Note on fuzzy monotonic interpolating splines of odd degree

Odd-degree elliptic-function lower-sideband polylithic crystal filters

IEE Proceedings G Circuits Devices and Systems ◽

10.1049/ip-g-2.1993.0014 ◽

1993 ◽

Vol 140 (2) ◽

pp. 91 ◽

Cited By ~ 1

Author(s):

S.K.S. Lu

Keyword(s):

Elliptic Function ◽

Odd Degree

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The C3 Piecewise Seventh-degree Hermite Interpolating Splines with Parameters

Journal of Computer-Aided Design & Computer Graphics ◽

10.3724/sp.j.1089.2017.16427 ◽

2017 ◽

Vol 29 (12) ◽

pp. 2204

Author(s):

Juncheng Li ◽

Chengzhi Liu ◽

Yeqing Yi

Keyword(s):

Interpolating Splines

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Quartic Hermite interpolating splines with parameters

Journal of Computer Applications ◽

10.3724/sp.j.1087.2012.01868 ◽

2013 ◽

Vol 32 (6) ◽

pp. 1868-1870 ◽

Cited By ~ 2

Author(s):

Jun-cheng LI ◽

Chun-ying LIU ◽

Lian YANG

Keyword(s):

Interpolating Splines

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Optimized CSIDH Implementation Using a 2-Torsion Point

Cryptography ◽

10.3390/cryptography4030020 ◽

2020 ◽

Vol 4 (3) ◽

pp. 20 ◽

Cited By ~ 1

Author(s):

Donghoe Heo ◽

Suhri Kim ◽

Kisoon Yoon ◽

Young-Ho Park ◽

Seokhie Hong

Keyword(s):

Elliptic Curve ◽

Group Action ◽

Large Degree ◽

Transitive Group ◽

Optimization Method ◽

Torsion Point ◽

Torsion Points ◽

Diffie Hellman ◽

Odd Degree ◽

Montgomery Curve

The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when recovering the coefficient of the image curve for large degree isogenies. Because the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) requires odd-degree isogenies up to at least 587, this inefficiency is the main bottleneck of using a Montgomery curve for CSIDH. In this paper, we present a new optimization method for faster CSIDH protocols entirely on Montgomery curves. To this end, we present a new parameter for CSIDH, in which the three rational two-torsion points exist. By using the proposed parameters, the CSIDH moves around the surface. The curve coefficient of the image curve can be recovered by a two-torsion point. We also proved that the CSIDH while using the proposed parameter guarantees a free and transitive group action. Additionally, we present the implementation result using our method. We demonstrated that our method is 6.4% faster than the original CSIDH. Our works show that quite higher performance of CSIDH is achieved while only using Montgomery curves.

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