A combinatorial approach to threshold schemes
SIAM Journal on Discrete Mathematics
Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group
SIAM Journal on Discrete Mathematics
Communications of the ACM
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Proceedings of the 1982 conference on Cryptography
Chinese remaindering with errors
IEEE Transactions on Information Theory
Generalized Mignotte's Sequences Over Polynomial Rings
Electronic Notes in Theoretical Computer Science (ENTCS)
General Secret Sharing Based on the Chinese Remainder Theorem with Applications in E-Voting
Electronic Notes in Theoretical Computer Science (ENTCS)
Threshold cryptography based on Asmuth-Bloom secret sharing
Information Sciences: an International Journal
A Verifiable Secret Sharing Scheme Based on the Chinese Remainder Theorem
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Lattice-based threshold-changeability for standard CRT secret-sharing schemes
Finite Fields and Their Applications
Compact sequences of co-primes and their applications to the security of CRT-based threshold schemes
Information Sciences: an International Journal
Information Processing Letters
| Hi-index | 0.00 |
Threshold schemes enable a group of users to share a secret by providing each user with a share. The scheme has a threshold t+1 if any subset with cardinality t + 1 of the shares enables the secret to be recovered.In 1983, C. Asmuth and J. Bloom proposed such a scheme based on the Chinese remainder theorem. They derived a complex relation between the parameters of the scheme in order to satisfy some notion of security. However, at that time, the concept of security in cryptography had not yet been formalized.In this paper, we revisit the security of this threshold scheme in the modern context of security. In particular, we prove that the scheme is asymptotically optimal both from an information theoretic and complexity theoretic viewpoint when the parameters satisfy a simplified relationship. We mainly present three theorems, the two first theorems strengthen the result of Asmuth and Bloom and place it in a precise context, while the latest theorem is an improvement of a result obtained by Goldreich et al.