  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.
