# Re: entropy depletion

I would love to have an information-theoretic argument for the security of my PRNG, but that's not what we have, and I don't think reducing the entropy_count by one bit per output bit gets us any closer to such an argument.

For starters, the entropy_count value before you output the bit is obviously not a measure of the real information-theoretic entropy in the PRNG's state. It is a guess implemented by a simple algorithm (the "entropy estimator"). So if we set the resulting entropy_count after outputting one bit to be equal to the previous entropy_count - 1, we really have no justification for thinking that the resulting entropy_count is any closer to the true information-theoretic entropy than if you had set it equal to the previous entropy_count - 2.

On the other hand, I've haven't heard an information-theoretic argument that the output bit contains a whole bit of entropy. There is a nice practical-cryptography argument that an observer gains a whole bit of information from seeing that output bit, but in pure information-theoretic terms an observer gains less than one bit of information from seeing that output. So perhaps when you output a bit from /dev/random you ought to decrement entropy_count by 0.9 instead?

In general, I've heard no persuasive information-theoretic argument to justify the practice of decrementing the entropy_count by 1 bit per bit. If that practice does indeed ever protect someone from a cryptanalytic attack on their PRNG, it will not be because the practice is Information Theoretically Correct, but because the entropy_count-bits-added-per-input-bit minus the entropy_count-bits-subtracted-per-output-bit were an engineering fudge factor that was turned up high enough to drown out the cryptanalytic weakness in the PRNG.

Of course using such a fudge factor has some other costs, including the cost of introducing new security risks. I estimate that the chance of a successful attack due to timing attacks, induced failure, taking advantage of accidental failure, social engineering, etc. outweighs the chance of a successful attack due to cryptanalysis of the PRNG, which is why I use /dev/urandom exclusively [*, **]. You may weigh those trade-offs differently, but you shouldn't think that by decrementing entropy_count you are achieving information-theoretic security.

`Regards,`

`Zooko`

[*] Of course I have to be aware of the regrettable possibility that /dev/urandom has *never* been properly seeded and protect against that in user space.
[**] ... and the possibility that the operating system is re-using stored random state which it already used just before an unclean shutdown.

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