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 costly and thus restricts speed. In this paper we present acceleration techniques for the recently proposed scalar conversion hardware based on division by $\tau^2$. Acceleration is achieved in two steps. First we perform computational optimizations to reduce the number of long subtraction operations during the conversion of scalar. This helps in reducing the number of integer adder/subtracter circuits from the critical paths of the conversion architecture. In the second step, we perform pipelining in the conversion architecture in such a way that the pipeline stages are always utilized. Due to bubble free nature of the pipelining, clock cycle requirement of the conversion architecture remains same, while operating frequency increases drastically. We present detailed experimental results to support our claims made in this paper.

Category / Keywords: public-key cryptography / Koblitz Curves, Scalar Conversion, Lazy Reduction, Point Multiplication, Hardware Architecture

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

Contact author: Sujoy Sinharoy at esat kuleuven be

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Version: 20130830:092620 (All versions of this report)

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