1. A Neural-Network Approach for Visual Cryptography
虞台文
Good afternoon, ladies & gentleman.
My presentation is “A Neural-Network Approach for Visual Cryptography and Authorization’”
I am Yue, Tai-Wen, from Taiwan.
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2. Content Overview The Q’tron NN Model The Q’tron NN Approach for
Visual Cryptography
Visual Authorization
Semipublic Encryption
General Access Scheme
Conclusion
It includes
Overview
The Neural Network Model and its applications on
Visual Cryptography
Visual Authorization
Finally, I will give a short conclusion

3. A Neural-Network Approach for Visual Cryptography
Overview
It is overview now.
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4. What is Visual Cryptography and Authorization?
Visual Cryptography (VC)
Encrypts secrete into a set of images (shares).
Decrypts secrete using eyes.
Visual Authorization (VA)
An application of visual cryptography.
Assign different access rights to users.
Authorizing using eyes.
Visual Cryptography is a topic to separate the secrete stored in an image into several shares.
The secrete can be rediscovered if only if some or all of shares are put together.
The tool used for decrypting is human’s eyes.
Visual Authorization is one of its application.
It assign different authorities to access a resource to different users.

5. What is Semipublic Encryption?
Visual Cryptography (VC)
Encrypts secrete into a set of images (shares).
Decrypts secrete using eyes.
Semipublic Encryption (SE)
An application of visual cryptography.
Hide only secret parts in documents
Right information is available if and only if a right key is provided
Visual Cryptography is a topic to separate the secrete stored in an image into several shares.
The secrete can be rediscovered if only if some or all of shares are put together.
The tool used for decrypting is human’s eyes.
Visual Authorization is one of its application.
It assign different authorities to access a resource to different users.

6. The Basic Concept of VC The (2, 2) access scheme. Access Scheme
Share 1
The most simple example is the so-called two-out-of-two scheme.
The image on the left is called target or secrete images, and the two images on the right are called shares.
They have completely different meaning.
The two-out-of-two scheme requires that the stacking of the two shares recalls the secrete, and this is the only way to recall the secrete.
Target Image
(The Secret)
Share 2

7. The Shares Produced by NN
We get shares after the NN settles down.
The Shares Produced by NN
Neural
Network
Share 1
In the following, I will describe the method to use our neural network model to achieve this goal.
Before getting deep, let’s see a small demonstration.
Target Image
(The Secret)
Share 2

8. Decrypting Using Eyes Share 1
Does this means that the mix of Lena and Mona Lisa will becomes Marilyn Monroe?
Of course, it is not.
Share 2

9. Example: (2, 2) Plane shares are used Share image1 Share image2
This slide shows an example for 2-out-of-2 access scheme.
The upper two images are called shares.
One can’t read out any information from these two images.
However, when stacking these two shares, the secrete information appears
Target image

10. Traditional Approach Naor and Shamir (2,2) The Code Book White Pixels
Probability
Shares
# #2
Superposition of
the two shares
White
Pixels
Black
Pixels

11. The VA Scheme Very Important Person. … … … … P VIP IP P VIP IP
user shares
(resource 1) …
stacking
Now, let’s see what is visual authorization.
Suppose there two resources.
To access a particular resource, a user need to present a share with a particular pattern.
<Click>
For example, to access resource 1, you need a Lena share, and to access resource 2, you need a Monroe share.
The administrator own a key share. <Click>
By stacking the key share with users’ shares, he can identify what sort of access rights a user has.
In this example, there are three different passports, VIP, IP, and P.
user shares
(resource 2)
key
share … …
VIP IP P

12. The SE Scheme 智慧型系統實驗室資料庫 使用者 Key 江素貞 AB 陳美靜 CD 張循鋰 XY 李作中 UV
Now, let’s see what is visual authorization.
Suppose there two resources.
To access a particular resource, a user need to present a share with a particular pattern.
<Click>
For example, to access resource 1, you need a Lena share, and to access resource 2, you need a Monroe share.
The administrator own a key share. <Click>
By stacking the key share with users’ shares, he can identify what sort of access rights a user has.
In this example, there are three different passports, VIP, IP, and P.

