On the Security Notions for Encryption in a Quantum World

Indistinguishability against adaptive chosen-ciphertext attacks (IND-CCA2) is usually considered the most desirable security notion for classical encryption. In this work, we investigate its adaptation in the quantum world, when an adversary can perform superposition queries. The security of quantum-secure classical encryption has first been studied by Boneh and Zhandry (CRYPTO’13), but they restricted the adversary to classical challenge queries, which makes the indistinguishability only hold for classical messages (IND-qCCA2). We extend their work by giving the first security notions for fully quantum indistinguishability under quantum adaptive chosen-ciphertext attacks, where the indistinguishability holds for superposition of plaintexts (qIND-qCCA2). This resolves an open problem asked by Gagliardoni et al. (CRYPTO’16). The qCCA2 security is defined in Boneh-Zhandry’s paper using string copying and comparison, which is inherent in the classical setting. Quantumly, it is unclear what it means for a ciphertext to be different from the challenge ciphertext, and how the challenger can check the equality. The classical approach would either violate the no-cloning theorem or lead to perturbing the adversary’s state, which may be detectable. To remedy these problems, from the recent groundbreaking compressed oracle technique introduced by Zhandry (CRYPTO’19), we develop a generic framework that allows recording quantum queries for probabilistic functions. We then give definitions for fully quantum real-or-random indistinguishability under adaptive chosen-ciphertext attacks (qIND-qCCA2). In the symmetric setting, we show that various classical modes of encryption are trivially broken in our security notions. We then provide the first formal proof for quantum security of the Encrypt-then-MAC paradigm, which also answers an open problem posed by Boneh and Zhandry. In the public-key setting, we show how to achieve these stronger security notions (qIND-qCCA2) from any encryption scheme secure in the sense of Boneh-Zhandry (IND-qCCA2). Along the way, we also give the first definitions of non-malleability for classical encryption in the quantum world and show that the picture of the relations between these notions is essentially the same as in the classical setting.