Summary

Add common methods to the CurveVar trait to retrieve the x and y affine coordinates of a group element.

Problem Definition

Circuit development often requires extracting the x-coordinate of a curve point. Currently, I'm using a sequence of to_bits_le() followed by le_bits_to_fp() to achieve this.

Currently, the CurveVar trait in arkworks lacks a standardized method for accessing the affine coordinates (x, y) of a curve point. Of course, it is possible to develop the same functionality using ToConstraintFieldGadget. However, when developing a circuit, the logic for extracting coordinates differs depending on whether the CurveVar is internally an AffineVar or a ProjectiveVar. This makes it difficult to write logic for a generic CurveVar.

Proposal

affine_x() should simply return a x-coordinate.
affine_y() should simply return a x-coordinate.
affine_xy() function is also required.

For Admin Use

• [] Not duplicate issue
• [] Appropriate labels applied
• [] Appropriate contributors tagged
• [] Contributor assigned/self-assigned