Image Hash using Neural Networks

Abstract

Hash functions have been used to generate hash codes for data authentication. Traditionally these functions are generated using byte oriented algorithms like MD5 and others. In our paper we propose a new method of generating hash code for images using neural networks. Three sample images namely, fingerprint, lena and football image have been considered and their hash values calculated using two neural network structures namely, 1) structure without feedback 2) structure with feedback. The original images are then subjected to bit modification,Gaussian noise and rotational noise. The hash values are recalculated for the modified images. Sensitivity and hit collision are calculated and are found to be comparable with that of MD5 algorithm.

Full text

International Journal of Computer Applications (0975 – 8887)
Volume 63– No.22, February 2013
12
Image Hash using Neural Networks
Veena Desai
Research Centre ,Dept of E&C,
GIT, Belgaum, India
D H Rao, PhD.
Jain College of Engg,
Belgaum, India
ABSTRACT
Hash functions have been used to generate hash codes for data
authentication. Traditionally these functions are generated
using byte oriented algorithms like MD5 and others. In our
paper we propose a new method of generating hash code for
images using neural networks. Three sample images namely,
fingerprint, lena and football image have been considered and
their hash values calculated using two neural network
structures namely, 1) structure without feedback 2) structure
with feedback. The original images are then subjected to bit
modification,Gaussian noise and rotational noise. The hash
values are recalculated for the modified images. Sensitivity
and hit collision are calculated and are found to be
comparable with that of MD5 algorithm.
General Terms
Neural Networks, Cryptography, Security
Keywords
Image hash, neural hash, hash sensitivity, hit collision
1. INTRODUCTION
A hash function H is a transformation that takes a variable-
size input message M and returns a fixed-size hash string H,
which is called the hash value. A Hash function f(M)
generates a unique hash value H for a particular image and
thus can be used for checking data integrity and authentication
purposes. When image messages are considered preimage
resistance and hit collision are parameters for evaluating the
performance of hash functions.
The applications of neural networks in areas of cryptography
in general are discussed in [1-8].The authors of [9-10] have
used both chaos and neural networks in data encryption
because of their cipher-suitable properties, such as parameter-
sensitivity, time-varying, random-similarity, etc. Based on
chaotic neural networks, a hash function is constructed, which
makes use of neural networks' diffusion property and chaos'
confusion property. This function encodes the plaintext of
arbitrary length into the hash value of fixed length (typically,
128-bit, 256-bit or 512-bit).
Another demonstration of hash function implementation based
on conservative chaotic system is proposed by authors of [11].
In their implementation the plaintext is divided into a group of
message blocks by a fixed length and each message block is
iterated some times through standard map. Both the iterations
results of every round and the plaintext block determine the
two initial values and the steps of iterations in next round.
Some items of the result in the final round are chosen to be
transformed into hash value of 128 bits. In the paper [12] a
hash function construction method based on cellular neural
network (CNN) with hyper-chaos characteristics is proposed.
The chaos sequence generated by iterating CNN with Runge-
Kutta algorithm, then the sequence iterates with every bit of
the plaintext continually. Then hash code is obtained through
the corresponding transform of the latter chaos sequence from
iteration. Hash code with different lengths could be generated
from the former hash result. In [13] The MLP network
structure developed for one way hashing consists of a hidden
layer and an output layer. The hidden layer contains 64
neurons with 61 input including the bias. The weights of the
hidden neurons are truncated to 3 decimal places, which α set
to 1000. The MLP network thus structured is shown to be pre
image resistance, 2nd pre image resistance and collision
resistance features.
In section 2 of our paper the neural network structures used in
the proposed implementation are illustrated and explained.
Section 3 provides the proposed algorithm details. Result
calculation and sample data are elucidated in section 4.
Conclusions are discussed in section 5.
2. NEURAL NETWORKS
Artificial neural network is an interconnected group of
artificial neurons which use a mathematical model or a
computational model for information processing based on
connectionist approach to computation. It is a network of
simple processing elements which can exhibit complex
behavior determined by the connections between processing
elements and element parameters. Artificial neural network is
an adaptive system that changes its structure based on external
or internal information that flows through the network.
The method of setting the values for the weights enables the
process of learning or training. The process of modifying the
weights of the connections between network layers with the
expected output is called training a network. The internal
process that takes place when a network is trained is called
learning. Figure 1 and Fig.2 show the neural network structure
implemented in this paper without feedback and with
feedback respectively.
The structure of feed-forward network as in Fig. 1 is made up
of layers of neurons. For the purpose of the one-way hashing
function, three layers of neurons are employed. The first layer
is called ‘input’ layer, the next is the ‘hidden’ layer and the
last layer is the ‘output’ layer. In our implementation, the
input and the hidden layers consist of 128 neurons and the
output layer consists of 64 neurons.
A sequence of binary bits are obtained from the image as
mentioned in section 3.These bits are elements of out(1,n)
from the input layer and are processed further by the hidden
layer. The output of hidden layer becomes the input for the
output layer. Due to the use of tan-sigmoidal function, non-
linearity is introduced in each neuron of the output layer. In
our structure, we have used a constant weight of 0.5 for each
neuron and the bias is set to 0 for each neuron. Diffusion
property is also satisfied due to the use of neural structure.
The structure of feedback network is again a structure of 3
layers of neurons. The interconnect between input and hidden
layer output are as in feed forward structure.

