Methods and apparatuses for increasing the leak-resistance of cryptographic systems are disclosed. A cryptographic token maintains secret key data based on a top-level key. The token can produce updated secret key data using an update process that makes partial information that might have previously leaked to attackers about the secret key data no longer usefully describe the new updated secret key data. By repeatedly applying the update process, information leaking during cryptographic operations that is collected by attackers rapidly becomes obsolete. Thus, such a system can remain secure against attacks involving analysis of measurements of the device's power consumption, electromagnetic characteristics, or other information leaked during transactions. Transactions with a server can be secured with the token.