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points set ,
, where is the number of the chaff points and .
The randomly generated set C needs to guarantee the following requirements:
∆ ∆0
(12)
The final vault V is obtained by taking the union of the two sets G and C. Before stor-
ing the set V into the database, we pass it through a scrambler component so that it is
hard to figure out which points are genuine points and which are not.
,
(13)
3.6
Fuzzy Vault Decoding
The fuzzy vault decoding is mainly based on the Lagrange polynomial interpolation.
Assume that the transformed feature vector of a user is , ,…, . For each
, we find the x-coordinate ( ) of one point in the vault set in such a way that the
satisfy the following rules:
, ∆ is a designed threshold of the system
| | , 1,2,…,
(14)
Fig. 5. Fuzzy vault decoding
, whose has just found, is the set of the
candidate points. These points are ranked by the corresponding nearest distance be-
tween and . To recover the 8-order polynomial, the Lagrange interpolation tech-
nique 2 needs 9 points. We choose the first I points ( 9 ) of the ranked candidate
set (the points have the highest possibility to be the real points) and then make the
2 Wolfram MathWorld, Lagrange Interpolating Polynomial: http://mathworld.wolfram.com/
LagrangeInterpolatingPolynomial.html (Oct 2014).
As a result, the set of points ,
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