Optimizing the decoy-state BB84 QKD protocol parameters

Thomas Attema,Niels M P Neumann,Joost W Bosman

doi:10.1007/s11128-021-03078-0

Thomas Attema, Niels M P Neumann + Show 1 more

Open Access

https://doi.org/10.1007/s11128-021-03078-0

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Abstract

Quantum key distribution (QKD) protocols allow for information theoretically secure distribution of (classical) cryptographic key material. However, due to practical limitations the performance of QKD implementations is somewhat restricted. For this reason, it is crucial to find optimal protocol parameters, while guaranteeing information theoretic security. The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making a number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and nonlinear programs describing the optimization problem. Our approach, focusing on the decoy-state BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the decoy-state BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.

Highlights

The goal of a key-distribution protocol is for two parties, Alice and Bob, to agree on a key k ∈ {0, 1}n over an insecure communication channel, such that even an adversary Eve with full control over this communication channel can only obtain a negligible amount of information about this key k
We presented a key-rate optimization approach for the decoy-state BB84 quantum key distribution (QKD) protocol
Our approach combines several linear and nonlinear programs to derive tighter protocol parameters and better key-rates, compared to previous approaches relying on heuristic assumptions

Summary

Introduction

The goal of a key-distribution protocol is for two parties, Alice and Bob, to agree on a key k ∈ {0, 1}n over an insecure communication channel, such that even an adversary Eve with full control over this communication channel can only obtain a negligible amount of information about this key k. If Alice and Bob are capable of communicating quantum information, they are able to achieve information-theoretic or unconditional security, i.e., security against adversaries with unlimited computational power. The information-theoretic security of the BB84 protocol against the most general attacks allowed by quantum mechanics was proven in 1996 by Mayers [3]. Universal security is proven by comparing the output of the protocol to the output of an ideal key-distribution protocol, i.e., a perfect key. If these two outputs are indistinguishable, the protocol is said to be universally secure. QKD protocols that satisfy Mayers’ weaker notion of security were shown to be universally secure [4]

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