International Journal of Computer Applications (0975 – 8887)
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Fig 1. Neural network structure without feedback
Fig 2. Neural network structure with feedback

International Journal of Computer Applications (0975 – 8887)
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Each output neuron is mapped from the output layer to two
consecutive input layer neurons. For each iteration the input
layer neuron takes into consideration the current input and
previous output due to which stability is introduced in the
structure thereby making it more immune to noise.
3. PROPOSED ALGORITHM
For neural network structure without feedback
1. Read the input image
2. Convert the image into two dimensional pixel values
3. Determine the number of rows and columns of image
4. Create a row matrix of content values
5. Resize the row matrix into a matrix of size(r * 128).
(r is the number of rows and it depends on the image
which is being read)
6. Initialise each neuron in the input layer, hidden layer
and output layer with a constant weight of 0.5 and a
bias of 0.
7. Initialise the final layer output [y1(1), y1(2). . .
.y1(64)] to zero
8. For k = 1 to r
9. If(k=1)
10. Let the final layer output be y1(1), y1(2) . . .
.y1(64)
11. End if
12. If (k>1)
13. hk-1 = [hk-2(1) EXOR yk(1)],[hk-2(2) EXOR
yk(2)] . . . . [hk-2(64) EXOR yk(64)]
14. End if
15. End for k
16. The hash value of image without noise is hk-1
17. Modify the image by introducing one of the following
four noises: One-bit change / Gaussian filtering / +5
degrees rotation / -5 degrees rotation.
18. Repeat Steps 7 to 15 for the modified image.
19. Let the hash of the modified image be Hnoise k-1.
20. Calculate the difference between hk-1 and Hnoise k-1.
For neural network structure with feedback
Repeat Steps 1 to 7 of without feedback
1. For k=1 to r
2. If(k>1)
3. Initialise t to1
4. for j = 1 to 128 in steps of 2
5. out1(k,j) = EXOR[y(k-1,t),out1(k,j)];
6. out1(k,j+1) = EXOR[y(k-1,t),out1(k,j+1)];
7. t=t+1;
8. if(t == 65)
9. End for j
10. End if
11. End for k
12. Repeat Steps 16 to 20 of Without Feedback
The input image is converted into two dimensional pixel
values. 128 values of this matrix are given at a time to the
input layer of the neural network. These values are passed
through the hidden layer and 64 values of 38 bits each are
obtained from each neuron of the output layer.
For the without feedback neural network structure, the output
obtained from the consecutive iterations are XOR’ed to get
the final hash value for the particular image.
For the with feedback neural network structure, the values
generated by each output neuron for the previous iteration are
Xor’ed with the input values to two consecutive neurons in
the current iteration. Let the hash value generated for the
original image for both without feedback and with feedback
structure be h1. Noise is introduced into the image and the
procedure is repeated to obtain the new hash for the modified
image. Let this hash be represented as h2.
Sensitivity gives the number of bits change in the original
image after addition of noise and is calculated as:
%Sensitivity= (Number of bits changed/ Total number of
bits) * 100
Hit collision is the number of digits (hex values) remaining
same in the hash after addition of noise in the original image
and is calculated as:
%Hit collision = (No. of hex values remaining same/ Total
No. of hex values) * 100
4. SAMPLE DATA AND RESULTS
The following figures, 3(a) to 3(e) show the sample set of
images that have been used for hash calculation. Fingerprint
image 1(a) is the original image of sample 1. Fig. 4(b) to 4(e)
are the modifications on sample 1 with 1 bit change, filtered
image ,with +5 degres rotation, and -5 degrees rotation
respectively.
3(a) 3(b) 3(c) 3(d)

