Elements of information theory
Elements of information theory
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
A Construction for Multisecret Threshold Schemes
Designs, Codes and Cryptography
On Some Methods for Unconditionally Secure Key Distributionand Broadcast Encryption
Designs, Codes and Cryptography - Special issue: selected areas in cryptography I
Communications of the ACM
Linear Key Predistribution Schemes
Designs, Codes and Cryptography
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Perfectly-Secure Key Distribution for Dynamic Conferences
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
An Optimal Multisecret Threshold Scheme Construction
Designs, Codes and Cryptography
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In a multisecret sharing scheme, several secret values are distributed among a set of n users, and each secret may have a different associated access structure. We consider here unconditionally secure schemes with multithreshold access structures. Namely, for every subset P of k users there is a secret key that can only be computed when at least t of them put together their secret information. Coalitions with at most w users with less than t of them in P cannot obtain any information about the secret associated to P. The main parameters to optimize are the length of the shares and the amount of random bits that are needed to set up the distribution of shares, both in relation to the length of the secret. In this paper, we provide lower bounds on this parameters. Moreover, we present an optimal construction for t = 2 and k = 3, and a construction that is valid for all w, t, k and n. The models presented use linear algebraic techniques.