How to design hardware prime field multipliers for bilinear pairing

Fujimoto, Daisuke; Nagahama, Yusuke; Matsumoto, Tsutomu

doi:10.1109/isocc.2016.7799858

Cited by 1 publication

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“…Its efficiency should then be improved for practical performance requirements. Since the computational costs of pairings and group operations defined over elliptic curves are expensive, investigation of fast algorithms and implementations is an important research topic, and there have been many studies on the mathematical foundation for algorithms [8–26], and efficient implementations [27–34]. A comprehensive survey was presented by [7].…”

Section: Introductionmentioning

confidence: 99%

Security analysis of elliptic curves with embedding degree 1 proposed in PLOS ONE 2016

Teruya

2019

PLoS ONE

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Wang et al. proposed a method for obtaining elliptic curves with embedding degree 1 for securing critical infrastructures, and presented several elliptic curves generated by their method with torsion points of 160 bits and 189 bits orders. They also presented some experimental results and claimed that their implementation of an elliptic curve generated with their method is faster than an implementation for embedded devices presented by Bertoni et al. In this paper, we point out that the security and efficiency claims given by Wang et al. are flawed. Specifically, we show that it is possible to solve finite field discrete logarithm problems defined over their elliptic curves in practice. On the elliptic curves with torsion points of 160 bits orders generated by Wang et al., their instances of finite field discrete logarithm problems are solved in around 4 hours by using a standard desktop PC. On the torsion points of 189 bits orders, their instances are solved in around 10 days by using two standard desktop PCs. The hardness of the finite field discrete logarithm problems is one of the most important bases of security; therefore, their elliptic curves should not be used for cryptographic purposes.

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Section: Introductionmentioning

confidence: 99%

Security analysis of elliptic curves with embedding degree 1 proposed in PLOS ONE 2016

Teruya

2019

PLoS ONE

View full text Add to dashboard Cite

show abstract

How to design hardware prime field multipliers for bilinear pairing

Cited by 1 publication

References 3 publications

Security analysis of elliptic curves with embedding degree 1 proposed in PLOS ONE 2016

Security analysis of elliptic curves with embedding degree 1 proposed in PLOS ONE 2016

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