International Journal of Computer Applications (0975 – 8887)
Volume 63– No.22, February 2013
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3(e) 3(f) 3(g)
Fig 3. (a)original fingerprint image (b) fingerprint image with 1 bit modification (c) fingerprimt image with gaussian noise
(d)fingerprint image with +5 degrees rotation (e)fingerprint image with -5degreees rotation (f)original lena image (g)original
football image
Hash value of fingerprint image :
BCC85FBEC44BB32600AA960A6EB3C1B538590D2254B4
8A4261E1290D73A67C360363684A938C2C8E7E687400CB
7FB2482D0C3BA6EB536BD379B766FF3EEE31216A0541
CA9FCBA72C0AF78F8F8EB4B87522A465C01B70B8EC74
B7CDAD8127B50E41DA38BA97BCD1DFA21A693507C6
CAFEBFE49BAD926FFA24B47615B37A99F738E0AF6CF6
7038559AE920A4DF5E76E84D20C836A353F9D889845C3
7E648D7735EBB1B672A189307C395FAE9BC0E1D8D10A
B73557321538CA765C816E5CC0B02B7238E2C5E7B57108
96A60D08DECF65D3109831F396F74FD65232153DEE2F6
4C2CD9A2FC31A38482513EECFE4D746B700F2AF6616B
A9ABD4211579786CF06ECC4EB08841CC1425A6BA3239
9518F3A1E07C69921243FFE5A835A89AD81969B3D21BA
9E47ACFC28AF19E7E40E0A0F400077B
Hash value for fingerprint image with 1-bit change without
feedback structure:
BE6098D3387B95840EC11E3EF088E417A82D3FB2F660FF80C
4AA37EE60FF6D61D829561132562504561EDE81FC7A6320D
D5E72B84B62A1FC2D156B1D3002B70D4AD8D9959CB61ACE
8D6E998F9A707D0970D4D9478EB0128A21A1A73F913D2E13
F7AFA58497B827ED09CA53A0E6CD272209CF9393ABB20EF4
1FC1FC6AFD7E46F526822749978B38C07BC69E9855D253A9
5198F086DDBED2C42E6BA4A224C21081CC62EAED4E9286C
AE17550B1CE3A76E2335B9DDDAB108866B8C5AEF6D3CF90
6CB460CC3089F0CEAB176533754B4D632DF794A29CC432D3
912252C3C3140287A35367650113DDAB03EED5900DC3AA3
DA3FD2DA0A739E199169C58FE3860F549A2EBE860738260A
46026CD9A50D14FEA4963FC95E0C
Number of bit changes observed in the New hash: 1174
Sensitivity: 48.2730 %
Hit Collision: 8.8816 %
Elapsed Time: 32.7 minutes
Hash value of fingerprint image with 1-bit change with
feedback structure
130F878378CE576E8E0298AE7D13489058DE5800B3DF2EFC
BD08AE41F27A2648B8079A3176DA3E8051D508B1B1EB6E92
5A383BFB45D42D6D8835C7EEBA90A8F30DFE32343D94AD4
1B7D9BE02308AB3180CA136AE3B11FFB301714FFEEC85222
D516DE64499773BC111A6F646B58E20880ED82AF655AEA89
0AC00CDA0E3785247CC83E621A928F8DBAEE4852E482E800
000002A4B942401E927101FFB3C733A65EEA3BC5C832A0AE
EC3712924FDCBC8BC4F4E55E0A33E69090F4A69A1D9DE226
C40C514052EEFA9D2F729A53409EF5E81DD1EAD829CC8FBA
9101FA2C8F1614749706130A417DEBA4E18D8B0AE0D92A59
654EC88DA7722590818EB49F4C30DDBE0828689219D480CF
F496A3FFF80C094B5DEB74A6267A568D386B66FEB3B38FDA
EC4BCAC51EABE2244D65AEC03CE5821C7
Number of bit changes observed in the New hash: 1115
Sensitivity: 45.8470 %
Hit Collision: 10.0329 %
Elapsed Time: 58.32 minutes
Table 1 provides the comparison of sensitivities for hash
values obtained from the neural network without feedback and
MD5 algorithm for the fingerprint image and Lena image. In
both cases we find that the sensitivity of the hash obtained
from the neural structure is comparable with that of MD5
algorithm.
Table 1: Comparison of sensitivities of sample images and
MD5
Comparison made for image fingerprint
Type of noise
Sensitivity
Sensitivity (MD5 Tool)
One-bit change
48.27 %
57.03 %
+5 degrees rotation
50.25 %
47.65 %
-5 degrees rotation
49.79 %
48.43 %
Filtering
48.23 %
49.21 %

