Chinese remainder theorem: applications in computing, coding, cryptography
Chinese remainder theorem: applications in computing, coding, cryptography
Communications of the ACM
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
Proceedings of the 1982 conference on Cryptography
Chinese remaindering with errors
IEEE Transactions on Information Theory
A modular approach to key safeguarding
IEEE Transactions on Information Theory
Information Processing Letters
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CRT-based threshold secret sharing schemes use sequences of pairwise co-prime positive integers in their construction. If these sequences are not ''compact'', then the CRT-based threshold secret sharing schemes may have a weak security in the sense of a massive loss of entropy or an arbitrarily large information rate. In this paper, compact sequences of co-primes are introduced, and their applications to the security of CRT-based threshold secret sharing schemes is throughout investigated. It is shown that all the results regarding the security of CRT-based threshold secret sharing schemes that use sequences of consecutive primes also hold for threshold secret sharing schemes that use compact sequences of co-primes. Moreover, compact sequences of co-primes may be significantly denser than sequences of consecutive primes of the same length, and their use in the construction of CRT-based threshold secret sharing schemes may lead to better security properties.