13. The SE Scheme AB CD XY UV user shares keys public share
(database in lab)
stacking
user
shares 素貞 美靜 循鋰 作中 AB CD XY UV
keys

15. A Neural-Network Approach for Visual Cryptography
The Q’tron
NN Model
Now, I introduce the neural network model we used.
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16. The Q’tron aiQi . . . Quantum Neuron i (ai ) Active value
Qi{0, 1, …, qi1}
. . . 1 2
qi1
IiR
External Stimulus
Q’tron is the shorthand for quantum neuron.
It may have multiple-level output. i
(ai )
Internal Stimulus Ni
Noise

17. The Q’tron aiQi . . . i (ai ) Free-Mode Q’tron Active value
Qi{0, 1, …, qi1}
. . . 1 2
qi1
External Stimulus
IiR
A Q’tron can be operated in a free-mode or clamp-mode.
In free-mode, its output level can be adjusted according to a level-transition rule. i
(ai )
Internal Stimulus Ni
Noise

18. The Q’tron aiQi . . . i (ai ) Clamp-Mode Q’tron Active value
Qi{0, 1, …, qi1}
External Stimulus
IiR
. . .
In clamp-mode, a Q’tron whose output-level will be fixed a particular level. i
(ai ) 1 2
qi1
Internal Stimulus Ni
Noise

19. Input Stimulus Noise Noise Internal Noise Stimulus Free External Term
. . .
Input Stimulus i
(ai )
Noise
Noise
Internal
Stimulus
The noise-added input to the ith Q’tron is denoted as Hi hat, which equal to the noise-free stimulus plus the noise.
The noise-free stimulus equals to the summation of internal and external stimulus.
In this application, the noise is always zero.
Noise
Free
Term
External
Stimulus

20. Level Transition Running Asynchronously . . . i (ai )
At each time step, only one Q’tron is selected for state updating.
When a Q’tron is selected, it updates its output-level according to this rule.
Running Asynchronously

21. Energy Function Monotonically Nonincreasing Constant Interaction
Among Q’trons
Constant
Interaction
with
External Stimuli
The energy of a Q’tron neural network comprises of three terms.
The first term arises from interaction among Q’trons, the second term from the external stimuli, and the third term K is a constant.
It has been proven that a Q’tron NN runs in a noise-free mode its energy will be monotonically nonincreasing.
This property allow us to solve problem by minimization energy or cost.
However, we need to know how to reformulate a problem into minimization the energy function of a Q’tron neuron network.

22. The Race Traffic Problem+1 1 v1 v2

23. +1
Operation Modes 1
Free
Clamped

24. Solving Problems by Releasing Energy
Free
Clamped

25. Solving Problems by Releasing Energy
Clamped
Free

26. Associative Adder Question-Answering & Associative Memory 8 4 7 3 6 +2 1 8 4 7 3 6 + 2 1
Question-Answering & Associative Memory

27. The Q’tron NN
A Q’tron neural network contain a set of connected Q’trons.
Some Q’trons are directly correlated to a problem’s input and output, some are not.

28. Interface/Hidden Q’trons
clamp-mode
Interface
Q’trons
free-mode
free mode  Hidden Q’trons
Therefore, we categorize Q’trons into two types.
One is hidden Q’trons, and another is interface Q’trons.
All hidden Q’trons usually run in free-mode.
However, interface Q’trons can run either in free-more or clamp-mode.

29. Question-Answering Feed a question by clamping some interface Q’trons.
clamp-mode
free-mode
free mode  Hidden Q’trons
Interface
Q’trons
Interface Q’trons allows a Q’tron neural network to function as a question-answering device.
For example, we now feed a question into the network using these green Q’trons.
This usually will pump the network into a high-energy state.
Therefore, other Q’trons become unstable.

30. Question-Answering Read answer when all interface Q’trons settle down.
clamp-mode
free-mode
free mode  Hidden Q’trons
Interface
Q’trons
As time passing, the energy of the network becomes lower and lower.
Finally, all of interface Q’trons settle down.
We can then read the answer.
In a noiseless environment, the hidden Q’trons will also settle down.
In a noisy environment, the hidden Q’trons may be unstable forever.

