

Ambainis, Bouda and Winter gave a definition of non-malleability for the

encryption of quantum data. In this work, we show that this definition is too

weak, as it allows adversaries to "inject" plaintexts of their choice into the

ciphertext. We give a new definition of quantum non-malleability which resolves

this problem. Our definition is expressed in terms of entropic quantities,

considers stronger adversaries, and does not assume secrecy. Rather, we prove

that quantum non-malleability implies secrecy; this is in stark contrast to the

classical setting, where the two properties are completely independent. For

unitary schemes, our notion of non-malleability is equivalent to encryption

with a two-design (and hence also to the definition of Ambainis et al.). Our

techniques also yield new results regarding the closely-related task of quantum

authentication. We show that "total authentication" (a notion recently proposed

by Garg, Yuen and Zhandry) can be satisfied with two-designs, a significant

improvement over the eight-design construction of Garg et al. We also show

that, under a mild adaptation of the rejection procedure, both total

authentication and our notion of non-malleability yield quantum authentication

as defined by Dupuis, Nielsen and Salvail.