Re: RNG in a Smart Card

Mike Rosing (eresrch@msn.fullfeed.com)
Thu, 16 Jul 1998 13:51:18 -0500 (CDT)

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On Thu, 16 Jul 1998, Ng Pheng Siong wrote:

> The question is: how does a smart card harvest entropy to generate "good"
> random numbers? There aren't UI events, network packets, etc.

A noise diode and a few gates. Saturated analog amplifiers to the gates
seems to work fine. Maintaining stability isn't exactly easy, but it's
probably good enough.

> If the entropy comes from sampling electrical noise, or whatever, what does
> physics tell us about the constraints on parameters like sampling rate,
> quantifying entropy, etc., in the context of operating within a smart card?

<Big Grin> Boy am I glad you asked that. The constraints depend on the
noise source: if it has a low frequency cut off of f_a and a high
frequency cutoff f_b with a power spectral density G(f) then the average
number of zero crossings is
              f_b f_b
             / /
        2*(( | f^2 G(f) df) / (| G(f) df))^.5
             / /
             f_a f_a

Murry shows (IEEE Trans. on Computers, Dec. 1970 p1210) that for G(f)
constant (white noise) and for f_a << f_b that the maximum possible
sample rate is f_b/3^.5 ~= .577*f_b.

In the context of a smart card, how well can you shield from outside
RF sources? (You can stop radio stations, not malicious RF swamping).
Is the noise source temperature dependent? (most likely it is, but as
things get hot it goes faster and there's a lower limit on temperature
operations, so you can build the sample rate to be secure at the lowest
possible temperature).

I guess I should explain the big grin. I just got back from the library
getting more papers on this subject. There's some 200 pages of math like
the above to dig thru. I'd say this is pretty well known in general, and
I would hope the guys and gals building smart cards have done lots of
homework. Converting theory into practice isn't always easy, but I bet
they tried pretty hard.

Patience, persistence, truth,
Dr. mike

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