Information Technology Reference
In-Depth Information
After several trials we selected to add 240 parity bits to 120 systematic bits, which
meet the requirement for cryptographical strength, of having at least 100 random bits.
As the distribution of minutiae in our database showed the average minutia point
number to be 40, this choice satisfied the need for real minutia points from the regis-
tered samples for the coding of the 0
th
bit, as 120+240 bits encoded 360/5=72 minutia
points, statistically having half of them, on average 36 chosen from real minutiae.
5 Finding the Best Fitting Transformation
When matching two fingerprints, the minutia vectors of one must be overlaid on the
other to be able to check whether they fit. To find the best transformation, we intro-
duced a goal function that would measure the quality of the fitting of points in the two
minutia point sets. The domain of this function was the 3-dimensional space defined
by the translation on the X and the Y axis, and the rotation angle α.
This goal function
f(
∆
x
,
∆
y
,
∆
ϕ
)
could be defined as following:
M
N
[
] [
]
∑∑
==
'
'
'
f(
∆
x
,
∆
y
,
∆
ϕ
)
=
f
00
(
d
(
x
,
y
,
α
,
x
,
y
,
α
))
(1)
ij
i
i
i
j
j
j
i
j
where
M
is the number of challenge minutia points,
N
is the number of minutia points
in the fingerprint sample and
f
ij
is the function that transforms the distance (
d
) of two
minutia points (denoted by
x, y
and
α
). After testing several
f
ij
functions, we chose one
that statistically showed the highest correlation between the maximum value of
f
and
the restoration of the binary codeword:
2
100
−
d
f
ij
(
d
)
=
0
<
d
<
10
f
ij
(
d
)
=
0
(2)
, if
, otherwise
100
6 Conclusion
As in the case of other biometric systems, in a biometric digital signature system the
most important quality parameters are the false rejection rate (FRR) and the false
acceptance rate (FAR). Several tests were done on our sample database, having nearly
6000 fingerprint samples of around 600 fingers to measure the FAR and the FRR. The
false acceptance rate was within the acceptable limit of 10
-6
, but the best theoretically
attainable false rejection rate appeared to be around 15%. The latter figure shows us
that further improvements should be made in the scheme to lower the FRR.
From a cryptographical point of view, the information quantity that can be stored
in a fingerprint using our method appeared to be enough to meet the requirement of
having a cryptographically strong RSA key pair, as we use 120 randomly chosen bits
to generate the private key.
In conclusion, we can state that our scheme to construct biometric digital signa-
tures is feasible, but several further enhancements should be made. We plan to im-
prove the image processing undertaken before minutia extraction to make it more
