# Information Security and Cryptography Research Group

## An Information-Theoretic Security Proof for QKD Protocols

### Renato Renner, Nicolas Gisin, and Barbara Kraus

Physical Review Letters A, American Physical Society, vol. 72, no. 012332, Jul 2005, eprint archive: http://arxiv.org/abs/quant-ph/0502064.

We present a new technique for proving the security of quantum key distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the BB84, the six-state, and the B92 protocol with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.

## BibTeX Citation

@article{ReGiKr05,
author       = {Renato Renner and Nicolas Gisin and Barbara Kraus},
title        = {An Information-Theoretic Security Proof for {QKD} Protocols},
journal      = {Physical Review Letters A},
number       = 012332,
volume       = 72,
year         = 2005,
month        = 7,
note         = {eprint archive: http://arxiv.org/abs/quant-ph/0502064},
publisher    = {American Physical Society},
}