Generation of Deterministic Identifiers and Random Numbers Using a Configurable Ring Oscillator Circuit

Objectives. The purpose of the study is to examine the operational characteristics of a digital circuit designed to analyze the output signal frequency of a configurable ring oscillator within a fixed measurement window. Methods. Methods of digital device synthesis and analysis were employed, including implementation on  programmable logic integrated circuits (FPGAs), fundamentals of digital circuit design, and methods for analyzing normally distributed random variables.

Results. A digital circuit for recording the period of a configurable ring oscillator, depending on the measurement time window and the value of its configuration has been developed. Experimental studies of the generated signal periods were conducted using Xilinx ZYNQ 7000 series FPGAs. It was demonstrated that upon repeated period measurements the bits of the recording counter can be categorized into three groups: group G₂: stable bits retaining constant values across all measurements; group G₁: weakly stable bits exhibiting minor distortions; group G₀: strongly unstable bits with a distortion probability approaching 1 between measurements. It was hypothesized that group G₀ represents the digitized noise component of the measured period value. Due to numerous independent factors (components within the configurable ring oscillator and digital recorder, supply voltage deviations, die and ambient temperature variations, quantization errors, etc.), it is assumed that this noise component follows a normal distribution. Analytical proof established that a normally distributed variable, quantized using multi-bit binary numbers under specific values of mathematical expectation μ and standard deviation σ , generates only two groups: G₂ and G₀. It was proven that the probability of a '1' appearing in any bit of group G₀ approaches 0,5, and the group size can be estimated as 3+ ⌊log₂ σ⌋ The bits of group G₁ can be converted to group G₂ using various methods, such as maximum likelihood estimation or by normalizing each measurement value to a theoretically justified separation into G₂ and G₀. The values of group G₂ bits can be interpreted as a response to a challenge defined by the ring oscillator circuit configuration and measurement window, forming a novel type of multi-bit Physical Unclonable Function (PUF) characterized by high stability. Conversely, the G₀ bits can serve as  single-bit sources of random variables with near-uniform distribution, providing a foundation for building random number generators.

Conclusion. The obtained results can be utilized in embedded systems for providing unclonable identification of digital devices and for random data generation. The application of a synchronous binary counter as a frequency recording circuit for a configurable ring oscillator opens new avenues for designing multibit physical unclonable function architectures with enhanced performance metrics in terms of stability, uniqueness, and randomness.

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