Abstract
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 language | English |
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Pages (from-to) | 810-818 |
Number of pages | 9 |
Journal | IEEE Transactions on Very Large Scale Integration (VLSI) Systems |
Volume | 23 |
Issue number | 5 |
Early online date | 9 Jun 2014 |
DOIs | |
Publication status | Published - May 2015 |
Keywords
- 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