Modelling 1/f Noise in TRNGs via Fractional Brownian Motion
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915310820392960 |
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| author | Skorski, Maciej |
| author_facet | Skorski, Maciej |
| contents | Security of oscillatory true random number generators remains not fully understood due to insufficient understanding of complex $1/f^α$ phase noise. To bridge this gap, we introduce fractional Brownian motion as a comprehensive theoretical framework, capturing power-law spectral densities from white to flicker frequency noise.
Our key contributions provide closed-form tractable solutions: (1) a quasi-renewal property showing conditional variance grows with power-law time dependence, enabling tractable leakage analysis; (2) closed-form min-entropy expressions under Gaussian phase posteriors; and (3) asymptotically unbiased Allan variance parameter estimation.
This framework bridges physical modelling with cryptographic requirements, providing both theoretical foundations and practical calibration for oscillator-based TRNGs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14205 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modelling 1/f Noise in TRNGs via Fractional Brownian Motion Skorski, Maciej Cryptography and Security Statistics Theory Security of oscillatory true random number generators remains not fully understood due to insufficient understanding of complex $1/f^α$ phase noise. To bridge this gap, we introduce fractional Brownian motion as a comprehensive theoretical framework, capturing power-law spectral densities from white to flicker frequency noise. Our key contributions provide closed-form tractable solutions: (1) a quasi-renewal property showing conditional variance grows with power-law time dependence, enabling tractable leakage analysis; (2) closed-form min-entropy expressions under Gaussian phase posteriors; and (3) asymptotically unbiased Allan variance parameter estimation. This framework bridges physical modelling with cryptographic requirements, providing both theoretical foundations and practical calibration for oscillator-based TRNGs. |
| title | Modelling 1/f Noise in TRNGs via Fractional Brownian Motion |
| topic | Cryptography and Security Statistics Theory |
| url | https://arxiv.org/abs/2410.14205 |