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 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.</p

Accelerating Scalar Conversion for Koblitz Curve Cryptoprocessors on Hardware Platforms

© 2015 IEEE. Koblitz curves are a class of computationally efficient elliptic curves where scalar multiplications can be accelerated using NAF representations of scalars. However, conversion from an integer scalar to a short NAF is a costly operation. In this paper, we improve the recently proposed scalar conversion scheme based on division by 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.status: publishe

Accelerating Scalar Conversion for Koblitz 1 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 costly and thus restricts speed. In this paper we present acceleration techniques for the recently proposed scalar conversion hardware based on division by τ2. 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. I