Methods for Estimating the Convergence of Inter-Chip Min-Entropy of SRAM PUFs

Abstract

For cryptographic applications based on physical unclonable functions (PUFs), it is very important to estimate the entropy of PUF responses accurately. The upper bound of the entropy estimated by compression algorithms, such as context-tree weighting, is too loose, while the lower bound estimated by the min-entropy calculation is too conservative, especially when the sample size is small. The actual min-entropy is between these bounds but is difficult to estimate accurately. In this paper, two models are proposed to estimate the convergence of the inter-chip min-entropy of static random-access memory (SRAM) PUFs. The basic idea is to find the relation between the expectation of the estimation result and the tested sample size, and then predict the convergence of the min-entropy. Furthermore, an improved Von Neumann extractor is used to increase the entropy per bit while retaining as many responses as possible for error correction. The experimental results demonstrate that the prediction error of the proposed estimation methods is less than 0.01/bit for the tested SRAM chips, and the improved Von Neumann extractor can reduce the number of required responses by approximately 11/16, the amount of helper data by 2/3, and the number of masks by 3/8 compared with the original method.