Energy-Efficient Software Implementation of Long Integer Modular Arithmetic

  • Johann Großschädl
  • Roberto M. Avanzi
  • Erkay Savaş
  • Stefan Tillich
Conference paper

DOI: 10.1007/11545262_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3659)
Cite this paper as:
Großschädl J., Avanzi R.M., Savaş E., Tillich S. (2005) Energy-Efficient Software Implementation of Long Integer Modular Arithmetic. In: Rao J.R., Sunar B. (eds) Cryptographic Hardware and Embedded Systems – CHES 2005. CHES 2005. Lecture Notes in Computer Science, vol 3659. Springer, Berlin, Heidelberg

Abstract

This paper investigates performance and energy characteristics of software algorithms for long integer arithmetic. We analyze and compare the number of RISC-like processor instructions (e.g. single-precision multiplication, addition, load, and store instructions) required for the execution of different algorithms such as Schoolbook multiplication, Karatsuba and Comba multiplication, as well as Montgomery reduction. Our analysis shows that a combination of Karatsuba-Comba multiplication and Montgomery reduction (the so-called KCM method) allows to achieve better performance than other algorithms for modular multiplication. Furthermore, we present a simple model to compare the energy-efficiency of arithmetic algorithms. This model considers the clock cycles and average current consumption of the base instructions to estimate the overall amount of energy consumed during the execution of an algorithm. Our experiments, conducted on a StrongARM SA-1100 processor, indicate that a 1024-bit KCM multiplication consumes about 22% less energy than other modular multiplication techniques.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Johann Großschädl
    • 1
  • Roberto M. Avanzi
    • 2
  • Erkay Savaş
    • 3
  • Stefan Tillich
    • 1
  1. 1.Institute for Applied Information Processing and CommunicationsGraz University of TechnologyGrazAustria
  2. 2.Faculty of Mathematics and Horst Görtz Institute for IT-SecurityRuhr University BochumBochumGermany
  3. 3.Faculty of Engineering and Natural SciencesSabanci UniversityIstanbulTurkey

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