This paper proposes and proves security of a QKD protocol which uses two-universal hashing instead of random sampling to estimate the number of bit flip and phase flip errors. For this protocol, the difference between asymptotic and finite key rate decreases with the number $n$ of qubits as $cn^{-1}$, where $c$ depends on the security parameter. For comparison, the same difference decreases no faster than $c'n^{-1/3}$ for an optimized protocol that uses random sampling and has the same asymptotic rate, where $c'$ depends on the security parameter and the error rate.

中文翻译：

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通过二元散列估计 QKD 参数导致更快收敛到渐近率

本文提出并证明了QKD协议的安全性，该协议使用二元散列而不是随机采样来估计位翻转和相位翻转错误的数量。对于该协议，渐近密钥率和有限密钥率之间的差异随着量子比特的数量 $n$ 减小为 $cn^{-1}$，其中 $c$ 取决于安全参数。相比之下，对于使用随机采样并具有相同渐近率的优化协议，相同的差异减小的速度不会比 $c'n^{-1/3}$ 快，其中 $c'$ 取决于安全参数和误差速度。