Interpolation function of the ML sumcheck verifier corrected #75
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Pratyush
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Jun 29, 2023
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| /// p_i.len()-1 passing through the y-values in p_i at x = 0,..., p_i.len()-1 | ||
| /// and evaluate this polynomial at `eval_at`. In other words, efficiently compute | ||
| /// \sum_{i=0}^{len p_i - 1} p_i[i] * (\prod_{j!=i} (eval_at - j)/(i-j)) |
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| /// p_i.len()-1 passing through the y-values in p_i at x = 0,..., p_i.len()-1 | |
| /// and evaluate this polynomial at `eval_at`. In other words, efficiently compute | |
| /// \sum_{i=0}^{len p_i - 1} p_i[i] * (\prod_{j!=i} (eval_at - j)/(i-j)) | |
| /// `p_i.len()-1` passing through the y-values in p_i at x = `0`, ..., `p_i.len()-1` | |
| /// and evaluate this polynomial at `eval_at`. In other words, efficiently compute | |
| /// \sum_{i=0}^{len p_i - 1} p_i[i] * (\prod_{j!=i} (eval_at - j)/(i-j)) |
Pratyush
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Jun 29, 2023
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Description
The verifier (file: src/ml_sumcheck/protocol/verifier.rs) contains a function (interpolate_uni_poly) which interpolates the unique polynomial of degree at most d passing through the points (0, y_0), (1, y_2), ..., (d, y_d); and returns the value of the interpolated polynomial at x = eval_at given as an argument.
In the pre-existing implementation, this function would crash if 0 <= eval_at <= d. In practice, eval_at is a challenge point generated pseudo-randomly by the verifier and so the problematic case could indeed be triggered.
The modified code now includes the check 0 <= eval_at <= d, returning y_eval_at if that is the case. The new checks come at essentially no performance cost (verified with a large example). A case has been added at the end of the unit test in the verifier.rs file which failed to pass with the previous code and passes with the modified one.
Furthermore, a slight inaccuracy has been corrected in the former description of the function: the returned polynomial does not necessarily have degree d, but at most d (and is unique with this property).
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Pendingsection inCHANGELOG.mdFiles changedin the Github PR explorer