As part of our ongoing work in the Allegro project, we investigated the complexity of Challenge-Response Pairs (CRPs) using a multiscale entropy approach — an essential step in characterizing Physical Unclonable Functions (PUFs) for secure embedded systems.
🧠 What does “complexity” mean in this context?
It’s not just about randomness — we quantify how much each CRP image deviates from two extremes:
▪️ A perfectly homogeneous (minimal randomness) image
▪️ A white noise (maximal randomness) image
📊 We analyzed 8 distinct datasets, each with 100 CRPs, where the number of white pixels in each challenge image followed the ratio N/i (N = 128×128 pixels), with i = 16, 8, 4, 2, 2, 4/3, 8/7, 16/15.
🌀 Interestingly, the structure is symmetric:
For every set j = 1, 2, 3, 4, the challenges are complementary to those in set 8 − j — meaning the white and black pixels are inverted, adding a rich layer of controlled variability.
📌 This analysis gives us deeper insights into the entropy, robustness, and quality of CRPs — vital properties for hardware-based cryptographic primitives.
#AllegroProject #HardwareSecurity #PUF #EntropyAnalysis #CRP #EmbeddedSystems #EdgeSecurity #TrustworthyHardware
