Relationship between source and output entropy True Random Number Generator (TRNG) use external physical phenomena to generate true randomness. I have a TRNG which uses two sources (oscillators) and gives an output of 256 bits. The entropy of TRNG output is 256 bits. The entropy of bit string with N distinct possible combinations is given by log2(N) bits (reference is given below). TRNG claims to have entropy of 1 bit for each input source i.e. totally unpredictable. Is there any relationship between TRNG’s source entropy and output entropy ? 

http://csrc.nist.gov/publications/drafts/800-90/draft-sp800-90b.pdf

Any help/reply is appreciated please.

Thanks &amp; Regards,
Qualified no.  There is no relationship between source entropy and the output entropy from a TRNG other than you can't output more entropy than you put in.  The actual source entropy rate can vary vastly.  Clearly the TRNG output entropy has to be 100%, 1 bit /bit or however you measure it.  Otherwise it wouldn't be a TRNG with a statistically flat output.

I like to talk in percentages, with 100% being absolute true randomness.  A physical source can produce entropy at any rate from 0 - 100%.  I can't imagine a physical source that can naturally produce 100% though. I have built two generators that produce entropy at the rates of 85% and 1.9%.  An experimental third outputs at a very very approximate 0.1%.

It's all to do with what happens to the source entropy once you've digitised it.  I think of entropy extraction as a distillation process akin to whiskey production.  The distillation process is a euphemism for lossy compression of the source entropy.  This might be a (non) cryptographic hash, matrix multiplication or just some simple bit folding.  Most TRNG devices use custom extraction techniques anyway.

If you start with 85% mash, you only need to refine /compress the mash /entropy by 17% to get 100% pure stuff.  Similarly the compression /refinement needs to be 52 fold for the 1.9% mash.  So 52 fold compression would result in a 100% rate of entropy.  But then consider that you might continue compression /refinement, so in the end you've compressed the 1.9% source entropy 100 fold.  Or 200 fold.  You still get 100% output entropy and the numbers are exactly just as random.  This is why there is no particular relationship between the source entropy and the output of a TRNG.