ECCFROG522PP: An Enhanced 522 bit Weierstrass Elliptic Curve

Abstract

This paper presents ECCFROG522PP, a 522-bit prime-field elliptic curve in short Weierstrass form, designed with a focus on deterministic generation and public reproducibility. The central design principle is that all critical parameters are derived from a fixed public seed through a transparent and verifiable procedure. While many deployed systems rely on NIST P-256 and secp256k1, which target approximately 128-bit classical security, higher security applications typically consider curves such as NIST P-521, Curve448, and Brainpool P512. ECCFROG522PP is intended for the same general classical security range as P-521, with emphasis on transparency, auditability, and reproducibility rather than performance optimization. The curve parameters are generated through a BLAKE3-based deterministic pipeline with publicly specified indices. The resulting construction has prime order, cofactor one, and a deterministically derived base point of full order. The quadratic twist has a large proven prime factor, and the construction includes a documented lower bound on the embedding degree together with standard sanity checks against low embedding degree reductions and basic CM discriminant anomalies. The full generation and validation procedure can be reproduced end to end from public artifacts and reference scripts, enabling independent verification of all parameters and checks.