Simple and tight bounds for information reconciliation and privacy amplification

Renato Renner, Stefan Wolf

Christian Cachin, Ueli M. Maurer

Christian Cachin, Ueli M. Maurer

Kun Zhang, Jia Hou, Yan Feng +4 more

In the conventional post-processing phase of Gaussian-modulated coherent state (GMCS) quantum key distribution (QKD) systems, the processes of information reconciliation (IR) and privacy amplification (PA) are typically carried out sequentially and separately. This approach incurs substantial computational complexity and may introduce potential security risks, such as key storage risks. In this paper, we propose a more efficient and secure post-processing scheme that integrates IR and PA into a single process by utilizing well-designed spinal codes. The proposed scheme significantly reduces computational complexity by employing the linear-complexity hash function instead of the superlinear complexity Toeplitz matrices used in conventional PA schemes, and effectively mitigates potential security risks associated with conducting IR and PA as separate processes. Experimental results show that the final secret key throughput of the proposed scheme is at least 250 times higher than that of the conventional PA scheme, with the improvement in throughput becoming even greater as the block lengths increase. More importantly, owing to the rateless property and the capacity-approaching performance of spinal codes, the GMCS QKD systems can achieve reconciliation efficiencies of higher than 97% across a broad range of signal-to-noise ratios from -22.5641 to 0.122 dB.

Boris Škorić, PT Tuyls

A fuzzy extractor is a security primitive that allows for reproducible extraction of an almost uniform key from a non-uniform noisy source. We analyze a fuzzy extractor scheme that uses universal hash functions for both information reconciliation and privacy amplification. This is a useful scheme when the number of error patterns likely to occur is limited, regardless of the error probabilities. We derive a sharp bound on the uniformity of the extracted key, making use of the concatenation property of universal hash functions and a recent tight formulation of the leftover hash lemma.

Esther Hänggi, Renato Renner, Stefan Wolf