Quantum non-malleability and authentication

TL;DR

This paper introduces a stronger definition of quantum non-malleability that prevents plaintext injection, links it to secrecy, and improves quantum authentication methods using two-designs.

Contribution

It proposes a new, more robust definition of quantum non-malleability, demonstrating its equivalence to encryption with two-designs and enhancing quantum authentication techniques.

Findings

New definition of quantum non-malleability that prevents plaintext injection.

Quantum non-malleability implies secrecy, unlike in classical encryption.

Quantum authentication can be achieved with two-designs, improving previous methods.

Abstract

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.