My favorite executive summary of the crypto elliptic curves is this: CURVE SECURITY RECOMMENDED BY ---------- --------- -----------------------

My favorite executive summary of the crypto elliptic curves is this: CURVE SECURITY RECOMMENDED BY ---------- --------- -------------------------------- SECP256R1 128 IANA, NIST, FRANCE, GERMANY SECP384R1 192 IANA, NIST, FRANCE, GERMANY, NSA X25519 128 IANA X448 224 IANA SECP256K1 128 BITCOIN BP384R1 GERMANY SECP521R1 FRANCE GC512A RUSSIA SM2 CHINA > Most cryptography libraries offer optimized assembly implementations of NIST P-256, which makes it less likely that your signing operations will leak timing information or become a significant performance bottleneck. Having implemented the nist curves in assembly myself before, I must say it always amused me, how a language even more memory unsafe than C, can actually make crypto implementations stronger.