# On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation
## 1 Introduction  
Pico-satellite constellations in Low Earth Orbit (LEO) have become a popular platform that allows earth observation, weather forecasting, space research and communications, among other applications. One of the main advantages of this emerging alternative to a conventional satellite is the cost. Pico-satellites are typically made of Commercial-Off-The-Shelf (COTS) components [1] as Field Programmable Gate Arrays (FPGAs) so the result is an inexpensive satellite network that could be deployed with a minimal budget.  
In this framework, the generation of secure encryption keys for use in satellite communications has emerged as a major challenge. The key generation typically relies on True Random Number Generators (TRNG) integrated into pico-satellites [2]. Due to their low-cost nature, TRNGs are embedded in some of the COTS avoiding expensive ad-hoc solutions. Several TRNGs approximations presented in the literature fit this low-cost requirement. Special attention deserves those TRNGs that can be straightforwardly implemented on FPGAs such as [3, 4].  
Due to their paramount importance in the communication security, these TRNGs are subjected to exhaustive quality randomness analysis on the ground in order to check their suitability for the mission. To that end, several well-known test suites such as NIST [5] or ENT [6] are used to guarantee the entropy of TRNGs in different scenarios including different temperatures, over-clocking, underpowering, etc. [7, 8]. In this context, where the TRNGs will be exposed to ionizing radiation from space, it is also necessary to check its functionality under this condition.  
The effects of Total Ionizing Dose (TID) in FPGAs have been widely studied in the scientific literature [9; 10]. TID effects are typically studied in circuits where for a given particular input, the output is always the same (deterministic logic). Therefore, the effects in this kind of circuits can be quantified using metrics as the Hamming distance between the expected output and the obtained output. A preliminary analysis of the radiation influence on a metastable-based TRNG was reported in [11]. However, TID effects were not studied. In this context, the main contribution of the present research is to study for the first time (to the best of our knowledge) the effects of ionizing radiation on non-deterministic logic as is the case of a TRNG. More specifically, we study the TID effects produced by radiation on two well-known TRNGs [12; 13] based on jitter sampling principle. To that end, a FPGA that contains the implementation of the two mentioned TRNGs has been exposed to a Co-60 radiation source. Finally, the statistical properties of the output have been evaluated for different accumulated TID in order to see how radiation affects the randomness quality of the output. The obtained results prove that an unacceptable degradation of the TRNGs happens earlier than the failures in deterministic blocks appear. Thus, the radiation-safe operating range of the entire system will be determined by the TRNGs.  
The rest of the paper is organized as follows: Section 2 provides some background on TRNGs, statistical tests and typical effects of TID on Flash-FPGAs. Section 3 describes the experimental set-up. Section 4 presents the experimental results for the accumulated doses. Finally, some conclusions are drawn in Section 5.