Accelerating Scalar Conversion for Koblitz Curve Cryptoprocessors on Hardware Platforms

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 τ
²
. 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.