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首页> 外文会议>International Conference on Cloud Computing and Security >An Efficient Speeding up Algorithm of Frobenius Based Scalar Multiplication on Koblitz Curves for Cloud Computing
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An Efficient Speeding up Algorithm of Frobenius Based Scalar Multiplication on Koblitz Curves for Cloud Computing

机译：云计算Koblitz曲线上基于Frobenius的标量乘法的高效加速算法

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摘要

With the rapid development of wireless sensor network, cloud computing and Internet of Things, the problems of security and privacy are becoming more and more serious. Elliptic curve cryptography as a public key cryptography plays an important role to solve the security issues, in which scalar multiplication is the most important and time-consuming operation. Koblitz curve is a special class of elliptic curve over binary field, Frobenius endomorphism can be used to accelerate the scalar multiplication. By converting single scalar multiplication into simultaneous multiple scalar multiplication, GLV method can use Straus-Shamir trick to calculate the scalar multiplication. In this paper, we combine the idea of Frobenius endomorphism and GLV method to speed up the scalar multiplication on Koblitz curve. Our algorithm can efficiently convert scalar multiplication into multi-scalar multiplication to reduce the cost of point additions and Frobenius operations. Theoretical analysis results show that: Compared with T-and-add algorithm, our 2-dimensional implementation provides a speedup over 19%, 3-dimensional implementation speeds up over 29%. Finally, a parallel scalar multiplication algorithm for Koblitz curve is designed, which can flexibly select the dimension of the parallel algorithm based on the number r of processing unit. Compared with the standard T-and-add algorithm, this algorithm can achieve a speedup of almost r times.
机译：随着无线传感器网络，云计算和物联网的飞速发展，安全和隐私问题变得越来越严重。椭圆曲线密码学作为公钥密码学在解决安全性问题中起着重要作用，其中标量乘法是最重要且最耗时的操作。 Koblitz曲线是二进制场上的一类特殊的椭圆曲线，Frobenius同态可用于加速标量乘法。通过将单标量乘法转换为同时的多标量乘法，GLV方法可以使用Straus-Shamir技巧来计算标量乘法。在本文中，我们结合了Frobenius同态和GLV方法，以加快Koblitz曲线上的标量乘法。我们的算法可以有效地将标量乘法转换为多标量乘法，以减少点加法和Frobenius运算的成本。理论分析结果表明：与T-and-add算法相比，我们的2维实现速度提高了19％以上，3维实现速度提高了29％以上。最后，设计了Koblitz曲线的并行标量乘法算法，可以根据处理单元数r灵活选择并行算法的维数。与标准的T-and-add算法相比，该算法可实现近r倍的加速。

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