Whilst many key exchange and digital signature systems still rely on NIST P-256 (secp256r1) and secp256k1, offering around 128-bit security, there is an increasing demand for transparent and reproducible curves at the 256-bit security level. Standard higher-security options include NIST P-521, Curve448, and Brainpool-P512. This paper presents ECCFROG522PP ("Presunto Powered"), a 522-bit prime-field elliptic curve that delivers security in the same classical approx 260-bit ballpark as NIST P-521, but with a fundamentally different design philosophy. All of the curve parameters are deterministically derived from a fixed public seed via BLAKE3, with zero hidden choices. The curve has prime order (cofactor = 1), a verified twist with a proven approx 505-bit prime factor, safe embedding degree (greater than or equal to 14), and passes anti-MOV checks up to k less than or equal to 200 and CM discriminant sanity up to 100k. Unlike prior opaque or ad-hoc constructions, ECCFROG522PP is fully reproducible: anyone can regenerate and verify it byte-for-byte using the published scripts. The intent is not to outperform NIST P-521 in raw speed, but to maximise trust, verifiability, and long-term auditability in a practical curve of equivalent security level

翻译：尽管许多密钥交换和数字签名系统仍依赖于提供约128比特安全性的NIST P-256（secp256r1）和secp256k1，但人们对256比特安全级别上的透明可复现曲线的需求日益增长。标准的高安全选项包括NIST P-521、Curve448和Brainpool-P512。本文提出ECCFROG522PP（"Presunto Powered"），一条522比特素域椭圆曲线，在经典安全性上提供与NIST P-521同等的约260比特安全强度，但采用根本不同的设计理念。所有曲线参数均通过BLAKE3从固定公开种子确定性导出，零隐藏选择。该曲线具有素阶（余因子=1）、经验证的扭曲线（具有可证明的约505比特素因子）、安全嵌入度（大于等于14），并通过了k≤200的抗MOV检验和不超过100k的CM判别式合理性检查。与先前不透明或临时性构造不同，ECCFROG522PP完全可复现：任何人都可通过公开脚本逐字节重新生成并验证。其目标并非在原始速度上超越NIST P-521，而是在等效安全级别的实用曲线中最大化可信度、可验证性与长期可审计性。