FpVar::{is_eq, is_neq}
only need two constraints
#133
Merged
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Description
Hi there, thanks for your amazing work!
This PR reduces 1 constraint in
FpVar::{is_eq, is_neq}
(and in turn,is_zero
, etc.), by observing that we can remove the booleanity check while preserving soundness.This is because:
(self - other) * multiplier = is_not_equal
guaranteesis_not_equal = 0
whenself - other = 0
. Otherwise, we cannot find amultiplier
such that(self - other) * multiplier = 0 * multiplier = is_not_equal != 0
(self - other) * not(is_not_equal) = 0
guaranteesis_not_equal = 1
whenself - other != 0
. Otherwise,not(is_not_equal) = 1 - is_not_equal != 0
, which indicates a contradictionself - other = 0
.See also gnark's implementation: https://github.com/Consensys/gnark/blob/870ef4efa8c9fa11a8778821c8376286207ca19b/frontend/cs/r1cs/api.go#L535-L569
Please correct me if I misunderstood something :)
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