THE GENERAL CHINESE REMAINDER THEOREM

The Chinese Remainder Theorem

General Secret Sharing Based on the Chinese Remainder Theorem

In this paper we extend the threshold secret sharing schemes based on the Chinese remainder theorem in order to deal with more general access structures. Aspects like verifiability, secret sharing homomorphisms and multiplicative properties are also discussed. AMS Subject Classification: 94A62, 11A07

Robustness in Chinese Remainder Theorem

Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to noises, the problem of robustly reconstructing integers via the erroneous residues has been intensively studied in the literature. In order to robustly reco...

A Multivariable Chinese Remainder Theorem

Using an adaptation of Qin Jiushao’s method from the 13th century, it is possible to prove that a system of linear modular equations ai1xi + · · · + ainxn = ~bi mod ~ mi, i = 1, . . . , n has integer solutions if mi > 1 are pairwise relatively prime and in each row, at least one matrix element aij is relatively prime to mi. The Chinese remainder theorem is the special case, where A has only one...

Sharing DSS by the Chinese Remainder Theorem

A new threshold scheme for the Digital Signature Standard is proposed using Asmuth-Bloom secret sharing based on the Chinese Remainder Theorem. The proposed scheme is simple and can be used practically in real life.