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 Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Connecting Legendre with Kummer and Edwards. Zbl 1409.14057Karati, Sabyasachi; Sarkar, Palash 2019 Cited by 2 Authors 1 Karati, Sabyasachi 1 Sarkar, Palash Cited in 1 Serial 1 Advances in Mathematics of Communications Cited in 3 Fields 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year