feat: add div-mod constraints #646
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## main #646 +/- ##
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+ Coverage 96.08% 96.14% +0.05%
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Lines 58897 59607 +710
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Can you make a PR with a LaTeX document with the constraints here:
https://github.com/spaceandtimelabs/sxt-proof-of-sql/tree/main/docs/protocols
We can then reference that in this PR.
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| // (r - b) * (r + b) * t' - b = 0 | ||
| let t = builder.try_consume_final_round_mle_evaluation()?; |
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Can you put all of these together? That way the order is clear, and separated from the constraints.
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Should I do this on the prove side as well? Put the constraints after the commitments?
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| // (r - b) * (r + b) * t' - b = 0 |
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There should be some comments indicating
// r - remainder
// t' - t
// u - b_div_q
// etc.Perhaps t should be t_prime.
| let sqrt_min_plus_s = verifier_evaluate_sign(builder, min_sqrt_eval + s, one_eval, None)?; | ||
| let sqrt_min_less_s = verifier_evaluate_sign(builder, min_sqrt_eval - s, one_eval, None)?; | ||
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| // MIN < q < -MIN |
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This isn't quite the constraint that is being enforced here.
It is actually
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Aren't we making the assumption that MIN = -2^B for some B for all our supported data types?
| // sign(sqrt(-min) + s) = 1 | ||
| // sign(sqrt(-min) - s) = 1 |
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Could we get away with
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We already need to show that
Additionally, we know that
So, as long as
This is true for all integer types (except u128, which I want to deprecate).
It is not true for all decimal types. (But is true for some of them.)
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What's the smallest order field we would ever use for our scalar type? Is i128 the biggest type we will use long term? Are decimals with high precision something that might be relevant here?
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| // (q′ − q) * (q + MIN) = 0 |
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NIT: ′ is not '. − is not -.
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| // (q' - MIN) * (q + MIN) * v - (q' - MIN) = 0 |
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This does the same thing. The definition of v changes, but it's just a hint anyway.
| // (q' - MIN) * (q + MIN) * v - (q' - MIN) = 0 | |
| // (q + MIN) * v - (q' - MIN) = 0 |
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Slightly prefer
(q + MIN) * v + (q' - MIN) = 0
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| // (r - b) * (r + b) * t' - b = 0 |
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Slightly prefer
(r - b) * (r + b) * t' + b = 0
| let sqrt_min_less_s = verifier_evaluate_sign(builder, min_sqrt_eval - s, one_eval, None)?; | ||
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| // MIN < q < -MIN | ||
| // We need at least an extra bit to allow for -MIN |
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We could avoid this extra bit if we do
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Please be sure to look over the pull request guidelines here: https://github.com/spaceandtimelabs/sxt-proof-of-sql/blob/main/CONTRIBUTING.md#submit-pr.
Please go through the following checklist
!is used if and only if at least one breaking change has been introduced.source scripts/run_ci_checks.sh.source scripts/check_commits.sh, and the commit history is certified to follow clean commit guidelines as described here: https://github.com/spaceandtimelabs/sxt-proof-of-sql/blob/main/COMMIT_GUIDELINES.mdmainhave been incorporated to this PR by simple rebase if possible, if not, then conflicts are resolved appropriately.Rationale for this change
The constraints for div and mod expr need to be added. This will allow it to be a fully secure gadget.
What changes are included in this PR?
All the constraints for div-and-mod-expr.
Are these changes tested?
Yes. There is a tamperproof test for each constraint, demonstrating that each constraint is necessary.