  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.
