Stimpson J. Cat
Graduate Poster
- Joined
- Sep 20, 2001
- Messages
- 1,949
jzs,
This has been explained to you repeatedly. If you acknowledge that there is a bias in the mean of the data coming from these RNGs, then it mathematically follows that the XORed data will also be biased, just in a different way.
They incorrectly believe that by applying the XOR mask they will be subtracting out the bias in the mean, and you seem to believe them, but I have analytically shown that this is not the case! The XOR operation does not subtract out the bias in the mean. It produces a new signal whose mean is not biased, but which has correlations whose strengths depend on the initial bias. This is has been mathematically shown. How can you continue to ignore this fact?
I can only assume that for some reason you do not agree that XORing a signal with a bitmask will transform biases in the mean into correlations in the output. Is this the case? Or do you disagree with the claim that correlations in the XORed data can bias the variance of the resulting sums? If you agree that both of these things are true, then how can you believe that they are correctly subtracting out the bias of the mean?
Dr. Stupid
But as I have already analytically proven, applying an XOR mask does not "subtract out" the bias in the mean. It instead converts it into correlations in the data. Correlations which will then bias the variance.Because we are dealing with a real-life, complex electronic machine that is generating the data, that we know has a small amount of bias that can be measured and subtracted out.Why is the RNG output XORed
This has been explained to you repeatedly. If you acknowledge that there is a bias in the mean of the data coming from these RNGs, then it mathematically follows that the XORed data will also be biased, just in a different way.
This is simply false. They do not "subtract it out". This is the entire point of my critique!The probability is dependant on the bias. If the bias is large, yes, that is a real problem. Since they know the bias, can estimate it, they subtract it out for that very reason.If the calculation assumes that the RNGs follow statistical laws which, in reality, they do not follow, the calculated probability will be wrong.
They incorrectly believe that by applying the XOR mask they will be subtracting out the bias in the mean, and you seem to believe them, but I have analytically shown that this is not the case! The XOR operation does not subtract out the bias in the mean. It produces a new signal whose mean is not biased, but which has correlations whose strengths depend on the initial bias. This is has been mathematically shown. How can you continue to ignore this fact?
I can only assume that for some reason you do not agree that XORing a signal with a bitmask will transform biases in the mean into correlations in the output. Is this the case? Or do you disagree with the claim that correlations in the XORed data can bias the variance of the resulting sums? If you agree that both of these things are true, then how can you believe that they are correctly subtracting out the bias of the mean?
Dr. Stupid