Paper 2019/1361
Efficient Elliptic Curve Diffie-Hellman Computation at the 256-bit Security Level
Kaushik Nath and Palash Sarkar
Abstract
In this paper we introduce new Montgomery and Edwards form elliptic curve targeted at the 256-bit security level. To this end, we work with three primes, namely $p_1:=2^{506}-45$, $p_2=2^{510}-75$ and $p_3:=2^{521}-1$. While $p_3$ has been considered earlier in the literature, $p_1$ and $p_2$ are new. We define a pair of birationally equivalent Montgomery and Edwards form curves over all the three primes. Efficient 64-bit assembly implementations targeted at Skylake and later generation Intel processors have been made for the shared secret computation phase of the Diffie-Hellman key agreement protocol for the new Montgomery curves. Curve448 of the Transport Layer Security, Version 1.3 is a Montgomery curve which provides security at the 224-bit security level. Compared to the best publicly available 64-bit implementation of Curve448, the new Montgomery curve over $p_1$ leads to a $3\%$-$4\%$ slowdown and the new Montgomery curve over $p_2$ leads to a $4.5\%$-$5\%$ slowdown; on the other hand, 29 and 30.5 extra bits of security respectively are gained. For designers aiming for the 256-bit security level, the new curves over $p_1$ and $p_2$ provide an acceptable trade-off between security and efficiency.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Preprint. MINOR revision.
- Keywords
- Elliptic curve cryptographyElliptic curve Diffie-Hellman key agreementMontgomery formEdwards form256-bit security.
- Contact author(s)
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kaushikn_r @ isical ac in
palash @ isical ac in - History
- 2019-11-27: received
- Short URL
- https://ia.cr/2019/1361
- License
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CC BY
BibTeX
@misc{cryptoeprint:2019/1361, author = {Kaushik Nath and Palash Sarkar}, title = {Efficient Elliptic Curve Diffie-Hellman Computation at the 256-bit Security Level}, howpublished = {Cryptology ePrint Archive, Paper 2019/1361}, year = {2019}, note = {\url{https://eprint.iacr.org/2019/1361}}, url = {https://eprint.iacr.org/2019/1361} }