31. A Neural-Network Approach for Visual Cryptography
The Q’tron NNs for
Visual Cryptography
Visual Authorization
Semipublic Encryption
We now reach the main topics VC & VA.
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32. + Energy Function for VC Visual Cryptography Image Halftoning Image
Stacking
First, let’s construct a neural network for VC.
Two main tasks have to be done for VC, image halftoning and image stacking.
The energy function hence include two terms, E_h and E_s.
Consider image halftoning first. +

33. Image Halftoning 255 0 (Transparent) 1 Graytone Image Halftone Image
Graytone image  halftone image can be formulated as to minimize the energy function of a Q’tron NN.
Image Halftoning
Graytone Image
Halftone Image
Halftoning
Image halftoning is a process that convert a gray image into a binary one.
Note that we use 0 to represent a white pixel, and 255 to represent black pixel in a gray image.
And, use 0 to represent a write pixel or 1 to represent a black pixel in a binary image.
This process can be formulated as to minimize an energy function.
255
0 (Transparent) 1

34. Image Halftoning 255 0 (Transparent) 1 Graytone Image Halftone Image
Graytone image  halftone image can be formulated as to minimize the energy function of a Q’tron NN.
Image Halftoning
In ideal case, each pair of corresponding small areas has the `same’ average graylevel.
Graytone Image
Halftone Image
Halftoning
The goal of the energy function is to make each small area has almost the same average graylevel.
We denote the energy function as E_h.
255
0 (Transparent) 1

35. The Q’tron NN for Image Halftoning
Plane-G
(Graytone image)
Base on E_h, we can construct a Q’tron neural network with two neuron planes to do the task.
Plane-H
(Halftone image)

36. Image Halftoning Plane-G (Graytone image) Clamp-mode Question
For halftoning, the upper plane is to run in clamp-mode, i.e., to feed your question, and the lower plane is in free-mode.
Just after a new question is entered, the energy of network is suddenly pumped high.
Hence, the free-mode Q’trons become unstable.
After the network reaches another stable state, you can read your answer.
Answer
Free-mode
Plane-H
(Halftone image)

37. Image Restoration Plane-G (Graytone image) Free-mode Answer
The paper also describes how to use the same network to reconstruct a gray image from a halftone one.
In this case, the lower-plane is for the question and the upper plane will returns the answer.
Question
Clamp-mode
Plane-H
(Halftone image)

38. Stacking Rule + + + + Now, we consider the stacking rule.
The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Q’tron NN.
Stacking Rule
Now, we consider the stacking rule.
When two binary images which are printed on transparencies are stacked together, each pixel’s value depends on a pair of stacked pixels.
Such a fact can also be described as to minimize an energy function. + + + +

39. Stacking Rule The energy function for the stacking rule.
The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Q’tron NN.
Stacking Rule
The energy function for the stacking rule.
See the paper for the detail.
We use E_s to denote the energy function. + + + +

40. The Total Energy + Total Energy Image Halftoning Stacking Rule
The total energy thus contains two terms, one is from halftoning, and another is for stacking.
Share 1 +
Share 2
Share 1
Share 2
Target
Target

41. The Q’tron NN for VC/VA Plane-GT Plane-HT Target
Three images are involved for visual cryptography, two for shares and one for target.
Therefore, we need three halftoning neural networks.
The energy term E_s will make these three networks correlated.
The outer three planes are for gray images, and the inner three are for binary images.
This network can be used both for visual cryptography and for authorization.
Plane-GS1
Plane-HS1
Share 1
Plane-HS2
Plane-GS2
Share 2

42. Application  Visual Cryptography
Plane-GT
Plane-HT
Target
Clamp-Mode
Free-Mode
For visual cryptography, the outer three planes are to run in clamp-mode, and the inner three are in free-mode.
After the network settles down, the result appears in the inner planes.
Free-Mode
Free-Mode
Plane-GS1
Plane-HS1
Share 1
Plane-HS2
Plane-GS2
Share 2
Clamp-Mode
Clamp-Mode

