We present the first physical side-channel attack on elliptic curve cryptography running on a PC. The attack targets the ECDH public-key encryption algorithm, as implemented in the latest version of GnuPG’s Libgcrypt. By measuring the target’s electromagnetic emanations, the attack extracts the secret decryption key within seconds, from a target located in an adjacent room across a wall. The attack utilizes a single carefully chosen ciphertext, and tailored timefrequency signal analysis techniques, to achieve full key extraction.