Quantum ciphertext authentication and key recycling with the trap code

TL;DR

This paper develops a quantum authentication scheme using trap codes that ensures ciphertext integrity and enables key recycling, even in complex quantum computation settings, by leveraging strong purity testing properties.

Contribution

It introduces a quantum authentication scheme based on trap codes with strong purity testing, allowing for ciphertext integrity and key recycling in interactive quantum computations.

Findings

The scheme guarantees ciphertext integrity with purity testing codes.

It enables key recycling even when authentication rejects.

The trap code-based construction supports natural computation on ciphertexts.

Abstract

We investigate quantum authentication schemes constructed from quantum error-correcting codes. We show that if the code has a property called purity testing, then the resulting authentication scheme guarantees the integrity of ciphertexts, not just plaintexts. On top of that, if the code is strong purity testing, the authentication scheme also allows the encryption key to be recycled, partially even if the authentication rejects. Such a strong notion of authentication is useful in a setting where multiple ciphertexts can be present simultaneously, such as in interactive or delegated quantum computation. With these settings in mind, we give an explicit code (based on the trap code) that is strong purity testing but, contrary to other known strong-purity-testing codes, allows for natural computation on ciphertexts.