Noise helps to increase the difficulty, but with a large enough sample size you can statistically exclude it, greatly simplified but essentially by doing X-avg(

Noise helps to increase the difficulty, but with a large enough sample size you can statistically exclude it, greatly simplified but essentially by doing X-avg(all X). Imagine you do the above bit for bit. So first you sample 1M times to find the baseline, then flip one bit and sample another 1M times to see if any deviations, and so on. There is also the chance of your PRNG being predictable, so attacker can predict what noise will be generated if they have seen enough of it.