1. A Novel Secret Sharing Scheme from Audio Perspective
In The Name of Allah
A Novel Secret Sharing Scheme from Audio Perspective
Mohammad Ehdaie
Taraneh Eghlidos
Mohammad Reza Aref
Sharif University of Technology, Tehran, Iran

2. M. Ehdaie, T. Eghlidos, M.R. Aref
Contents
Introduction
Preliminaries
Shares Generation
Secret Reconstruction
Security
Simulation
Ideality & Practical Issues
Discussions and Results
Conclusions & Further Research
References
Q & A
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M. Ehdaie, T. Eghlidos, M.R. Aref

3. M. Ehdaie, T. Eghlidos, M.R. Aref
Secret Sharing
Definition:
Secret sharing is a method to distribute a secret between some participants such that particular subsets (i.e. authorized subsets) could obtain the secret, whereas unauthorized subsets could not.
Significance:
The risk of fully authorizing a person
The risk of Information Disruption
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M. Ehdaie, T. Eghlidos, M.R. Aref

4. M. Ehdaie, T. Eghlidos, M.R. Aref
Terminology
Threshold Scheme
Cardinality of all minimum allowed subsets, k, is constant.
Perfect Scheme
Unauthorized subsets could not get any information about the secret by pooling their shares together.
Ideal Scheme
The size of each share is equal to the size of the secret.
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M. Ehdaie, T. Eghlidos, M.R. Aref

5. M. Ehdaie, T. Eghlidos, M.R. Aref
The History
Geometric Scheme, Blakley, 1979
Interpolation Scheme, Shamir, 1979 …
Visual Secret Sharing, Naor & Shamir, 1994
Audio Secret Sharing, Desmedt et al., 1998
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M. Ehdaie, T. Eghlidos, M.R. Aref

6. M. Ehdaie, T. Eghlidos, M.R. Aref
Motivation
What is an Audio Secret Sharing Scheme (ASSS)?
Audio Shares and/or Audio Secret
Why?
Audio Applications …
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M. Ehdaie, T. Eghlidos, M.R. Aref

7. Previous Works - Ultimate Goal
The Scheme
DHQ
LLY
Goal
Threshold
(2, n)
(k, n)
Perfect 
Without Computation
Ideal 
Audio Shares
Audio Secret
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M. Ehdaie, T. Eghlidos, M.R. Aref

8. M. Ehdaie, T. Eghlidos, M.R. Aref
Preliminaries
The audio file F corresponds to an Amplitude Vector A.
Vector c*A corresponds to the amplified audio file F with the coefficient c.
Playing two audio files simultaneously, leads to an audio file which corresponds to the sum of their corresponding vectors.
If a*A + b*B = c*C, then we can hear the amplified C by playing simultaneously amplified A & B with the coefficients a & b respectively.
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M. Ehdaie, T. Eghlidos, M.R. Aref

9. M. Ehdaie, T. Eghlidos, M.R. Aref
Setup
divide the audio secret file into some small intervals.
generate the shares in each interval independently.
put all share parts of each participant together and generate an audio share.
Let A be the amplitude of the secret file in a particular interval.
Let S1, S2, …, Sn be the amplitudes of the n share files in the same interval.
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M. Ehdaie, T. Eghlidos, M.R. Aref

10. M. Ehdaie, T. Eghlidos, M.R. Aref
Shares Generation
Generate S1, S2, …, Sk-1 Randomly.
Generate an (n-k+1)×k matrix with non-zero random elements:
Return to step 2, if C contains any singular submatrix.
For , compute Si from the equation below:
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M. Ehdaie, T. Eghlidos, M.R. Aref

11. Secret Reconstruction (1)
Lemma: Assume are k participants who want to reconstruct the secret. There is a linear combination of equations ek, ek+1, …, en leading to an equation of the form below:
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M. Ehdaie, T. Eghlidos, M.R. Aref

12. Secret Reconstruction (2)
Proof:
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M. Ehdaie, T. Eghlidos, M.R. Aref

13. M. Ehdaie, T. Eghlidos, M.R. Aref
Security (1)
Lemma: There is no linear combination of equations ek, ek+1, …, en, such that the coefficients of only k-1 or fewer shares are nonzero.
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M. Ehdaie, T. Eghlidos, M.R. Aref

14. M. Ehdaie, T. Eghlidos, M.R. Aref
Security (2)
Proof:
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M. Ehdaie, T. Eghlidos, M.R. Aref

15. M. Ehdaie, T. Eghlidos, M.R. Aref
Simulation
The audio secret
The noisy reconstructed secret
The reconstructed secret
One of the shares
Another share
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M. Ehdaie, T. Eghlidos, M.R. Aref

16. Ideality & Practical Issues
The file size of the secret = The file size of each share
Practical Issues:
Physical properties of amplifiers …
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M. Ehdaie, T. Eghlidos, M.R. Aref

17. Discussions and Results
The Scheme
DHQ
LLY
New
Threshold
(2, n)
(k, n)
Perfect 
Secure
Without Computation
Ideal 
It seems to be Ideal
Audio Shares
Audio Secret
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M. Ehdaie, T. Eghlidos, M.R. Aref

18. M. Ehdaie, T. Eghlidos, M.R. Aref
Conclusions
A new audio secret sharing scheme
Secure and it seems to be ideal
(k, n) threshold scheme
Audio shares and audio secret
Secret reconstruction without any computation
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M. Ehdaie, T. Eghlidos, M.R. Aref

19. M. Ehdaie, T. Eghlidos, M.R. Aref
Further Research
Generation of non-suspicious shares
Implementation and summing up practical issues
Extending the new scheme to the visual case
Perfectness & Ideality proof from Information Theoretical view
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M. Ehdaie, T. Eghlidos, M.R. Aref

20. M. Ehdaie, T. Eghlidos, M.R. Aref
References
Shamir A., "How to share a secret", Comm. ACM 22, pp , (1979).
Blakley G. R., "Safeguarding cryptographic keys", Proc. of the National Computer Conf., v. 48, pp , (1979).
Naor M., Shamir A., "Visual cryptography", Eurocrypt 94, pp
Desmedt Y., Hou S., Quisquater J., "Audio and optical cryptography", in Advances in Cryptology-Asiacrypt ’98, Springer-Verlag LNCS, pp
Lin C. C., Laih C. S., Yang C. N., "New Audio Secret Sharing Schemes With Time Division Technique", J. of Information Science and Engineering 19, (2003).
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