💚Trustworthy Call Girls Pune Call Girls Service Just Call 🍑👄6378878445 🍑👄 Top...
UTP_Secret_Sharing_Malaysia_Sonali_Patil.pptx
1. Prof. Dr. Sonali Patil, IEEE Senior Member (93890098)
Head, Department of Information Technology
Pimpri Chinchwad College of Engineering, Pune, India
IEEE University Technology PETRONAS (UTP) Student Branch, Malaysia
20th July 2023
2. Secret Sharing
Verifiable Secret Sharing
Publicly Verifiable Secret Sharing with Cheater Identification
General Access Structure Sharing Scheme
Secure Secret Sharing with embedding of shares
Probable Applications
Opportunities
References
2
3. Secrets are protected by more than one key.
Backup copies are created to protect cryptographic keys
from loss or corruption.
The greater the number of copies made, the greater the risk
of security exposure.
The smaller the number the greater the chance that all of
them are lost.
Secret Sharing Schemes (SSS) allows improving the level
of protection without increasing the risk of exposure.
3
4. 11 scientists are working on a secret project. They wish to
lock up the documents in a cabinet so that cabinet can be
opened if and only if six or more of the scientists are present.
What is the smallest number of locks needed?
What is the smallest number of keys to the lock each
scientist must carry?
4
5. Minimum number of locks:
11C6= 462
Smallest number of keys to the locks each scientist must
carry:
10C5=252
SSS is very useful in such situations.
5
6. General idea of secret sharing
Need of secret sharing scheme
• Distribute the secret among n participants
• Any t participants can reconstruct the secret
• Any t-1 or fewer participants unable to reconstruct secret
• Gives tight control and removes single point vulnerability
• Individual key share holder cannot change/access the data
6
8. Polynomial Based Secret Sharing Schemes
Vector Space Based Secret Sharing Schemes
Matrix Projection Based Secret Sharing Schemes
Circuit Based Secret Sharing Schemes
Chinese Remainder Theorem Based Secret Sharing Schemes
√
√
√
√
√
8
9. Shamir developed the idea of a (t, n) threshold based secret sharing
technique.
The technique allows a polynomial function of order (t-1) constructed with
constant term as secret and other coefficients are unknown non zero
elements.
No group of (t-1) or fewer secret shares can discover the secret value. The
secret value can be easily obtained by using Lagrange Interpolation.
Shamir’s SSS is regarded as Perfect scheme because knowing even (t-1)
equations doesn’t expose any information about the secret.
9
11. 11
Construction of Shares
A simple (3, 5) threshold based example is shown for secret S=15
Random variables a1=1, a2=2
f(x)=S+a1x+a2x2 =15+x+2x2
f(1)=18, f(2)=25, f(3)=36, f(4)=51, f(5)=70
12. 12
Reconstruction of Secret
Take randomly 3 shares to construct secret..
(x0, y0)=(1, 18)
(x1, y1)=(2, 25)
(x2, y2)=(3, 36)
f(x)=[(x-2)(x-3)/(1-2)(1-3)]*18+[(x-1)(x-3)/(2-1)(2-3)]*25 +[(x-
1)(x-2)/(3-1)(3-2)]*36= 15+x+2x2
14. 14
The secret sharing schemes are having a threat of corruption of
shares in transmission or cheating by dishonest participants/Dealer.
Proposed Verifiable Secret Sharing Scheme (VSSS) allows the
participants to verify the correctness of reconstructed secret.
The scheme uses public image to add verifiability in the existing
scheme.
The accuracy of retrieved public image verifies correctness of
secret image
16. PVSS allows anybody to verify the correctness of Received Shares.
The functionality of proposed scheme is based on asymmetric key
algorithm.
The scheme can identify up to n number of cheaters.
The proposed scheme is accurate, secure and with small size of
shares than the original secret image.
16
18. To withstand Mobile Adversaries the life-time of the secret is
divided into time periods.
At the start of each time period, the players initialize a shares
refreshment phase.
Any information gained by the adversary during any time period
becomes obsolete in the next time period.
18
19. 19
Reconstructed Secret Image from
new shares
Secret Image
Old Shares and New Shares
Wrong Secret Reconstructed Using
1 Old and 1 New Share
20. LSB Technique is used to embed the created shares in cover images
Due to small size of shares less data hiding scheme is used
Simple embedding technique is making complexity of scheme low
It adds security as it avoids attackers attention
20
22. Provides flexibility to decide which specified subsets of participants
will reconstruct the secret and which subsets cannot.
Allowed specific groups will reconstruct the secret and forbidden
subsets will not able to reconstruct the secret
Sometimes multiple assignments of shares for single shareholder
It is better in terms of the information rate due to highly reduced
size shares.
22
23. 23
Reconstructed Secret Image
from qualified set of participants
Secret Image Shares with Participants (2 Shares with each Participant)
Reconstructed Secret Image from
forbidden set of participants
25. Application Type Required Feature of Secret Sharing
Transfer Money from a Bank Threshold Schemes
Authentication Systems Threshold, Embedding of Shares in Cover Images
Launching of a Missile Threshold, General Access Structure
Communications Networks Ideal, Perfect, Low complexity
Untrusted Dealer, Untrusted
Participants
Verifiable Secret Sharing, Publicly Verifiable Secret Sharing
Electronic Voting Publicly Verifiable Secret Sharing
Private Querying of Database Low Complexity, Threshold
Collective Control
Periodically Renewal of Shares, Enrollment /dis-enrollment
of Participants
Escrow-cryptosystems Publicly Verifiable Secret Sharing
Secure Storage Ideal, Reliable, General Access Structure
25
26. Secret Sharing Schemes (SSS) allows improving the level of protection
without increasing the risk of exposure
There is a lot advancing (steadily but surely) in secret sharing
Applications for secret sharing schemes seem to be getting more important
There is a need to extend the research for analysis for finding relation in
Application Semantics and Extended Capabilities
We can expect more rationalization of secret sharing schemes in the near
future
26
