Connecting Legendre with Kummer and Edwards

Sabyasachi Karati; Palash Sarkar

Paper 2017/1205

Connecting Legendre with Kummer and Edwards

Sabyasachi Karati and Palash Sarkar

Abstract

Scalar multiplication on 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Elliptic curve Legendre form Edwards form Kummer line
Contact author(s): sabyasachi karati @ gmail com
History: 2017-12-18: received
Short URL: https://ia.cr/2017/1205
License: CC BY

BibTeX

@misc{cryptoeprint:2017/1205,
      author = {Sabyasachi Karati and Palash Sarkar},
      title = {Connecting Legendre with Kummer and Edwards},
      howpublished = {Cryptology ePrint Archive, Paper 2017/1205},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/1205}},
      url = {https://eprint.iacr.org/2017/1205}
}