# Multiple Observations for Secret-Key Binding with SRAM PUFs
## 1 Introduction
### Related Work  
A first implementation of a key binding scheme for generating and reconstructing a cryptographic key from SRAM PUFs was presented by [PERSON] et al. in [4]. There, the fuzzy commitment scheme [6] was used to construct the helper data and later to reproduce the key. It is known that within one SRAM-PUF, some cells are more reliable (smaller error probability) than other cells [3]. The reliability information of the SRAM cells can be used to improve the performance of the helper data schemes. For example, a Soft-Decision (SD) helper data scheme [7; 8] publicly shares the error probability of each SRAM cell to improve the decoder performance. Furthermore, a Selection-based helper data scheme [9; 10; 11] selects only the most reliable SRAM cells to reduce the average error probability of the SRAM-PUF observations. Both schemes assume that reliability of each SRAM cell is known during enrollment. However, in general this information is not available. Either, special measurement techniques must be applied, or a sufficient number of observations is required to estimate these values before enrollment. We propose a new scheme that accepts standard SRAM-PUF observation vectors as an input, i.e., the MO helper data scheme. In [12] multiple enrollment observations are used under various environmental conditions. The focus of [12] is on experimental validation of new strategies that consider multiple enrollment temperatures; however, a mathematical analysis of the strategies is missing. Our work focuses instead on finding an optimal multiple observations strategy. In the future, our analysis may be extended to consider temperature dependence as well, see Section 2.  
Applying multiple observations for key binding (and generation) has been studied from information-theoretic perspective in [13; 14; 15]. It is shown that the secret-key rate can be improved when multiple observations are used by the encoder or the decoder. Achievable rate regions are analyzed for various multiple enrollments and multiple entities scenarios, but no code constructions are proposed or investigated.  
Multiple enrollment scenarios are studied from leakage perspective in [16; 17]. In these papers, scenarios are considered (e.g., the reverse fuzzy extractor [18]) in which enrollment is repeated multiple times and correspondingly multiple helper data are generated. Please  
Figure 1: Key binding scheme for reliable secret-key reconstruction from noisy observations.  
note that the additional helper data are not generated to increase performance; instead, they are considered to be a security challenge that follows from the repeated enrollments. The decoder performs a classic reconstruction that is based on a single helper data sequence only, whereas an attacker may have stored all previously generated helper data. It is shown in [17] that zero leakage is ensured in these multiple enrollment scenarios, when the SRAM PUFs meet a certain symmetry condition. Inspired by the zero leakage results of [17], we have developed the MO helper data scheme which produces a single helper data sequence based on repeated enrollments. In contrast to the scenarios discussed in the previous paragraph, the decoder now benefits from the additional observations which are embedded in the helper data.