Identification of integrated circuits

A computing device effective to identify integrated circuits the computing device comprising:

• a memory effective to store an identification number for an integrated circuit;
• a processor configured in communication with the memory;
• the processor effective to:
• select one or more circuit elements of the integrated circuit;
• evaluate measurements of one or more attributes for the selected one or more circuit elements, wherein the measurements are associated with corresponding input vectors applied to the integrated circuit;
• formulate one or more equations based at least in part on the measurements of the one or more attributes;
• solve the one or more equations to determine scaling factors for the selected one or more circuit elements, wherein the scaling factors reflect a relationship between nominal values for the attributes and the measured values for the attributes;
• transform the determined scaling factors for the selected one or more circuit elements to generate transformed scaling factors;
• and
• generate the identification number of the integrated circuit based on the transformed scaling factors.

A combination of an integrated circuit and a computing device, the computing device effective to identify integrated circuits, the combination comprising:

• the integrated circuit, wherein the integrated circuit is associated with an identification number and includes one or more circuit elements;
• and
• the computing device, where the computing device includes:
• a processor effective to:
• select one or more circuit elements of the integrated circuit;
• the integrated circuit effective to:
• receive one or more input vectors at inputs of the one or more circuit elements;
• and
• generate outputs of the one or more circuit elements in response to the one or more input vectors;
• the processor further effective to:
• evaluate measurements of one or more attributes for the selected one or more circuit elements, wherein the measurements are associated with corresponding input vectors applied to the integrated circuit;
• formulate one or more equations based at least in part on the measurements;
• solve the one or more equations to determine scaling factors for the selected one or more circuit elements, wherein the scaling factors reflect a relationship between nominal values for the attributes and the measured values for the attributes;
• transform the determined scaling factors for the selected one or more circuit elements to generate transformed scaling factors;
• and
• generate the identification number of the integrated circuit based on the transformed scaling factors.

An apparatus arranged to determine an identification number of an integrated circuit (IC) including circuit elements, the apparatus comprising:

• a storage medium configured to store programming instructions;
• and
• a processor coupled to the storage medium and configured to execute the programming instructions to perform or cause to be performed:
• initiate an application of input vectors to one or more of the circuit elements included in the IC;
• evaluate measurement values responsive to the application of input vectors, wherein the measurement values correspond to values measured for one or more attributes of the one or more circuit elements in response to the application of input vectors;
• formulate a plurality of equations based on the corresponding measurement values, wherein each of the plurality of equations includes one or more scaling factors of the corresponding one or more circuit elements where the scaling factors reflect a relationship between nominal values for the attributes and the measurement values for the attributes;
• solve the plurality of equations to determine the one or more scaling factors of the corresponding one or more circuit elements;
• and
• transform the determined one or more scaling factors to generate the identification number of the IC.

A method for a computing device to generate an identification number of an integrated circuit (IC) including circuit elements, the method comprising:

• initiating an application of input vectors to one or more of the circuit elements included in the IC;
• evaluating measurement values responsive to the application of input vectors, wherein the measurement values correspond to values measured for one or more attributes of the one or more circuit elements in response to the application of input vectors;
• formulating a plurality of equations based on the corresponding measurement values, wherein each of the plurality of equations includes one or more scaling factors of the corresponding one or more circuit elements, where the scaling factors reflect a relationship between nominal values for the attributes and the measurement values for the attributes;
• solving the plurality of equations to determine the one or more scaling factors of the corresponding one or more circuit elements;
• and
• transforming the determined one or more scaling factors to generate the identification number of the IC.