Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Elliptic curve, Legendre form, Edwards form, Kummer line

Date: received 15 Dec 2017

Contact author: sabyasachi karati at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20171218:210244 (All versions of this report)

Short URL: ia.cr/2017/1205


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