System access using a mobile device

Techniques are disclosed relating to electronic security, e.g., for authenticating a mobile electronic device to allow access to system functionality (e.g., physical access to the system, starting an engine/motor, etc.). In some embodiments, a system and mobile device exchange public keys of public key pairs during a pairing process. In some embodiments, an asymmetric transaction process includes generating a shared secret using a key derivation function over a key established using a secure key exchange (e.g., elliptic curve Diffie-Hellman), and verifying a signature of the system before transmitting any information identifying the mobile device. In various embodiments, disclosed techniques may increase transaction security and privacy of identifying information.