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 this kind of sources. This paper focuses on secure sketch. We propose an explicit construction for secure sketch. We show correctness and security to all sources with meaningful min-entropy at least a single bit. Besides, 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 for random error. The above result offers polynomial time solution to two NP-complete coding problems, suggesting P=NP.