An explication of secret sharing schemes
Designs, Codes and Cryptography
Communications of the ACM
All-or-Nothing Encryption and the Package Transform
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Publicly verifiable secret sharing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Optimum secret sharing scheme secure against cheating
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Exposure-resilient functions and all-or-nothing transforms
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Updating the parameters of a threshold scheme by minimal broadcast
IEEE Transactions on Information Theory
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A multi-stage secret sharing (MSS) scheme is a method of sharing a number of secrets among a set of participants, such that any authorized subset of participants could recover one secret in every stage. The first MSS scheme was proposed by He and Dawson in 1994, based on Shamir's well-known secret sharing scheme and one-way functions. Several other schemes based on different methods have been proposed since then. In this paper, the authors propose an MSS scheme using All-Or-Nothing Transform (AONT) approach. An AONT is an invertible map with the property that having “almost all” bits of its output, one could not obtain any information about the input. This characteristic is employed in the proposed MSS scheme in order to reduce the total size of secret shadows, assigned to each participant. The resulted MSS scheme is computationally secure. Furthermore, it does not impose any constraint on the order of secret reconstructions. A comparison between the proposed MSS scheme and that of He and Dawson indicates that the new scheme provides more security features, while preserving the order of public values and the computational complexity.