Cause Analysis Method of Entropy Loss in Physically Unclonable Functions

The use of physically unclonable functions (PUFs) as a new cryptographic technique is gaining attention. Challenge-response authentication and key generation (key storage) are well known as major applications using PUFs. When PUFs are applied to these applications, min-entropy estimation is essential. The min-entropy is a measure of the lower bound of the unpredictability of PUF responses. Many studies have estimated the min-entropy of PUFs, and several of these studies dealt with PUFs with independent and identically distributed (IID) PUF responses. Few studies have focused on non-IID PUFs. One reason is that some causes of entropy loss are complicatedly intertwined, and the entropy estimation of non-IID PUFs is hard. Thus, it is first necessary to break down the intertwined causes to estimate min-entropy. In this paper, we present typical causes of entropy loss during PUF implementation and propose a cause analysis method using the Inter-Hamming distance (HD), which is one of major performance metrics of PUFs. And the proposed method was applied to prototyped PUFs designed with a 180-nm CMOS process. We demonstrate that the causes of entropy loss on each PUF can be broken down according to the analysis results.