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.
KeywordsCryptography Secret sharing schemes Detection of cheaters Robust and secure schemes
Unable to display preview. Download preview PDF.
- 1.G.R. Blakley. Safeguarding cryptographic keys. AFIPS Conference Proceedings 48 (1979) 313–317.Google Scholar
- 7.M. Carpentieri, A. De Santis and U. Vaccaro. Size of shares and probability of cheating in threshold schemes. Advances in Cryptology, EUROCRYPT 93, Lectures Notes in Computer Science 765, Springer-Verlag (1994) 118–125.Google Scholar
- 8.W. Ogata and K. Kurosawa. Optimum Secret Sharing Scheme Secure against Cheating. Advances in Cryptology, EUROCRYPT 96, Lecture Notes in Computer Science 1070 (1996) 200–211.Google Scholar
- 14.G.J. Simmons. An Introduction to Shared Secret and/or Shared Control Schemes and Their Application. Contemporary Cryptology. The Science of Information Integrity. IEEE Press (1991) 441–497.Google Scholar