Author: Russell O'Connor 2018-08-04 12:22:28
Published on: 2018-08-04T12:22:28+00:00
The proposed change is to the verification equation of a quadratic residue, which currently reads "Let *R = sG - eP*" and would be changed to "Let *R = sG + eP*". The proposed change would result in faster verification as it avoids negating a point or a coefficient. In the current method, reconstructing R from r requires verifying "*sG - eP = R*", which effectively verifies "*0 = sG - eP - R*" or "*0 = R - sG + eP*", requiring at least one point or coefficient to be negated due to opposite signs between sG and eP. However, under the revised verification scheme, verification would instead require "*0 = sG + eP + (-R)*", which does not require negating R. (-R) can be constructed directly from r by finding a y coordinate that is not a quadratic residue, which is the same amount of work required to construct R from r. This change would remove one negation operation from the cost of doing verification in either verification procedure.
Updated on: 2023-05-20T17:21:29.723222+00:00