Secure sketch produces public information of its input $w$ without revealing it, yet, allows the exact recovery of $w$ given another value $w'$ that is close to $w$. Therefore, it can be used to reliably reproduce any error-prone secret (i.e., biometrics) stored in secret storage. However, some sources have lower entropy compared to the error itself, formally called "more error than entropy", a standard secure sketch cannot show its security promise perfectly to these kind of sources. This paper focuses on secure sketch. We propose a concrete construction for secure sketch. We show security to all noisy sources, including the trivial source with zero min-entropy. In addition, our construction comes with efficient recovery algorithm operates in polynomial time in the sketch size, which can tolerate high number of error rate arbitrary close to 1/2. Above result acts in conjunction to our derivation on the solution to two NP-complete coding problems, suggesting P=NP.

中文翻译：

---

所有噪声源的安全草图（嘈杂）

安全草图生成其输入 $w$ 的公开信息而不泄露它，然而，在给定接近 $w$ 的另一个值 $w'$ 的情况下，允许 $w$ 的精确恢复。因此，它可以用来可靠地复制存储在秘密存储中的任何容易出错的秘密（即生物特征）。然而，一些来源与误差本身相比具有较低的熵，正式称为“比熵更多的误差”，标准安全草图无法完美地向这些来源展示其安全承诺。本文重点介绍安全草图。我们为安全草图提出了一个具体的结构。我们对所有噪声源显示安全性，包括具有零最小熵的平凡源。此外，我们的构造带有高效的恢复算法，在草图大小的多项式时间内运行，可以容忍任意接近1/2的高错误率。以上结果与我们对两个 NP 完全编码问题的解决方案的推导相结合，表明 P=NP。