# Optimal attacks on qubit-based Quantum Key Recycling

## TL;DR

This paper analyzes the security of a quantum key recycling scheme with 8-state encoding, providing bounds on privacy amplification and identifying optimal attacks, showing 8-state encoding offers the highest capacity.

## Contribution

It offers the first detailed security bounds for noisy channels in the 8-state QKR scheme and compares its effectiveness with 4-state and 6-state encodings.

## Key findings

- 8-state encoding achieves the highest capacity.
- Shannon entropy analysis aligns with Quantum Key Distribution.
- 4-state and 6-state encodings have additional security leaks.

## Abstract

Quantum Key Recycling (QKR) is a quantum-cryptographic primitive that allows one to re-use keys in an unconditionally secure way. By removing the need to repeatedly generate new keys it improves communication efficiency. Skoric and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate bounds on the privacy amplification. We determine optimal attacks against the message and against the key, for 8-state encoding as well as 4-state and 6-state conjugate coding. We show that the Shannon entropy analysis for 8-state encoding reduces to the analysis of Quantum Key Distribution, whereas 4-state and 6-state suffer from additional leaks that make them less effective. We also provide results in terms of the min-entropy. Overall, 8-state encoding yields the highest capacity.