Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Combination Frequency Differencing for Identifying Design Weaknesses in Physical Unclonable Functions



charles prado, vinay patil, Raghu N. Kacker, D. Richard Kuhn, M S Raunak


Combinatorial coverage measures have been defined and applied to a wide range of problems. These methods have been developed using measures that depend on the inclusion or absence of t-tuples of values in inputs and test cases. We extend these coverage measures to include the frequency of occurrence of combinations, in an approach that we refer to as combination frequency differencing (CFD). This method is particularly suited to artificial intelligence and machine learning (AI/ML) applications, where training data sets used in learning systems are dependent on the prevalence of various attributes of elements of class and non-class sets. We illustrate the use of this method by applying it to analyzing the susceptibility of physical unclonable functions (PUFs) to machine learning attacks. Preliminary results suggest that the method may be useful for identifying bit combinations that have a disproportionately strong influence on PUF response bit values.
Conference Dates
April 4-13, 2022
Conference Location
Valencia, ES
Conference Title
IEEE International Workshop on Combinatorial Testing


combinatorial frequency, combinatorial testing, PUF


Prado, C. , patil, V. , Kacker, R. , Kuhn, D. and Raunak, M. (2022), Combination Frequency Differencing for Identifying Design Weaknesses in Physical Unclonable Functions, IEEE International Workshop on Combinatorial Testing, Valencia, ES, [online],, (Accessed May 29, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created April 4, 2022, Updated December 22, 2022