ECDLP in Disguise — Elliptic Nodes, Real Curve Crypto, Double and Broken

cryptohack

Task: three CryptoHack ECC challenges that each kill ECDLP in an unusual setting — a singular (node) curve, a curve over the real numbers, and a side-channel double-and-add on secp256k1. Solution: map the node to F_p^* and run Pohlig-Hellman; linearize the real curve via the elliptic logarithm and recover the scalar with an LLL lattice; denoise SPA traces by averaging + 2-means and decode each sample as one key bit (LSB-first).