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fuzzy vaults created using imprints of same fingerprint, he can reconstruct the poly-
nomial using vault that has same x and y value. Therefore K.Nandakumar proposed
the secure fuzzy vault scheme using minutiae points on fingerprint[4].
Figure 7 and Figure 8 show enrollment and authentication stages on the biometric
authentication system of server-client structure in K.Nandakumar scheme.
Fig. 7.
Enrollment stage on fuzzy vault scheme using password
Fig. 8.
Authentication stage on fuzzy vault scheme using password
Each minutiae points are represented as an element in the Galois fields GF(2
16
).
Let (u, v, θ) be a minutia point, where u and v indicate row and column indices in
image, and θ indicate angle of the minutia point with respect to horizontal axis. The
minutia attributes are uniformly and are expressed as binary strings Q
u
, Q
v
and Q
θ
.
The length of Q
u
, Q
v
and Q
θ
are B
u
, B
v
and B
θ
. If B
u
, B
v
and B
θ
is 6, 5, 5, we get 16
bits number by concatenating the Q
u
, Q
v
and Q
θ
. The polynomial P can be selected by
minutiae points and these points are elements of unlocking set. At this time,
K.Nandakumar uses the minutiae points transformation module using password. As-
sume the length of password is 64 bits(8 characters). The password is divided into 4
units of 16 bits. We classify the minutiae points into 4 classes by grouping minutiae
lying in each quadrant of the image into a different class and assign one password unit
to each class. We generate a permutation sequence of 4 numbers using a one way
function on the password. Using this permutation sequence, we permute the 4 quad-
rants of the image. At this time, each quadrant is not changed. Each 16 bits password
unit will be same format as a 16 bits minutia point representation. Therefore password
units are divided into T
u
, T
v
and T
θ
of length B
u
, B
v
and B
θ
. T
u
and T
v
are determined
by amount of translation along x axis and y axis. And T
θ
. is determined by amount
change in minutia point angle. New minutiae points are obtained by adding the trans-
lation value to the original values modulo appropriate range.
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