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On the security of oscillator-based random number generators. (English) Zbl 1251.94021
Summary: 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.

MSC:
94A60 Cryptography
60G35 Signal detection and filtering (aspects of stochastic processes)
62M07 Non-Markovian processes: hypothesis testing
65C10 Random number generation in numerical analysis
94A17 Measures of information, entropy
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