2010/01/23 by Jean‐Guillaume Dumas, Dumas, Jean-Guillaume, Thierry Gautier +3
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Cryptography and Data Security #Distributed #FOS: Computer and information sciences #Parallel #Parallel Computing and Optimization Techniques #Symbolic Computation (cs.SC) #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1001.4150
openalex publication_date 2010/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a radix ladder, for the intermediate storage and computations. Our design is structured into three main modules: a black box residue computation in charge of computing each residue; a Chinese remaindering controller in charge of launching the computation and of the termination decision; an integer builder in charge of the reconstruction computation. We then show that this design enables many different forms of Chinese remaindering (e.g. deterministic, early terminated, distributed, etc.), easy comparisons between these forms and e.g. user-transparent parallelism at different parallel grains.