With the introduction of quantum computing and realizing it capabilities through Shor's algorithm and other advancements, cryptographers shifted their focus on post-quantum cryptography, where they would use classical encryption schemes (classical input, classical output) that are secure against quantum computers. When it comes to quantum encryption schemes, where the input and output are quantum, the one that is introduced in introductory textbooks is the quantum one-time pad, whose key is actually a pair of classical strings. Interestingly enough, quantum one-time pad is the only quantum encryption scheme that I have come across so far.

My question is: Are there other quantum encryption schemes potentially with quantum, non-classical, keys? If so, is there a survey/reference summarizing these schemes?

Basically I am looking for quantum counterparts of AES, RSA, and LWE in the context of private key and public key cryptography, conceptually speaking. I understand that QKD is used for establishing secure keys, but that is different than encryption schemes. Furthermore, I understand that from a practical point of view, most probably quantum encryption schemes may not be that relevant, at least for the time being. My question is mainly out of curiosity.


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Although much research focuses on Quantum Key Distribution, there are other facets of quantum cryptography like quantum encryption, quantum signatures, quantum zero-knowledge proofs and many more. One of the simplest that comes to my mind is Kak's Three-stage protocol, where a sender can securely send a quantum state to a receiver. The protocol is, in some sense, a quantum equivalent of Shamir’s three-pass protocol in classical cryptography.

There are many survey papers on quantum cryptography, although I should admit that most of them focus on QKD. You could have a look at the paper "A Survey of Important Issues in Quantum Computing and Communications". In section VI.C of that paper, you will be able to find an unexhaustive list of works in quantum cryptography that do not involve quantum key distribution.


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