Fully dynamic secret sharing schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Chinese remainder theorem: applications in computing, coding, cryptography
Chinese remainder theorem: applications in computing, coding, cryptography
Finding smooth integers in short intervals using CRT decoding
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Efficient and Unconditionally Secure Verifiable Threshold Changeable Scheme
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
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
Noisy Chinese remaindering in the Lee norm
Journal of Complexity - Special issue on coding and cryptography
Proceedings of the 1982 conference on Cryptography
Generalized privacy amplification
IEEE Transactions on Information Theory - Part 2
Chinese remaindering with errors
IEEE Transactions on Information Theory
A modular approach to key safeguarding
IEEE Transactions on Information Theory
Analysis and Design of Multiple Threshold Changeable Secret Sharing Schemes
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
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We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have secure channels between shareholders. In contrast, we show how to increase the threshold parameter of the standard CRT secret-sharing scheme without secure channels between the shareholders. Our method can thus be applied to existing CRT schemes even if they were set up without consideration to future threshold increases. Our method is a positive cryptographic application for lattice reduction algorithms, and we also use techniques from lattice theory (geometry of numbers) to prove statements about the correctness and information-theoretic security of our constructions.