Chapter

Cryptographic Hardware and Embedded Systems - CHES 2002

Volume 2523 of the series Lecture Notes in Computer Science pp 484-499

Date:

Scalable and Unified Hardware to Compute Montgomery Inverse in GF(p) and GF(2n)

  • Adnan Abdul-Aziz GutubAffiliated withDepartment of Electrical & Computer Engineering, Oregon State University
  • , Alexandre F. TencaAffiliated withDepartment of Electrical & Computer Engineering, Oregon State University
  • , Erkay SavaşAffiliated withDepartment of Electrical & Computer Engineering, Oregon State University
  • , RCCetin K. KoçAffiliated withDepartment of Electrical & Computer Engineering, Oregon State University

Abstract

Computing the inverse of a number in finite fields GF(p) or GF(2n) is equally important for cryptographic applications. This paper proposes a novel scalable and unified architecture for a Montgomery inverse hardware that operates in both GF(p) and GF(2n) fields. We adjust and modify a GF(2n) Montgomery inverse algorithm to accommodate multi-bit shifting hardware, making it very similar to a previously proposed GF(p) algorithm. The architecture is intended to be scalable, which allows the hardware to compute the inverse of long precision numbers in a repetitive way. After implementing this unified design it was compared with other designs. The unified hardware was found to be eight times smaller than another reconfigurable design, with comparable performance. Even though the unified design consumes slightly more area and it is slightly slower than the scalable inverter implementations for GF(p) only, it is a practical solution whenever arithmetic in the two finite fields is needed.