Relationships between quantum IND-CPA notions

Relationships between quantum IND-CPA notions (TCC 2021)
Tore Vincent Carstens, Ehsan Ebrahimi, Gelo Tabia, Dominique Unruh
[ eprint | official ]

An encryption scheme is called indistinguishable under chosen plaintext attack (short IND-CPA) if an attacker cannot distinguish the encryptions of two messages of his choice. There are other variants of this definition but they all turn out to be equivalent in the classical case. In this paper, we give a comprehensive overview of these different variants of IND-CPA for symmetric encryption schemes in the quantum setting. We investigate the relationships between these notions and prove various equivalences, implications, non-equivalences, and non-implications between these variants.