International Journal of Computer Applications (0975 – 8887)
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Comparison made for image Lena
Type of noise
Sensitivity
Sensitivity (MD5 Tool)
One-bit change
49.09 %
53.90 %
+5 degrees rotation
47.82 %
53.90 %
-5 degrees rotation
48.97 %
49.21 %
Filtering
47.62 %
53.13 %
Figures 4,5,6 and 7 are plots of bit changes, sensitivity, hit
collision and time elapsed for variations in 1 bit change,
Gaussian noise,+5 degree rotation and -5 degree rotation.
Fig 4: plot of bit changes for variations in noise types
Fig 5: plot of sensitivity for variations in noise types
Fig 5: plot of hit collision for variations in noise types
Fig 7: plot of time delay for variations in noise types
Table. 2 and Table. 3 show the results of the hash algorithm
obtained from neural structures without feedback and with
feedback for lena image and fingerprint image respectively.
Figure 8 and fig.9 are plots of bit changes for each neuron in
ouput layer for without feedback structure and with feedback
structure.
Fig. 8 plot of bit changes for each neuron in ouput layer for
without feedback structure
Fig. 9 plot ob bit changes for each neuron in ouput layer for with
feedback structure
1040
1060
1080
1100
1120
1140
1160
1180
1200
1220
1240
1 bit change Gaussian
filter +5 degree
rotation - 5 degree
rotation
Fingerprint image without
feedback
Fingerprint image with
feedback
Lena image without
feedback
Lena image with feedback
Football image without
feedback
Football image with
feedback
42.00
43.00
44.00
45.00
46.00
47.00
48.00
49.00
50.00
51.00
1 bit
change Gaussian
filter +5 degree
rotation - 5 degree
rotation
Fingerprint image without
feedback
Fingerprint image with
feedback
Lena image without
feedback
Lena image with feedback
Football image without
feedback
football image with
feedback
0.00
2.00
4.00
6.00
8.00
10.00
12.00
1 bit change Gaussian
filter +5 degree
rotation - 5 degree
rotation
Fingerprint image without
feedback
Fingerprint image with
feedback
Lena image without
feedback
Lena image with feedback
Football image without
feedback
Football image with
feedback
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
1 bit change Gaussian
filter +5 degree
rotation - 5 degree
rotation
Fingerprint image without
feedback
Fingerprint image with
feedback
Lena image without feedback
Lena image with feedback
Football image without
feedback
football image with feedback

International Journal of Computer Applications (0975 – 8887)
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Table 2: Results for lena image
Structure
Type of Noise
Bit Changes
Sensitivity
Hit collision
Time elapsed
Without feedback
1 bit change
1194
49.09
7.0724
5.33
Gaussian filter
1158
47.61
7.0724
5.52
+5 degree rotation
1163
47.82
8.7171
5.51
- 5 degree rotation
1191
48.97
6.2500
5.41
With feedback
1 bit change
1167
47.98
9.0461
9.35
Gaussian filter
1102
45.31
9.5395
9.23
+5 degree rotation
1146
47.12
10.3618
9.00
- 5 degree rotation
1170
48.10
7.2368
9.13
Table 3: Results for fingerprint image
Structure
Type of Noise
Bit Changes
Sensitivity
Hit collision
Time elapsed
Without feedback
1 bit change
1180
48.51
7.5658
15.66
Gaussian filter
1178
48.43
5.0985
15.38
+5 degree rotation
1149
47.24
6.9079
15.31
- 5 degree rotation
1169
48.06
7.2368
15.35
With feedback
1 bit change
1196
49.17
9.2105
25.58
Gaussian filter
1125
46.125
10.5263
26.15
+5 degree rotation
1152
47.36
8.3882
26.08
-5 degree rotation
1170
48.10
7.5658
26.43
5. CONCLUSION
In this paper a unique hash value for a given image using
neural networks is obtained. The code is implemented in
MATLAB and tested for a wide range of images and a unique
hash obtained for each image. From the results it can be
inferred that the unique hash value obtained is sensitive to
modifications made to the input image. The sensitivity
obtained is in the range of 40-50%. For without feedback
neural network structure sensitivity has been calculated using
MD5 tool. These sensitivity values are compared with the
values obtained from the proposed scheme using neural
networks. The hit collisions obtained for the modified image
is found to be less than 10%. Lesser the hit collision better is
the efficiency of the algorithm and thereby making
cryptanalysis difficult. The limitation of this implementation
is that the time taken to generate the unique hash depends
upon the resolution and the information carried by the image.
Hence it is observed that the elapsed time is more for the
fingerprints as compared to the standard lena image.
In this paper an image hash has been generated using simple
feed-forward and feedback neural network structures. Other
neural network structures like back propagation
network(BPN), radial basis function network(RBFN),discrete
Hopfield networks, continuous Hopfield networks etc can be
explored and checked for better sensitivity.
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