how to find the “true” entropy of std::random_device?

Question

I want to check whether my implementation of std::random_device has non-zero entropy (i.e. is non-deterministic), using std::random_device::entropy()

Answer 1

Entropy is just one measure of RNG quality (and true, exact entropy is impossible to measure). For a practical and reasonably-accurate measurement of your std::random_device's random number quality, consider using a standard randomness test suite such as TestU01, diehard, or its successor dieharder. These run a battery of statistical tests designed to stress your RNG, ensuring it produces statistically random data.

Note that statistical randomness by itself does not certify that the RNG is suitable for cryptographic applications.

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Many modern computers have easily-accessible sources of hardware randomness, namely the analog-to-digital converters found in the audio input, camera, and various sensors. These exhibit low-level thermal or electrical noise which can be exploited to produce high-quality random data. However, no OS that I know of actually uses these sensors to supply their system random-number sources (such as /dev/[u]random), since the bitrate of such physical random number sources tends to be very low.

Instead, OS-provided random number sources tend to be seeded by hardware counters and events, such as page faults, device driver events, and other sources of unpredictability. In theory, these events might be fully predictable given the precise hardware state (since they aren't based on e.g. quantum or thermal noise), but in practice they are sufficiently unpredictable that they produce good random data.