Eccfrog512ck2: An Enhanced 512-bit Weierstrass Elliptic Curve

Víctor Duarte Melo; William J Buchanan

Paper 2025/660

Eccfrog512ck2: An Enhanced 512-bit Weierstrass Elliptic Curve

Víctor Duarte Melo

William J Buchanan

, Edinburgh Napier University

Abstract

Whilst many key exchange and digital signature methods use the NIST P256 (secp256r1) and secp256k1 curves, there is often a demand for increased security. With these curves, we have a 128-bit security. These security levels can be increased to 256-bit security with NIST P-521 Curve 448 and Brainpool-P512. This paper outlines a new curve - Eccfrog512ck2 - and which provides 256-bit security and enhanced performance over NIST P-521. Along with this, it has side-channel resistance and is designed to avoid weaknesses such as related to the MOV attack. It shows that Eccfrog512ck2 can have a 61.5% speed-up on scalar multiplication and a 33.3% speed-up on point generation over the NIST P-521 curve.

Metadata

Available format(s): PDF
Category: Applications
Publication info: Preprint.
Keywords: Weierstrass Elliptic Curve Elliptic Curve Cryptography
Contact author(s): victormeloasm @ gmail com
b buchanan @ napier ac uk
History: 2025-04-13: revised; 2025-04-11: received; See all versions
Short URL: https://ia.cr/2025/660
License: CC BY

BibTeX

@misc{cryptoeprint:2025/660,
      author = {Víctor Duarte Melo and William J Buchanan},
      title = {Eccfrog512ck2: An Enhanced 512-bit Weierstrass Elliptic Curve},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/660},
      year = {2025},
      url = {https://eprint.iacr.org/2025/660}
}