43. Application  Visual Authorization
Key Share
Application  Visual Authorization
User Share
Authority
Plane-GT
Plane-HT
VIP IP P
For visual authorization, three pairs of Q’tron planes are renamed.
One for key share, one for user share, and one for authority assignment.
You can decide what patterns you want for key share, user share and authorities.
In the next, I will show how to produce a binary key share and a set of user shares for different authorities.
Plane-GS1
Plane-HS1
Plane-HS2
Plane-GS2
Key Share
User Share

44. Application  Visual Authorization
Producing key Share &
the first user share.
Key Share
Application  Visual Authorization
User Share
Authority
Clamp-Mode
Plane-GT
VIP IP P
Free-Mode
Plane-HT
To produce a key share and the first user share, you clamp the graylevel images onto the corresponding gray image planes.
The inner three image planes are completely free.
After the network settles down, you will obtain the key share and one user share.
We now already has the key share.
To produce other user shares is very easy.
Free-Mode
Free-Mode
Plane-GS1
Plane-HS1
Plane-HS2
Plane-GS2
Clamp-Mode
Clamp-Mode
Key Share
User Share

45. Application  Visual Authorization
Producing other user shares.
Key Share
Application  Visual Authorization
User Share
Authority
Clamp-Mode
Plane-GT
VIP IP P
Some are clamped and some are free.
Plane-HT
The gray image plane for key share now is useless, you can let it run in any mode.
But, its binary image plane must be clamped.
Now, clamping a different gray image for different authority into the authority plane, you will obtain the corresponding user share.
This slide shows how to get the second one.
Repeat the same process, you can get the third one.
Clamp-Mode
Free-Mode
Plane-HS1
Plane-HS2
Plane-GS2
Plane-GS1
Clamp-Mode
Key Share
User Share

46. Application  Visual Authorization
Producing other user shares.
Key Share
Application  Visual Authorization
User Share
Authority
Clamp-Mode
Plane-GT
VIP IP P
Some are clamped and some are free.
Plane-HT
Clamp-Mode
Free-Mode
Plane-HS1
Plane-HS2
Plane-GS2
Plane-GS1
Clamp-Mode
Key Share
User Share

47. Application  Visual Authorization
Key Share
Application  Visual Authorization
User Share
Authority
Clamp-Mode
Plane-GT
VIP IP P
Some are clamped and some are free.
Plane-HT
This slide shows all binary images we obtained from the above process.
Clamp-Mode
Free-Mode
Plane-HS1
Plane-HS2
Plane-GS2
Plane-GS1
Clamp-Mode
Key Share
User Share

48. VIP IP P User Share User Share Key Share User Share
This is the demonstration of one experimental result.
Key Share
User Share P

49. A Neural-Network Approach for Visual Cryptography
General
Access Scheme
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50. Full Access Scheme  3 Shares
朝 辭 白 帝 彩 雲 間
朝辭白帝彩雲間
Shares
This slide shows all binary images we obtained from the above process.

51. Full Access Scheme  3 Shares
朝 辭 白 帝 彩 雲 間
朝辭白帝彩雲間
Shares
This slide shows all binary images we obtained from the above process.
Theoretically, unrealizable.
We did it in practical sense.

52. Full Access Scheme  3 Shares
This slide shows all binary images we obtained from the above process.
S1+S2
S1+S3
S2+S3
S1+S2+S3

53. Access Scheme with Forbidden Subset(s)
Anyone knows what is it?

54. Access Scheme with Forbidden Subset(s)
人 之 初 性 本 X 善
人之初性本善
Shares
This slide shows all binary images we obtained from the above process.
Theoretically, realizable.

55. Access Scheme with Forbidden Subset(s)
This slide shows all binary images we obtained from the above process.
S1+S2
S1+S3
S2+S3
S1+S2+S3

56. A Neural-Network Approach for Visual Cryptography
Conclusion
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57. Conclusion Different from traditional approaches:
No codebook needed.
Operating on gray images directly.
Complex access scheme capable.
Our approach is completely different from the traditional approach.
For example, code book is totally not needed in our approach. For complex access scheme, a codebook is, in fact, difficult to be found. And, even it is not existent.
In addition, traditional approach deals with binary images, but our approach deal with gray images directly.
Our method is also capable for very complex access schemes.
More information is available in our web site.

58. Thanks for Attention 謝謝