Compact multiplicative inverter for hardware elliptic curve cryptosystem

M. M. Wong*, M. L.D. Wong, Ka Lok Man

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingConference Proceedingpeer-review


This paper presents a compact design of a multiplicative inverter for elliptic curve cryptosystems. Using a methodology based on the composite field arithmetic, we propose a combinatorial solution to mitigate the usage of look up tables as commonly adopted by the conventional software based approach. In particular, we perform further isomorphism in the subfield, such that the required arithmetic are constructed using logical AND and XOR gates only. In this work, we demonstrate our proposed methodology with the field GF((2 8)41) ≅ GF((((22)2) 2)41) in optimal normal type II basis. The chosen field is both secure and results in efficient computation. An analysis of the resultant hardware complexity of our inverter is reported towards the end.

Original languageEnglish
Title of host publicationNetwork and Parallel Computing - 9th IFIP International Conference, NPC 2012, Proceedings
Number of pages8
Publication statusPublished - 2012
Event9th IFIP International Conference on Network and Parallel Computing, NPC 2012 - Gwangju, Korea, Republic of
Duration: 6 Sept 20128 Sept 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7513 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th IFIP International Conference on Network and Parallel Computing, NPC 2012
Country/TerritoryKorea, Republic of


  • Composite field arithmetic (CFA)
  • Elliptic curve (EC) cryptosystems
  • Itoh and Tsujii inversion algorithm (ITIA)
  • Multiplicative inversion

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