Cox-Rower Architecture for Fast Parallel Montgomery Multiplication

  • Shinichi Kawamura
  • Masanobu Koike
  • Fumihiko Sano
  • Atsushi Shimbo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1807)


This paper proposes a fast parallel Montgomery multiplication algorithm based on Residue Number Systems (RNS). It is easy to construct a fast modular exponentiation by applying the algorithm repeatedly. To realize an efficient RNS Montgomery multiplication, the main contribution of this paper is to provide a new RNS base extension algorithm. Cox-Rower Architecture described in this paper is a hardware suitable for the RNS Montgomery multiplication. In this architecture, a base extension algorithm is executed in parallel by plural Rower units controlled by a Cox unit. Each Rower unit is a single-precision modular multiplier-and-accumulator, whereas Cox unit is typically a 7 bit adder. Although the main body of the algorithm processes numbers in an RNS form, efficient procedures to transform RNS to or from a radix representation are also provided. The exponentiation algorithm can, thus, be adapted to an existing standard radix interface of RSA cryptosystem.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Shinichi Kawamura
    • 1
  • Masanobu Koike
    • 2
  • Fumihiko Sano
    • 2
  • Atsushi Shimbo
    • 1
  1. 1.Toshiba Research and Development CenterKawasakiJapan
  2. 2.Toshiba System Integration Technology CenterTokyoJapan

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