Physically Unclonable Function Circuits and Methods of Performing Key Enrollment in Physically Unclonable Function Circuits

A method of generating a secure key for an electronic device including a nonvolatile memory, the method comprising:

• generating a plurality of first key values, each of the plurality of first key values including a plurality of first bits;
• reading a plurality of first helper data values stored in the nonvolatile memory, each of the plurality of first helper data values corresponding to the each of the plurality of first key values;
• performing bit error correction operation on the each of the plurality of first key values using the plurality of first helper data values to generate a plurality of second key values;
• reading second helper data stored in the nonvolatile memory;
• performing block error correction operation on the plurality of second key values using the second helper data to correction an error in the plurality of second key values;
• and
• outputting the plurality of second key values in which the error is corrected as the secure key.

An electronic device comprising:

• a nonvolatile memory;
• a secure key source configured to generate a plurality of first key value, each of the plurality of first key value including a plurality of first bits;
• and
• an error correction unit configured to correct errors in each of the plurality of first key values,
• wherein the error correction unit comprises:
• a bit encoder configured to perform bit encoding on each of the plurality of first key values to generate a plurality of second bits and a plurality of mask values, each of the plurality of second bits corresponding to hamming weight in the each of the plurality of first key values, each of the plurality of mask values corresponding to the each of the plurality of first key values;
• and
• a block encoder configured to perform block encoding on the plurality of second bits using an error correction code to generate a third level key and second helper data, and to output the second helper data to the nonvolatile memory,
• wherein a logical operation between one of the plurality of first key values and corresponding one of the mask values generates a predetermined value.