2012/03/08 by Haining Fan, Musong Gu, Jiaguang Sun +1 · 1 citation
Computer Science · Mathematics · #Cryptography and Residue Arithmetic #Coding theory and cryptography #Polynomial and algebraic computation #Chinese remainder theorem #Remainder #Mathematics #Division (mathematics) #Integer (computer science) #Multiplication (music) #Division algorithm #Arithmetic #Binary number #Moduli #Discrete mathematics #Algebra over a field #Combinatorics #Computer science #Pure mathematics
paper · doi:10.1049/iet-ifs.2010.0114
openalex publication_date 2012/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
The aim of this study is to find more Karatsuba-like formulae for a fixed set of moduli polynomials in GF(2)[x]. To this end, a theoretical framework is established. The authors first generalise the division algorithm, and then present a generalised definition of the remainder of integer division. Finally, a generalised Chinese remainder theorem is used to achieve their initial goal. As a by-product of the generalised remainder of integer division, the authors rediscover Montgomery's N-residue and present a systematic interpretation of definitions of Montgomery's multiplication and addition operations.