Cryptology ePrint Archive: Report 2013/535

Accelerating Scalar Conversion for Koblitz Curve Cryptoprocessors on Hardware Platforms

Sujoy Sinha Roy and Junfeng Fan and Ingrid Verbauwhede

Abstract: Koblitz curves are a class of computationally efficient elliptic curves where scalar multiplications can be accelerated using $\tau$NAF representations of scalars. However conversion from an integer scalar to a short $\tau$NAF is a costly operation. In this paper we improve the recently proposed scalar conversion scheme based on division by $\tau^2$. 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.

Category / Keywords: Koblitz Curve, Lazy Reduction, Scalar Multiplication, Cryptography, FPGA, Architecture, Pipelining

Date: received 26 Aug 2013, last revised 29 Apr 2014

Contact author: sujoy sinharoy at esat kuleuven be

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