On the generalisation of special moduli for faster interleaved montgomery modular multiplication


Akleylek S., CENK M., ÖZBUDAK F.

IET INFORMATION SECURITY, vol.7, no.3, pp.165-171, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.1049/iet-ifs.2010.0271
  • Journal Name: IET INFORMATION SECURITY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.165-171
  • Keywords: logic gates, multiplying circuits, public key cryptography, moduli generalisation, faster interleaved Montgomery modular multiplication algorithm, simplified precomputational phase, prime number, positive integer, elliptic curve crytographic applications, pairing-based cryptography, elliptic curve parameters, AND gates, XOR gates
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this study, the authors give a generalisation of special moduli for faster interleaved Montgomery modular multiplication algorithm with simplified pre-computational phase for GF(p(n)), where p 2 is a prime number and n is a positive integer. The authors propose different sets of moduli that can be used in elliptic curve crytographic applications and pairing-based cryptography. Moreover, this method also leads to efficient implementations for the elliptic curve parameters given in standards. It is shown that one can obtain efficient Montgomery modular multiplication architecture in view of the number of AND gates and XOR gates by choosing proposed sets of moduli. The authors eliminate final substraction step with proposed sets of moduli. These methods are easy to implement for hardware.