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An efficient hybrid hash based privacy amplification algorithm for quantum key distribution

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Abstract

Privacy amplification (PA) is an essential part in a quantum key distribution (QKD) system, distilling a highly secure key from a partially secure string by public negotiation between two parties. The optimization objectives of privacy amplification for QKD are large block size, high throughput and low cost. For the global optimization of these objectives, a novel privacy amplification algorithm is proposed in this paper by combining multilinear-modular-hashing and modular arithmetic hashing. This paper proves the security of this hybrid hashing PA algorithm within the framework of both information theory and composition security theory. A scheme based on this algorithm is implemented and evaluated on a CPU platform. The results on a typical CV-QKD system indicate that the throughput of this scheme (\(261\,\mathrm{Mbps}@2.6\times 10^8\) input block size) is twice higher than the best existing scheme (\(140\,\mathrm{Mbps}@1\times 10^8\) input block size). Moreover, this scheme is implemented on a mobile CPU platform instead of a desktop CPU or a server CPU, which means that this algorithm has a better performance with a much lower cost and power consumption.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 62071151, 61301099.

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Authors and Affiliations

  1. Harbin Institute of Technology, Harbin, 150000, China

    Bingze Yan, Qiong Li, Haokun Mao & Nan Chen

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  1. Bingze Yan
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  2. Qiong Li
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  3. Haokun Mao
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  4. Nan Chen
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Correspondence to Qiong Li.

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Appendices

A Universal hashing family

A (D; N, M) hashing family is a set F of D functions that \(f:X \rightarrow Y\) for each \(f \in F\), \(|X|=N\) and \(|Y|=M\).

A (D; N, M) hashing family F is \(\delta \)-universal hashing means for two distinct elements \(x_1,x_2 \in X\), there exist at most \(\delta D\) functions \(f \in F\) such that \(f(x_1)=f(x_2)\). The parameter \(\delta \) is the collision probability of the hash family.

B Renyi entropy and collision probability

Let \((X,p_x)\) be a probability space. The Renyi entropy of \((X,p_x)\), denoted \(H_{\mathrm{{Ren}}}(p_x)\), is defined to be

$$\begin{aligned} {H_{{\mathop {\mathrm{Re}}\nolimits } n}}({p_x}) = - {\log _2}{\Delta _{{p_x}}} \end{aligned}$$

where \(\Delta _{{p_x}}\) denotes the collision probability of the probability distribution \(p_x\), is defined by

$$\begin{aligned} {\Delta _{{p_x}}} = \sum \limits _{x \in X} {{{\left( {p(x)} \right) }^2}} . \end{aligned}$$

A property of the Renyi entropy is useful in this paper:

Lemma 4

Let \((X,p_x)\) be a probability space. \({H_{{\mathop {\mathrm{Ren}}\nolimits } }}(p_x) \le H(p_x)\).

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Yan, B., Li, Q., Mao, H. et al. An efficient hybrid hash based privacy amplification algorithm for quantum key distribution. Quantum Inf Process 21, 130 (2022). https://doi.org/10.1007/s11128-022-03462-4

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