Quantum Key Distribution

Functionality

Quantum key distribution 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

Protocols

• BB84 Quantum Key Distribution: Category: Prepare and Measure Network Stage
• Device-Independent Quantum Key Distribution:Category: Entanglement Distribution Network Stage

Device-Independent Quantum Key Distribution (DI-QKD) has better security guarantees than BB84 QKD.

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 totally ignorant about the final key.

• Correctness A QKD protocol is $\epsilon _{\rm {corr}}$-correct if the probability that the final key of Alice differs from the final key of Bob, is smaller than $\epsilon _{\rm {corr}}$

• Secrecy A QKD protocol is $\epsilon _{\rm {sec}}$-secret if for every input state it holds that

${\frac {1}{2}}{\|{\rho _{K_{A}E}}-{\tau _{K_{A}}\otimes \rho _{E}}\|}_{1}\leq \epsilon _{\rm {sec}},$ where $\tau _{K_{A}}={\frac {1}{|K_{A}|}}\sum _{k}|{k}\rangle \langle {k}|_{A}$ is the maximally mixed state in the space of strings $K_{A}$, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\|\cdot \|}_1} is the trace norm.

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

Discussion

The security definition presented here, Definition \ref{def:correct} and \ref{def:secret}, are proven to be sufficient to guarantee universal composability for standard QKD in (2). For device-independent quantum key distribution, attacks presented in (1) show that security can be compromised if the same devices are used to implement another instance of the protocol.

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

References

1. C. Portmann and R. Renner, Cryptographic security of quantum key distribution}
2. J. Barrett, R. Colbeck, and A. Kent, [ Phys. Rev. Lett., vol. 110, p. 010503, (2013) Memory attacks on device-independent quantum cryptography]