# Elliptic Curves

## EccChip

halo2_gadgets provides a chip that implements EccInstructions using 10 advice columns. The chip is currently restricted to the Pallas curve, but will be extended to support the Vesta curve in the near future.

### Chip assumptions

A non-exhaustive list of assumptions made by EccChip:

• is not an -coordinate of a valid point on the curve.
• Holds for Pallas because is not square in .
• is not a -coordinate of a valid point on the curve.
• Holds for Pallas because is not a cube in .

### Layout

The following table shows how columns are used by the gates for various chip sub-areas:

• - witnessing points.
• - incomplete point addition.
• - complete point addition.
• - Fixed-base scalar multiplication.
• - variable-base scalar multiplication, incomplete rounds.
• - variable-base scalar multiplication, complete rounds.
• - variable-base scalar multiplication, overflow check.