Input-Dependent Error Sketching Model Enabled Information Theoretical Secure Sketch

Secure sketch conceals any random string w by generating a helper string ss (known as a sketch). It allows the exact recovery of w from ss given another value w' that is close to w. A secure sketch can be utilized to protect any error-prone secret, e.g., biometrics, stored in secret storage to promote secure authentication. When error tolerance is demanded, a secure sketch can be used as an error correction code to tolerate the noise over an unreliable, noisy communication channel. However, when both security and error tolerance are of interest, the error tolerance property of a secure sketch imposes entropy loss. It leads to a weak security guaranty on a low entropy input string. Recent work by Fuller et al. (2016) has exploited the structure of the input string. They showed that having precise knowledge over the input strings' distribution is essential to construct a secure sketch for an input string of low entropy. We formalized a new model for secure sketch construction to realize precise knowledge of the input distribution setting. With the formalized new model, we devised an explicit secure sketch construction to a large family of noisy sources. The devised secure sketch can tolerate an error rate close to 1/2 in polynomial time, i.e., O(n
⁴
), and meets the best possible secure sketch's security bound with optimal entropy loss.