# Secure Signatures and Chosen Ciphertext Security in a Quantum Computing World

**Authors:**

*D. Boneh and M. Zhandry*

** Abstract: **

We initiate the study of quantum-secure digital signatures and quantum
chosen ciphertext security. In the case of signatures, we enhance the
standard chosen message query model by allowing the adversary to issue
quantum chosen message queries: given a superposition of messages, the
adversary receives a superposition of signatures on those
messages. Similarly, for encryption, we allow the adversary to issue
quantum chosen ciphertext queries: given a superposition of
ciphertexts, the adversary receives a superposition of their
decryptions. These adversaries model a natural ubiquitous quantum
computing environment where end-users sign messages and decrypt
ciphertexts on a personal quantum computer.

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.

** Reference:**

In Proceedings of Crypto 2013, pp. 461-478.
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**Full paper:**
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