Secret Sharing Schemes with Detection of Cheaters for a General Access Structure

In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefits. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure.

[1]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[2]  Carles Padró.  Robust Vector Space Secret Sharing Schemes , 1998, Inf. Process. Lett..

[3]  Douglas R. Stinson,et al.  Cryptography: Theory and Practice , 1995 .

[4]  Alfredo De Santis,et al.  Lower Bounds for Robust Secret Sharing Schemes , 1997, Inf. Process. Lett..

[5]  Carles Padró,et al.  Secret Sharing Schemes with Bipartite Access Structure , 1998, EUROCRYPT.

[6]  Josep Rifa-Coma.  How to avoid the cheaters succeeding in the key sharing scheme , 1993 .

[7]  Alfredo De Santis,et al.  Tight Bounds on the Information Rate of Secret Sharing Schemes , 1997, Des. Codes Cryptogr..

[8]  Douglas R. Stinson,et al.  An explication of secret sharing schemes , 1992, Des. Codes Cryptogr..

[9]  Douglas R. Stinson,et al.  Decomposition constructions for secret-sharing schemes , 1994, IEEE Trans. Inf. Theory.

[10]  Alfredo De Santis,et al.  Size of Shares and Probability of Cheating in Threshold Schemes , 1994, EUROCRYPT.

[11]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[12]  Carles Padró,et al.  Detection of Cheaters in Vector Space Secret Sharing Schemes , 1999, Des. Codes Cryptogr..

[13]  Ernest F. Brickell,et al.  On the classification of ideal secret sharing schemes , 1989, Journal of Cryptology.

[14]  Alfredo De Santis,et al.  Graph decompositions and secret sharing schemes , 2004, Journal of Cryptology.

[15]  Kaoru Kurosawa,et al.  Optimum Secret Sharing Scheme Secure against Cheating , 1996, EUROCRYPT.

[16]  Ernest F. Brickell,et al.  Some Ideal Secret Sharing Schemes , 1990, EUROCRYPT.