Detection and identification of cheaters in (t, n) secret sharing scheme
Designs, Codes and Cryptography
A coding theorem for cheating-detectable (2, 2)-threshold blockwise secret sharing schemes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Flaws in some secret sharing schemes against cheating
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Efficient (k, n) threshold secret sharing schemes secure against cheating from n - 1 cheaters
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Foundations and Trends in Communications and Information Theory
Cryptography and Communications
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ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
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EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
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Tompa and Woll introduced a problem of cheating in $(k,n)$ threshold secret sharing schemes. In this problem $k-1$ malicious participants aim to cheat an honest one by opening forged shares and causing the honest participant to reconstruct the wrong secret. We first derive a tight lower bound on the size of shares $|\cV_i|$ for secret sharing schemes that protect against this type of attack: $ |\cV_i| \geq (|\cS|-1)/\delta + 1 $, where $\cV_i$ denotes the set of shares of participant $P_i$, $\cS$ denotes the set of secrets, and $\delta$ denotes the cheating probability. We next present an optimum scheme, which meets the equality of our bound, by using "difference sets." A partial converse and some extensions are also shown.