Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
Some ideal secret sharing schemes
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
An explication of secret sharing schemes
Designs, Codes and Cryptography
A course in computational algebraic number theory
A course in computational algebraic number theory
Chinese remainder theorem: applications in computing, coding, cryptography
Chinese remainder theorem: applications in computing, coding, cryptography
Communications of the ACM
Primality and Cryptography
Secret Sharing in Multilevel and Compartmented Groups
ACISP '98 Proceedings of the Third Australasian Conference on Information Security and Privacy
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
On the Security of the Threshold Scheme Based on the Chinese Remainder Theorem
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Verifiable secret-ballot elections
Verifiable secret-ballot elections
A practical scheme for non-interactive verifiable secret sharing
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Multi-authority secret-ballot elections with linear work
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Proceedings of the 1982 conference on Cryptography
Chinese remaindering with errors
IEEE Transactions on Information Theory
An improved algorithm for computing logarithms over and its cryptographic significance (Corresp.)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A modular approach to key safeguarding
IEEE Transactions on Information Theory
New efficient and practical verifiable multi-secret sharing schemes
Information Sciences: an International Journal
Verifiable multi-secret sharing based on LFSR sequences
Theoretical Computer Science
An efficient lattice-based secret sharing construction
WISTP'12 Proceedings of the 6th IFIP WG 11.2 international conference on Information Security Theory and Practice: security, privacy and trust in computing systems and ambient intelligent ecosystems
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Threshold secret sharing based on the Chinese remainder theorem has been considered by Mignotte [Mignotte, M., How to share a secret, in: T. Beth, editor, Cryptography-Proceedings of the Workshop on Cryptography, Burg Feuerstein, 1982, Lecture Notes in Computer Science 149 (1983), pp. 371-375] and Asmuth and Bloom [Asmuth, C.A. and J. Bloom, A modular approach to key safeguarding, IEEE Transactions on Information Theory IT-29 (1983), pp. 208-210]. In this paper we demonstrate that the Chinese remainder theorem can be used for realizing more general access structures, as the compartmented or the weighted threshold ones. We also prove that there exist some non-weighted threshold access structures whose realizations require the general variant of the Chinese remainder theorem, i.e., the variant in which the modules are not necessarily pairwise coprime. As an application of the proposed secret sharing schemes, we present a multi-authority e-voting schemes in which, as a novelty, the tallying authorities may have non-equal weights.