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On the Security of Oscillator-Based Random Number Generators
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  • Published: 20 October 2010

On the Security of Oscillator-Based Random Number Generators

  • Mathieu Baudet1,
  • David Lubicz2,3,
  • Julien Micolod2 &
  • …
  • André Tassiaux1 

Journal of Cryptology volume 24, pages 398–425 (2011)Cite this article

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  • 58 Citations

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Abstract

Physical random number generators (a.k.a. TRNGs) appear to be critical components of many cryptographic systems. Yet, such building blocks are still too seldom provided with a formal assessment of security, in comparison to what is achieved for conventional cryptography. In this work, we present a comprehensive statistical study of TRNGs based on the sampling of an oscillator subject to phase noise (a.k.a. phase jitters). This classical layout, typically instantiated with a ring oscillator, provides a simple and attractive way to implement a TRNG on a chip. Our mathematical study allows one to evaluate and control the main security parameters of such a random source, including its entropy rate and the biases of certain bit patterns, provided that a small number of physical parameters of the oscillator are known. In order to evaluate these parameters in a secure way, we also provide an experimental method for filtering out the global perturbations affecting a chip and possibly visible to an attacker. Finally, from our mathematical model, we deduce specific statistical tests applicable to the bitstream of a TRNG. In particular, in the case of an insecure configuration, we show how to recover the parameters of the underlying oscillator.

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Author information

Authors and Affiliations

  1. ANSSI, 51 blv de la Tour Maubourg, 75007, Paris, France

    Mathieu Baudet & André Tassiaux

  2. CÉLAR, BP 7419, 35174, Bruz, France

    David Lubicz & Julien Micolod

  3. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes, France

    David Lubicz

Authors
  1. Mathieu Baudet
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  2. David Lubicz
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  3. Julien Micolod
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  4. André Tassiaux
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Corresponding author

Correspondence to David Lubicz.

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Cite this article

Baudet, M., Lubicz, D., Micolod, J. et al. On the Security of Oscillator-Based Random Number Generators. J Cryptol 24, 398–425 (2011). https://doi.org/10.1007/s00145-010-9089-3

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  • Received: 01 September 2009

  • Published: 20 October 2010

  • Issue Date: April 2011

  • DOI: https://doi.org/10.1007/s00145-010-9089-3

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Key words

  • Hardware random number generators
  • Ring oscillators
  • Jitter model
  • Entropy
  • Statistical tests
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