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Evaluation of TRNG Bit Distribution via Stable Entropy Source Synchronization on FPGA
Ryoichi Sato1, Mitsuki Fujiwara1, Yasuyuki Nogami1
1Graduate School of Environmental, Life, Natural Science and Technology, Okayama University, Okayama 700-8530, Japan.
Entropy (Basel, Switzerland)
|January 28, 2026
Summary
Adding two or more delay flip-flops (D-FFs) after ring oscillators (ROs) significantly enhances the bit distribution of random number sequences generated by RO-based random number generators (RNGs). This improvement is crucial for reliable random number generation.
Area of Science:
- Hardware Security
- Random Number Generation
- Digital Circuit Design
Background:
- Unstable input signals to XOR gates in ring oscillator (RO)-based random number generators (RNGs) can lead to biased bit distributions.
- Previous research highlighted the impact of signal instability on the randomness of generated sequences.
Purpose of the Study:
- To investigate the correlation between the number of delay flip-flops (D-FFs) and the bit distribution of random number sequences from RO-based RNGs.
- To analyze the effect of combining biased and metastable signals via XOR gates on overall bit distribution.
- To evaluate the efficacy of multi-D-FFs as synchronization circuits for RO signals in RNGs.
Main Methods:
- Simulated the impact of combining signals with varying distributions (including metastable states) through XOR gates.
- Proposed and analyzed the use of multiple D-FFs as synchronization circuits for RO signals.
- Estimated metastable output conditions and performed NIST SP 800-22 tests on RO-based RNG implementations.
Main Results:
- Combining signals with biased distributions through XOR gates affects the overall bit distribution.
- The inclusion of three-state signals, incorporating metastable states, was simulated.
- Inserting two or more D-FFs after RO signals demonstrably improves the bit distribution of RO-based RNGs.
Conclusions:
- Multi-D-FFs serve as effective synchronization circuits for RO signals in RNG applications.
- The number of D-FFs post-RO is a critical factor in achieving uniform bit distribution.
- Implementing at least two D-FFs after ring oscillators is recommended for enhanced random number generator performance.
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