Encoding Private Key in Fingerprint - Computer Network Security - page 433

deletion pattern, and the receiver can denote erasure errors following the same pattern
before the encoding occurs. This way we can gain an arbitrary code rate.

Bits 1-4 dFi Bits 1-4 dFi

0000 0,00 1100 90,00

0001 11,25 1101 101,25

0011 22,50 1111 112,50

0010 33,75 1110 123,75

0110 45,00 1010 135,00

0111 56,25 1011 146,25

67,50 157,50

0101 1001

78,75 168,75

0100 1000

Fig. 1. The encoding method and the encoding of the values added to angles. This is a Gray-
coding of the angle modification values from 0° to 180° in steps of 11.25°, a feature of this
coding being that the Hamming distance of the codes for two neighboring values is 1.

Decoding is done similarly to decoding of the convolutional codes [7]. We esti-
mate the value of the sent bits depending on the received channel codes.
To make the previously introduced minutia point coding and decoding error-
tolerant, we introduced the Non-symmetric Binary Erasure Channel (NBEC). This
channel handles both simple and erasure errors, and is not symmetric, which means
that it has different probabilities for different error types and bit values. Thus, the
NBEC channel can be described by four parameters: p 01 and p 10 denote the probability
that a simple error occurs, while p 0x and p 1x denote the probability that erasure occurs
(e.g. the angle value is ambiguous) if the original bit is 0 or 1 respectively.
As we encode minutia points to five bits, and these bits are derived in different
ways, we can define different error parameters for each bit position (0-4). Thus we
modeled the fingerprint as an NBEC 5 communication channel, which is actually a set
of five independent NBEC channels.
Applying an arbitrary channel model to Turbo coding can be done by isolating and
modifying the function that returns the transfer probabilities of the channel, as de-
scribed in [8]. The NBEC channel model and the measured transfer probabilities for
different bits of the NBEC 5 channel using the above described minutia point coding
are shown in figure 2.

0 1 2 3 4

p 00 0,53 0,46 0,45 0,42 0,36

p 0X 0,00 0,02 0,02 0,03 0,05

p 01

0,01 0,02 0,02 0,04 0,09

p 10 0,13 0,02 0,02 0,04 0,08

p 1X 0,03 0,02 0,02 0,03 0,05

p 11 0,31 0,45 0,46 0,42 0,38

Fig. 2. The Non-symmetric Binary Erasure Channel (NBEC) and the statistically determined
transfer probabilities of NBEC 5