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Detection and identification of
cheaters in (t, n) secret
sharing scheme
Presented by
Outline
• Problem definition
• Literature survey
• System features
• System Architecture
• Analysis Models
• UML diagrams
...
Problem definition
In a (t, n) secret sharing scheme, a secret s is divided
into n shares and shared among a set of n shar...
Literature survey
 There are many research papers in the literatures to investigate the problem of cheater
detection and/...
System features
 Hardware & Software Requirements
Hard disk 80 GB
RAM 1GB
Technology Java
Tools Net-beans IDE
Processor I...
System features continued..
Quality Attributes
• Usability : The application seem to user friendly since the GUI is
inter...
System architecture
• Thien-Lin scheme and the intractability of the
discrete logarithm:
• IT contains three phases: Initi...
System architecture
Construction phase: H randomly chooses an integer s0∈[2,N] such that s0 is
relatively prime to (p−1) a...
System architecture
 Reconstruction and verification phase : Without loss of generality, members of M′={M1,
M2,…, Mt} wil...
Use case
Activity
State transition
System Implementation Plan
SR
No
Task Name Duration
1 Project topic finalization 10 days
2 Studying Core java,J2SE 10 days...
Grant chart & cost implementation
model
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Training System
installation
...
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Detection and identification of cheaters in (t, n) secret

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Transcript of "Detection and identification of cheaters in (t, n) secret"

  1. 1. Detection and identification of cheaters in (t, n) secret sharing scheme Presented by
  2. 2. Outline • Problem definition • Literature survey • System features • System Architecture • Analysis Models • UML diagrams • System Implementation Plans • Grantt chart, Cost implementation model
  3. 3. Problem definition In a (t, n) secret sharing scheme, a secret s is divided into n shares and shared among a set of n shareholders by a mutually trusted dealer in such a way that any t or more than t shares will be able to reconstruct this secret; but fewer than t shares cannot know any information about the secret.
  4. 4. Literature survey  There are many research papers in the literatures to investigate the problem of cheater detection and/or identification for secret sharing schemes.  In 1979, Shamir and Blakley first developed the concept of the (t,n) threshold secret sharing scheme. Then Naor and Shamir extended the secret sharing concept into image research, and referred it as image secret sharing in 1994, which was based on the model of secret sharing proposed by the two above- mentioned scholars: For image information P, we would like to generate n shadow images so that any t or more participants can reconstruct the original secret image, but any t-1 or less participants can not get sufficient information to reconstruct the original secret image.  After Naor and Shamir, many secret sharing schemes have been proposed for processing 256 gray-level image. But in these schemes, shadow images have larger image sizes compared to that of the original secret image. The contrast ratio in the reconstructed image is quite poor
  5. 5. System features  Hardware & Software Requirements Hard disk 80 GB RAM 1GB Technology Java Tools Net-beans IDE Processor Intel Pentium IV or above Operating System Windows XP
  6. 6. System features continued.. Quality Attributes • Usability : The application seem to user friendly since the GUI is interactive. • Maintainability : This application is maintained for long period of time since it will be implemented under java platform . • Reusability : The application can be reusable by expanding it to the new modules • Portability: The application is purely a portable mobile application since it can only be operated on android Operating system.
  7. 7. System architecture • Thien-Lin scheme and the intractability of the discrete logarithm: • IT contains three phases: Initialization phase, Construction phase and Reconstruction & Verification phase: • • Initialization phase: In this phase, the holder and the participants need some intercommunication, but this can be done over a public channel. Firstly, H chooses two prime numbers, p and q, and computes N=pq. Both p and q should satisfy the same properties as the two primes used in RSA cryptosystem which can prevent anybody factor N efficiently. Subsequently, H chooses an integer g∈[N1/2,N] such that g is relatively prime to p and q. Publishes {g, N}.Each participant Mi∈M randomly chooses an si∈[2, N] asher/his own secret shadow and computes Ri =gsi modN, finally Mi provides Ri to H. H must ensure that Ri≠Rj for all Mi≠Mj. Once Ri=Rj, H should demand these Mi s to choose new si s. Publishes Ri.
  8. 8. System architecture Construction phase: H randomly chooses an integer s0∈[2,N] such that s0 is relatively prime to (p−1) and (q−1). Then H computes f and makes s0 f=1modφ(N), whereφ(N) is the Euler phi-function; H Computes R0 =gs0 modN and Ii =Rs0 i modN, i=1, 2,…, n. Publishes {R0, f}; The new image P′ is divided into several sections according to lexicography order. Each section contains t pixels, and each pixel of the image belongs to one and only one section. For the section j, H constructs (t−1) th-degree polynomial hj(x) mod 251 as follows: hjðxÞ ¼ b0 þ b1x þ: : : þ bt_1xt_1mod251: Here b0, b1,…, bt − 1 are the t pixels of the section; H evaluates yi=hj(Ii), i=1, 2,…, n. Publishes (y1, y2,…,y
  9. 9. System architecture  Reconstruction and verification phase : Without loss of generality, members of M′={M1, M2,…, Mt} will cooperate to reconstruct the image P′. 1) Mi∈M′ computes her/his own sub-secret(pseudo shadow) Ii V¼ Rsi 0 modN, where si is secret shadow of Mi; 2) Anybody can verify Ii′ provided by Mi: if I′I f=Ri mod N, then Ii′ is true; otherwise Ii′ is false and Mi may be a cheater; Reconstruct the image P′: with the knowledge of t pairs of (Ii′,yi) and the Lagrange interpolating polynomial, the (t−1)th-degree polynomial hj(x) can be uniquely determined as follows:  In initialization phase, each participant Mi chooses her/his own secret shadow si, the holder H is absolutely not a cheater
  10. 10. Use case
  11. 11. Activity
  12. 12. State transition
  13. 13. System Implementation Plan SR No Task Name Duration 1 Project topic finalization 10 days 2 Studying Core java,J2SE 10 days 3 Implementation of Shamir’s SSS system 30 days 4 Implementation of detecting system 7 days 5 Implementation of identifying cheaters 10 days
  14. 14. Grant chart & cost implementation model 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Training System installation Studying Core java Implementation of Modules Testing Documentation Cost(in RS) Time(in days)
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