How to share a secret with cheaters
Proceedings on Advances in cryptology---CRYPTO '86
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Theoretical Computer Science
Fully dynamic secret sharing schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
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Mathematical Programming: Series A and B
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Communications of the ACM
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FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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WISA'05 Proceedings of the 6th international conference on Information Security Applications
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IEEE Transactions on Information Theory
Detection and identification of cheaters in (t, n) secret sharing scheme
Designs, Codes and Cryptography
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In this paper, we investigate the problem of increasing the threshold parameter of the Shamir (t,n)-threshold scheme without interacting with the dealer. Our construction will reduce the problem of secret recovery to the polynomial reconstruction problem which can be solved using a recent algorithm by Guruswami and Sudan. In addition to be dealer-free, our protocol does not increase the communication cost between the dealer and the n participants when compared to the original (t,n)-threshold scheme. Despite an increase of the asymptotic time complexity at the combiner, we show that recovering the secret from the output of the previous polynomial reconstruction algorithm is still realistic even for large values of t. Furthermore the scheme does not require every share to be authenticated before being processed by the combiner. This will enable us to reduce the number of elements to be publicly known to recover the secret to one digest produced by a collision resistant hash function which is smaller than the requirements of most verifiable secret sharing schemes.