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small characteristic. It works especially well when the characteristic
is fixed. Indeed, in this case, we obtain a total complexity of $L(1/4+o(1)).$
We construct classical systems that remain secure when exposed to such quantum queries. For signatures we construct two compilers that convert classically secure signatures into signatures secure in the quantum setting and apply these compilers to existing post-quantum signatures. We also show that standard constructions such as Lamport one-time signatures and Merkle signatures remain secure under quantum chosen message attacks, thus giving signatures whose quantum security is based on generic assumptions. For encryption, we define security under quantum chosen ciphertext attacks and present both public-key and symmetric-key constructions.