Eccfrog512ck2: An Enhanced 512-bit Weierstrass Elliptic Curve
For cryptographers and security practitioners, this provides a more efficient alternative to NIST P-521 for high-security applications.
The paper introduces Eccfrog512ck2, a new 512-bit elliptic curve offering 256-bit security with 61.5% faster scalar multiplication and 33.3% faster point generation compared to NIST P-521.
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.