# Quantum Key Distribution

## Functionality Description

Quantum key distribution (QKD) is a task that enables two parties, Alice and Bob, to establish a classical secret key by using quantum systems. A classical secret key is a random string of bits known to only Alice and Bob, and completely unknown to any third party, namely an eavesdropper. Such a secret key can for example be used to encrypt a classical message sent over a public channel.

Tags: Two Party, Quantum Enhanced Classical Functionality, Specific Task, unconditional security (information theoretical security), random number generator, key generation, secret key

## Use Cases

• QKD can replace Diffie-Hellman key agreement protocols. For example in TLS, SSL, IPsec, etc.
• If secure key rate is sufficiently high, one can use QKD to generate a secure key that will be used for information theoretically secure authenticated encryption scheme, e.g. using one-time pad together with an authentication scheme like those presented in [1] .

## Protocols

Device-Independent Quantum Key Distribution (DI-QKD) is secure under weaker assumptions than BB84 QKD. In particular, and contrary to BB84 QKD, DI-QKD relaxes the assumption that the operations performed by the parties' measurement devices are known and well characterized.

## Properties

A quantum key distribution protocol is secure if it is correct and secret. Correctness is the statement that Alice and Bob share the same string of bits, namely the secret key, at the end of the protocol. Secrecy is the statement that the eavesdropper is (nearly) ignorant about the final key.

• Correctness A QKD protocol is ${\displaystyle \epsilon _{\rm {corr}}}$-correct if the probability that the final key of Alice differs from the final key of Bob, is smaller than ${\displaystyle \epsilon _{\rm {corr}}}$
• Secrecy A QKD protocol is ${\displaystyle \epsilon _{\rm {sec}}}$-secret if for every input state it holds that

${\displaystyle {\frac {1}{2}}{\|{\rho _{K_{A}E}}-{\tau _{K_{A}}\otimes \rho _{E}}\|}_{1}\leq \epsilon _{\rm {sec}},}$ where ${\displaystyle \tau _{K_{A}}={\frac {1}{|K_{A}|}}\sum _{k}|{k}\rangle \langle {k}|_{A}}$ is the maximally mixed state in the space of strings ${\displaystyle K_{A}}$, and ${\displaystyle {\|\cdot \|}_{1}}$ is the trace norm.

• A protocol implements a ${\displaystyle (n,\epsilon _{\rm {corr}},\epsilon _{\rm {sec}},\ell )}$-QKD if with ${\displaystyle n}$ rounds it generates an ${\displaystyle \epsilon _{\rm {corr}}}$-correct and ${\displaystyle \epsilon _{\rm {sec}}}$-secret key of size ${\displaystyle \ell }$ bits.

## Further Information

The security definition presented here, are proven to be sufficient to guarantee universal composability for standard QKD in [2] . For device-independent quantum key distribution, attacks presented in [3] show that security can be compromised if the same devices are used to implement another instance of the protocol.

## References

1. Codes for Interactive Authentication
2. PR (2014) discusses security of various QKD schemes composed in other cryptographic protocols.
3. BCK (2013) Analyses device independent QKD

contributed by Bas Dirke, Victoria Lipinska, Gláucia Murta and Jérémy Ribeiro