## Possible gas savings in `_jAdd`

The method used by `_jAdd`

to calculate the sum of two points given in Jacobian coordinates is to use the formulas termed "add-2007-bl" in the Explicit-Formulas Database↗. In the EVM, the gas cost of `addmod`

and `mulmod`

is the same, and there is no cheaper way to square or multiply by a power of 2. This makes the formulas termed "add-1998-cmo-2↗" more efficient. In the verification of the `_jAdd`

formulas we carried out in section ref↗, the change would correspond to removing factors of two, so that at the end in, for example, case 3, one obtains $(r1,r2,r3)=(x_{3},y_{3},z_{3})$ directly rather than $(r1,r2,r3)=(4x_{3},8y_{3},2z_{3})$ --- both represent the same point on the elliptic curve.

Biconomy Labs was provided a proof of concept patch for this optimization, which saved 1.48% gas when running the Wycheproof test suite.