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Paper 2019/1259

“Nice” Curves

Kaushik Nath and Palash Sarkar

Abstract

Within the Transport Layer Security (TLS) Protocol Version 1.3, RFC 7748 specifies elliptic curves targeted at the 128-bit and the 224-bit security levels. For the 128-bit security level, the Montgomery curve Curve25519 and its birationally equivalent twisted Edwards curve Ed25519 are specified, while for the 224-bit security level, the Montgomery curve Curve448 and its birationally equivalent Edwards curve Edwards448 are specified. The contribution of this work is to propose new pairs of Montgomery-Edwards curves at both the 128-bit and the 224-bit security levels. The new curves are nice in the sense that they have very small curve coefficients and base points. Compared to the curves in RFC 7748, the new curves lose two bits of security. The main advantage of the new curves over those in RFC 7748 is that for 64-bit implementation, all the reduction steps on the outputs of additions and subtractions in the ladder algorithm can be omitted. For 64-bit implementations on the Skylake and the Kaby Lake processors, about 21% improvement in speed is achieved at the 128-bit security level and about 28% improvement in speed is obtained at the 224-bit security level.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Preprint. MINOR revision.
Keywords
Elliptic curve cryptographyMontgomery formEdwards formTransport Layer Security.
Contact author(s)
kaushikn_r @ isical ac in,palash @ isical ac in
History
2020-08-12: last of 2 revisions
2019-11-05: received
See all versions
Short URL
https://ia.cr/2019/1259
License
Creative Commons Attribution
CC BY
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