1. A computer-implemented method, comprising: under the control of a computer system configured with executable instructions, receiving passcode information comprising, for each passcode of a plurality of passcodes, a value derived based at least in part on the passcode and usable, with a hardware secret, to verify purported passcodes, the hardware secret maintained in a hardware device so as to be unobtainable to any processor executing code outside of the hardware device; receiving a purported passcode; causing the hardware device to provide a reference value calculated based at least in part on the purported passcode and the hardware secret; determining, based at least in part on whether the calculated reference value matches a corresponding value of the passcode information, whether the purported passcode is valid; enabling access to computing functionality as a result of determining that the purported passcode is valid; and as a result of a limit on a number of passcode verifications being exceeded, causing the computer system to become unable to use the hardware secret to verify purported passcodes such that the computer system is unable to unilaterally restore an ability to use the hardware secret to verify purported passcodes.