Article Type

Research Article

Publication Title

Advances in Mathematics of Communications

Abstract

Scalar multiplication on suitable Legendre form elliptic curves can be speeded up in two ways. One can perform the bulk of the computation either on the associated Kummer line or on an appropriate twisted Edwards form elliptic curve. This paper provides details of moving to and from between Legendre form elliptic curves and associated Kummer line and moving to and from between Legendre form elliptic curves and related twisted Edwards form elliptic curves. Further, concrete twisted Edwards form elliptic curves are identified which correspond to known Kummer lines at the 128-bit security level which provide very fast scalar multiplication on modern architectures supporting SIMD operations.

First Page

41

Last Page

66

DOI

10.3934/amc.2019003

Publication Date

2-1-2019

Comments

Open Access, Gold, Green

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