A computer-implemented method for authentication of a queried device having an electrical circuit exhibiting physically unclonable functions (PUFs). The method includes: at the queried device, generating a first random number based on an initial first counter value; matching the first random number against a first value of a record stored in a database of a querying device, the record including second (shuffled) and third values; at the queried device, generating a second random number based on a once incremented first counter value, deterministically generating a de-shuffled second value based on an initial second counter value, determining that the second random number matches the de-shuffled second value, and submitting sub-challenges corresponding to the second random number to the electrical circuit to generate a response; and, at the querying device, determining that the response matches the third value of the record to complete a first authentication of the queried device.