# Total Ionizing Dose Effects on a Delay-Based Physical Unclonable Function Implemented in FPGAs
## 2 Background  
### Ring Oscillator Based PUF  
A Ring Oscillator (RO) is a delay loop that oscillates at a particular frequency. Thanks to its straightforward implementation in FPGAs, ROs have been widely used in the implementation of secure primitives such as true random number generator (TRNG). RO-PUFs are delay-based PUFs that use Challenge-Response scheme as a chip authentication mechanism. A traditional RO-PUF [2] makes use of many identically laid out ROs to quantify the manufacturing variability. RO oscillation frequencies depend on (i) fixed conditions established at the design phase (i.e., number of stages, place&route, etc.); (ii) random process variations (that once manufactured are fixed for each single device); (iii) dynamic conditions derived from the operation environment (i.e., supply voltage, temperature, surrounding logic, etc.). Figure 1 depicts the traditional RO-PUF scheme [2] that consists of many identical ROs, counters and comparators.  
During the authentication process, a pair of ROs (selected by a user challenge) are quantized by measuring and comparing the RO frequencies \((f_{a},f_{b})\) and generating a response bit \(r\):  
Figure 1: Ring Oscillator Physical Unclonable Function (RO-PUF) general scheme.  
\[r=\left\{\begin{array}{ll}1&\text{if }f_{a}>f_{b}\\ 0&\textit{otherwise}\end{array}\right. \tag{1}\]  
An n-bit signature of the chip is computed from n different comparisons between RO frequencies. The quality of the PUF is evaluated by analysing the signatures. In most of the literature, major security metrics like uniformity, reliability and uniqueness are used to assess the PUF quality [5].  
* **Uniformity** is a metric related to the entropy of the system. This metric estimates the ratio of '1' vs. '0' in all the response bits generated by a PUF. The uniformity is computed as follows for an n-bit PUF response: \[Uniformity=\frac{1}{n}\sum_{l=1}^{n}r_{i,l}\times 100\%\] (2) where \(r_{i,l}\) is the l-th bit of an n-bit PUF response. An uniform distribution of 0's and 1's (50%) is expected in PUFs that have full entropy.
* **Reliability** is a metric that quantifies how stable the PUF response is over varying operating conditions (voltage, temperature, aging, etc.). To that end, a specific challenge is applied to the RO-PUF in order to obtain an n-bit reference response \((r_{i})\) for normal conditions (room temperature, ideal power supply voltage). The same n-bit response is collected at different operating conditions \((r_{i}^{\prime})\). Finally, the reliability is obtained using the Hamming distance (HD) analysis of responses. \[Reliability=\frac{1}{x}\sum_{y=1}^{x}\frac{HD(r_{i}r_{i,y}{}^{\prime})}{n}\times 1 00\%\] (3) where \(x\) is the number of samples for each condition and \(r_{i,y}{}^{\prime}\) is the y-th sample of \((r_{i}^{\prime})\). A lower value of intra-die HD leads to a higher reliability.
* **Uniqueness** is a measure of how different the PUF responses of different chips among a set of chips are. The uniqueness of a population of k-chips is obtained by computing the inter-HD of the n-bit responses for the same challenge: \[Uniqueness=\frac{2}{k(k-1)}\sum_{l=1}^{k-1}\sum_{j=i+1}^{k}\frac{HD(r_{i},r_{j}) }{n}\times 100\%\] (4) where \(r_{i}\) and \(r_{j}\) are the PUF responses of chips \(i\) and \(j\) (\(i\
eq j\)). An ideal uniqueness of 50% is desired for the complete set of chips.