Connecting Legendre

swMATH ID: 29706
Software Authors: Karati, Sabyasachi; Sarkar, Palash
Description: Connecting Legendre with Kummer and Edwards. 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.
Homepage: https://github.com/skarati/Connecting-Legendre-with-Kummer-and-Edwards
Source Code: https://github.com/skarati/Connecting-Legendre-with-Kummer-and-Edwards
Dependencies: MAGMA; SAGE
Keywords: elliptic curves; Legendre form; Kummer line; Edwards form
Related Software: KummerLineV02; Curve25519; GitHub; EFD
Cited in: 1 Publication

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1 Publication describing the Software, including 1 Publication in zbMATH Year
Connecting Legendre with Kummer and Edwards. Zbl 1409.14057
Karati, Sabyasachi; Sarkar, Palash

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