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.

翻译：虽然许多密钥交换和数字签名方法使用NIST P256（secp256r1）和secp256k1曲线，但通常存在对更高安全性的需求。这些曲线提供128比特的安全级。通过NIST P-521、Curve 448和Brainpool-P512，可将安全级提升至256比特。本文提出一种新曲线——Eccfrog512ck2——它提供256比特安全级，并较NIST P-521具有增强的性能。此外，该曲线具有侧信道抗性，并设计避免诸如与MOV攻击相关的弱点。研究表明，与NIST P-521曲线相比，Eccfrog512ck2在标量乘法上可实现61.5%的加速，在点生成上可实现33.3%的加速。