Improved Modular Multiplication for Optimal Prime Fields

  • Hwajeong Seo
  • Zhe Liu
  • Yasuyuki Nogami
  • Jongseok Choi
  • Howon KimEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8909)


Optimal Prime Fields (OPFs) are considered to be one of the best choices for lightweight elliptic curve cryptography implementation on resource-constraint embedded processors. In this paper, we revisit efficient implementation of the modular arithmetic over the special prime fields, and present improved implementation of modular multiplication for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) method. OPF-CIOC method follows the general idea of (consecutive) operand caching technique, but has been carefully optimized and redesigned for Montgomery multiplication in an integrated fashion. We then evaluate the practical performance of proposed method on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC method outperforms the previous best known results in ACNS’14 by a factor of 5 %. Furthermore, our method is implemented in a regular way which helps to reduce the leakage of side-channel information.


Montgomery multiplication Optimal prime fields Embedded processors Public key cryptography Operand caching Consecutive operand caching 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hwajeong Seo
    • 1
  • Zhe Liu
    • 2
  • Yasuyuki Nogami
    • 3
  • Jongseok Choi
    • 1
  • Howon Kim
    • 1
    Email author
  1. 1.School of Computer Science and EngineeringPusan National UniversityBusanRepublic of Korea
  2. 2.Laboratory of Algorithmics, Cryptology and Security (LACS)University of LuxembourgLuxembourg-kirchbergLuxembourg
  3. 3.Graduate School of Natural Science and TechnologyOkayama UniversityOkayamaJapan

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