Threshold secret sharing based on the Chinese remainder theorem has been considered by Mignotte [23] and Asmuth and Bloom [1]. In this paper we demonstrate that the Chinese remainder theorem can be used for realizing more general access structures, as the compartmented or the weighted threshold ones. We also prove that there exist some non-weighted threshold access structures whose realizations...

We start by giving a brief description of the classical Chinese remainder theorem for integers, after whichwe define the greatest common divisor of two polynomials and congruences modulo a polynomial. These concepts allow us to state and prove the Chinese remainder theorem for polynomials. After presenting some important consequences of that theorem, we give its applications to the factorizatio...

In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for...

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...