The document outlines a system for detecting and identifying cheaters in a (t,n) secret sharing scheme. It discusses the problem definition, related work, proposed system features and architecture. The system architecture uses a Thien-Lin secret sharing scheme and includes initialization, construction, and reconstruction/verification phases. It also provides use cases, state transitions, implementation plans with a Gantt chart and cost model.

1. Detection and identification of
cheaters in (t, n) secret
sharing scheme
Presented by

2. Outline
• Problem definition
• Literature survey
• System features
• System Architecture
• Analysis Models
• UML diagrams
• System Implementation Plans
• Grantt chart, Cost implementation model

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. 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. 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. 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. 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. 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. 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. Use case

11. Activity

12. State transition

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. Grant chart & cost implementation
model
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Training System
installation
Studying Core
java
Implementation
of Modules
Testing Documentation
Cost(in RS)
Time(in days)