Proceedings of CRYPTO 84 on Advances in cryptology
Nonperfect secret sharing schemes and matroids
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
On Ideal Non-perfect Secret Sharing Schemes
Proceedings of the 5th International Workshop on Security Protocols
A Generalized Secret Image Sharing and Recovery Scheme
PCM '01 Proceedings of the Second IEEE Pacific Rim Conference on Multimedia: Advances in Multimedia Information Processing
Sharing multiple secrets in digital images
Journal of Systems and Software
A new multi-secret images sharing scheme using Largrange's interpolation
Journal of Systems and Software
An image-sharing method with user-friendly shadow images
IEEE Transactions on Circuits and Systems for Video Technology
A Matrix-Based Secret Sharing Scheme for Images
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
A Secret Sharing Scheme for Digital Images Based on Cellular Automata and Boolean Functions
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
A secret sharing scheme for digital images based on two-dimensional linear cellular automata
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
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A non-perfect secret sharing scheme is a method to distribute a secret among a set of participants, in such a way that some qualified subsets of participants, pooling together their information, can reconstruct the secret, whereas, other subsets of participants may have some information about the secret. In this journal, Feng et al. (2005) [A new multi-secret image sharing scheme using Lagrange's interpolation. The Journal of Systems and Software, 76 (3), 327-339] recently considered the situation in which there are many secrets to be shared among a set of participants, in such a way that each qualified subset of participant can reconstruct a different secret. They proposed a polynomial-based construction using as a main tool a particular sequence of participants, called a sharing-circle, and having the feature that the smaller the length of the sharing-circle, the smaller the size of the shares distributed to participants. They proposed a simple recursive algorithm to find a minimal length sharing-circle. Since their algorithm is exponential-time, they left the task of finding a better one as an open problem. In this paper we first answer their question, showing that a polynomial-time algorithm computing a minimal-length sharing-circle is unlikely to exist. Indeed, we prove that the problem of finding a sharing-circle having minimal length is NP-hard. Afterwards, we propose a construction which is simpler than the one of Feng et al. and that does not require the participants to perform polynomial interpolation in order to reconstruct the secrets. Moreover, our scheme distributes shares having a smaller size.