Computational Security of Quantum Encryption
This work addresses the foundational problem of securing quantum data for cryptography, representing a novel extension of classical encryption theory rather than an incremental improvement.
The paper tackles the problem of encrypting quantum data in a computational security setting, establishing quantum versions of classical encryption definitions and showing that quantum-secure one-way functions and trapdoor permutations imply secure symmetric-key and public-key quantum encryption schemes, respectively.
Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.