A Closed-Form Robust Chinese Remainder Theorem and Its Performance Analysis

The Chinese Remainder Theorem

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...

Modified Chinese Remainder Theorem and Its Application to Proxy Signatures

Chinese Remainder Theorem has been used for hundreds of years and has been applied to many domains such as integers and polynomials. An assumption made is that the component moduli are pairwise co-prime. In this paper, rst we remove this assumption; then we give an algorithm to nd whether a given system of congruent equations has a solution, and if so, how to nd the solution in an eecient manne...

Robust Threshold Schemes Based on the Chinese Remainder Theorem

Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing.

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...