Accelerating scalar conversion for Koblitz curve cryptoprocessors on hardware platforms

Sujoy Sinha Roy, Junfeng Fan, Ingrid Verbauwhede

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Koblitz curves are a class of computationally efficient elliptic curves where scalar multiplications can be accelerated using τNAF representations of scalars. However, conversion from an integer scalar to a short τNAF is a costly operation. In this paper, we improve the recently proposed scalar conversion scheme based on division by τ2. We apply two levels of optimizations in the scalar conversion architecture. First, we reduce the number of long integer subtractions during the scalar conversion. This optimization reduces the computation cost and also simplifies the critical paths present in the conversion architecture. Then we implement pipelines in the architecture. The pipeline splitting increases the operating frequency without increasing the number of cycles. We have provided detailed experimental results to support our claims made in this paper.

Original languageEnglish
Pages (from-to)810-818
Number of pages9
JournalIEEE Transactions on Very Large Scale Integration (VLSI) Systems
Issue number5
Early online date9 Jun 2014
Publication statusPublished - May 2015


  • Architecture
  • cryptography
  • field-programmable gate array (FPGA)
  • Koblitz curve
  • lazy reduction
  • pipelining
  • scalar multiplication

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Electrical and Electronic Engineering


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