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• System Implementation Plans• Grantt chart, Cost implementation model

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.

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

System features

Hardware & Software RequirementsHard disk 80 GB

RAM 1GB

Technology Java

Tools Net-beans IDE

Processor Intel Pentium IV or above

Operating System Windows XP

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.

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.

System architectureConstruction 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 

 

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

Use case UML DIAGRAMS

Activity UML DIAGRAMS

State transition UML DIAGRAM

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

Grant chart & cost implementation model

Training System installation Studying Core java Implementation of Modules

Testing Documentation0

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