Bibliographic Details
| Title: |
Constructing Elliptic Curves for the GLV Method with Low-cost Decomposition. |
| Authors: |
Wroński, Michał1 michal.wronski@wat.edu.pl, Dryło, Robert2 rdrylo@sgh.waw.pl, Kijko, Tomasz1 tomasz.kijko@wat.edu.pl, Bora, Piotr1 piotr.bora@wat.edu.pl |
| Source: |
Fundamenta Informaticae. 2017, Vol. 153 Issue 4, p399-413. 15p. |
| Subjects: |
Elliptic curves, Complex multiplication, Computable functions, Endomorphisms, Mathematical decomposition, Integers |
| Abstract: |
The GLV method allows to improve scalar multiplication on an elliptic curve E/Fq with an efficiently computable endomorphism Φ : E → E over Fq. For points in a subgroup of large prime order r this requires decomposition of scalar k = k0 + k1λ mod r, where Φ acts on the subgroup of order r as multiplication by λ ∊ Fr and k0, k1 are integers O(√r) . In this note we consider the case when λ is of the form λ = 2s + a, where a is a small integer and λ=O(√r), which allows very easy and fast decomposition of k especially in hardware implementations. We give a method to construct such elliptic curves based on the complex multiplication method, and give examples of elliptic curves for λ ∊ {2s, 2s - 1} and various security levels. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
