Combined random number generator via the generalized Chinese remainder theorem

Poisson statistics via the Chinese Remainder Theorem

We consider the distribution of spacings between consecutive elements in subsets of Z/qZ, where q is highly composite and the subsets are defined via the Chinese Remainder Theorem. We give a sufficient criterion for the spacing distribution to be Poissonian as the number of prime factors of q tends to infinity, and as an application we show that the value set of a generic polynomial modulo q ha...

The Chinese Remainder Theorem

Elementary Number Theory and the Chinese Remainder Theorem

This paper explores basic number theory including the groups, the rings and the units of modulo classes. It concludes with the Chinese Remainder Theorem. The goal is to examine these objects, their properties and to gain insight into their relationship with other sets.

Parallel computational algorithms for generalized Chinese remainder theorem

Recently, the residue number system (RNS) has been intensively studied. The Chinese remainder theorem (CRT) is a solution to the conversion problem of a number to RNS with a general moduli set. This paper introduces the generalized CRT (GCRT) with parallel algorithms used for the conversion. The GCRT differs from the CRT because it has the advantage of having more applications than does the CRT...

Modular exponentiation via the explicit Chinese remainder theorem

Fix pairwise coprime positive integers p1, p2, . . . , ps. We propose representing integers u modulo m, where m is any positive integer up to roughly √ p1p2 · · · ps, as vectors (u mod p1, u mod p2, . . . , u mod ps). We use this representation to obtain a new result on the parallel complexity of modular exponentiation: there is an algorithm for the Common CRCW PRAM that, given positive integer...