Add a noise model analysis pass for LWE/CGGI
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- MLIR
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Description
The tfhe-rs project tracks noise standard deviation along with the ciphertext. They seem to have a "nominal" noise level (equal to 1), bootstrapping resets the noise to the nominal level, and adding adds the noise, multiplying multiplies the noise, and scaling by a constant scales the noise. There is not a clear indication in tfhe-rs about how to determine what is the max allowable noise, but IceTDrinker pointed me to section 5 of https://eprint.iacr.org/2022/704.pdf which contains the detailed approach they use in tfhe-rs.
I'd like to port the noise analysis from https://jeremykun.com/2023/11/15/mlir-a-global-optimization-and-dataflow-analysis/ to HEIR, and try bootstrap injection while also retaining some of the low-degree addition operations, so that the circuit can be made smaller. The same analysis should be useful for noise tracking in arithmetic schemes.
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