The fuzzy vault operates on the fingerprint minutiae features. These features are defined as abrupt changes in the regular ridge structure on the fingertip, characterized by either ending or bifurcation of the ridges.Typically, they are represented as (x,y,θ) triplets (see Fig.1), denoting their row indices (x), column indices (y) and angle of the associated ridge ,respectively.

Fig. 2 depicts the operation of a fingerprint-based fuzzy vault scheme.Suppose that a user wishes to hide a secret K using his or her fingerprint minutiae features which is represented as an unordered set X . The user selects a polynomial that encodes the secret K and evaluates the polynomial P on all elements in X. The user then chooses a large number of random chaff points which do not lie on the polynomial P. The entire collection of points consisting of both points lying on P and those that do not lie on P constitute the vault V. The chaff points conceal the genuine points lying on P from an attacker. Since the points lying on P encode the complete information about fingerprint minutiae features’s set X and the secret K, concealing these points secures both the template and the secret simultaneously.

The user can retrieve the secret K from the vault V by providing another f fingerprint minutiae features (query). Let the query be represented as another unordered set X’. If X’ overlaps substantially with X, then the user can identify many points in V that lie on P. If a sufficient number of points on P can be identified, an error correction scheme can be applied to exactly reconstruct P and thereby decode the secret K. If X’ does not overlap substantially with X, it is infeasible to reconstruct P and the authentication is unsuccessful. Since the secret can be retrieved from the vault even when X and X’ are not exactly the same.

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