…compiles into add_eth_tests

Co-authored-by: Nacho Avecilla <nachoavecilla@gmail.com>

Co-authored-by: Nacho Avecilla <nachoavecilla@gmail.com>

Co-authored-by: Nacho Avecilla <nachoavecilla@gmail.com>

* Finish fp2 arithmetic

* Add more precomputed values

* Fix fp2 inv

* Add EOF

* Rename module

…into pairing

* Finish fp2 arithmetic

* Add more precomputed values

* Add arithmetic operations for fp6

* Update constant name

Co-authored-by: Ivan Litteri <67517699+ilitteri@users.noreply.github.com>

* Replace epsilon for XI

* Change script name

* Add multiplication by xi in fp2 and fp6

* Add alternative inverse method

* Fix inverse operation

---------

Co-authored-by: Iván Litteri <ilitteri@fi.uba.ar>
Co-authored-by: Ivan Litteri <67517699+ilitteri@users.noreply.github.com>

* WIP

* add fp12 arithmetics

* fix typo

* add addition tests

* add sub test

* rename gamma function

* add mul tests

* fix function call

* fix typo

* mul fixes

* fix mul by 1

* fix square

* fix fp12 inverse

* add multiply by 2 asserts

* add EOF

---------

Co-authored-by: Iván Litteri <ilitteri@fi.uba.ar>

…into pairing

* Rename file

* Add implementation for jacobian projective coordinates

* Fix fp12 merge error

* Fix addition

* Rename function to check inifinity and add extra comments

* Add fp2 arithmetics

* Add fp6 arithmetics

* Rename funcs

* Fix compilation errors in fp6 operations

* Add tests for inverse and sub for fp2

* Fix square and multiplication for fp6

* Add tests for add, mul, sub and square in fp6

* add fp12 arithmetic

* Fix inverse in fp6

* Add tests for inverse in fp6

* add fp12 tests

* add inverse test for fp12

* changes mul for sub

---------

Co-authored-by: Iván Litteri <ilitteri@fi.uba.ar>
Co-authored-by: Joaquin Carletti <joaquin.carletti@lambdaclass.com>

* Move point doubling and line evaluation to pairing file

* Change return type in point adding and line evaluation to match with doubling

* Remove incorrect parameter

* Change name to match with other pairing function

* Change fp6 return type to single tuple

* change return to single tuple

---------

Co-authored-by: Joaquin Carletti <joaquin.carletti@lambdaclass.com>

* add millers loop basics

* add PI functions to loop

* add neg of a G2 point

* add loop counter

* fix return of negate funciton

* fix loop_counter values

* rename utils file

* fix imports

* change constants to fp6 file

* fix miller loop set up

* add comment

* fix comment

* fix typo

* Add ten in montgomery form as constant

* Add frobenius operations

* Add negate operation for fp6

* Add conjugate operation for fp2

* Add operations in fp2 used in final exponentiation

* Add final exponentiation function

* Fix return types to match with new changes

* Add corrections to n_square function

* Use montgomery for gamma factors and add frobenius tests

* Add test for cyclotomic square

* Add another final exponentiation implementation and test

* Add function utils to check elements in curve and twisted curve

* Add conditional for g2 from affine

* Add tests for conjugate in fp12 and fp2

* Fix miller loop errors

* Add pair function

* Add pairing test from eth tests

* Correct NAF representation

* Change exponentiation impl to be able to test it correctly

* Correct point doubling and miller loop

* Add test for point doubling and line evaluation

* add addition tests

* Add tests for frobenius

* Add line evaluation test after point addition

* Add point doubling and adding functions for projective coordinates

* Fix in miller loop function

* Add test refactors with new functions

* Fix constant for fp12

* Add functions for g2 in projective and affine

* Fix NAF representation

* add eth tests

* add tests names

* add expt

* change final_exp

* fix fp6 square

* Delete test generator for pairing in python

* Delete unnecesary comments

* Delete unused exponentiation function

* Delete unused import and old todo

* Improve naming of doubling and addition steps in miller loop

---------

Co-authored-by: Joaquin Carletti <joaquin.carletti@lambdaclass.com>

* Implement Frobenius operator in Yul

* Fix Frobenius functions returns

* Fix Frobenius functions returns

* Add tests

* Update comment

* Add function utils to check elements in curve and twisted curve

* Add conditional for g2 from affine

* Add tests for conjugate in fp12 and fp2

* Fix miller loop errors

* Add pair function

* Add pairing test from eth tests

* Correct NAF representation

* Change exponentiation impl to be able to test it correctly

* Correct point doubling and miller loop

* Add test for point doubling and line evaluation

* add addition tests

* Add tests for frobenius

* Add line evaluation test after point addition

* Add point doubling and adding functions for projective coordinates

* Fix in miller loop function

* Add test refactors with new functions

* Fix constant for fp12

* Add functions for g2 in projective and affine

* Fix NAF representation

* add eth tests

* add tests names

* add expt

* change final_exp

* fix fp6 square

* Delete test generator for pairing in python

* Delete unnecesary comments

* Delete unused exponentiation function

* Delete unused import and old todo

* Improve naming of doubling and addition steps in miller loop

* add mix addition in yul

* fix function

* Update precompiles/Playground.yul

Co-authored-by: Ivan Litteri <67517699+ilitteri@users.noreply.github.com>

---------

Co-authored-by: IAvecilla <iavecilla@fi.uba.ar>
Co-authored-by: Iván Litteri <ilitteri@fi.uba.ar>
Co-authored-by: Ivan Litteri <67517699+ilitteri@users.noreply.github.com>

* Add function utils to check elements in curve and twisted curve

* Add conditional for g2 from affine

* Add tests for conjugate in fp12 and fp2

* Fix miller loop errors

* Add pair function

* Add pairing test from eth tests

* Correct NAF representation

* Change exponentiation impl to be able to test it correctly

* Correct point doubling and miller loop

* Add test for point doubling and line evaluation

* add addition tests

* Add tests for frobenius

* Add line evaluation test after point addition

* Add point doubling and adding functions for projective coordinates

* Fix in miller loop function

* Add test refactors with new functions

* Fix constant for fp12

* Add functions for g2 in projective and affine

* Fix NAF representation

* add eth tests

* add tests names

* add expt

* change final_exp

* fix fp6 square

* Delete test generator for pairing in python

* Delete unnecesary comments

* Delete unused exponentiation function

* Delete unused import and old todo

* Improve naming of doubling and addition steps in miller loop

* add cyclotomic square

* fix assignments

* add nSquare

---------

Co-authored-by: IAvecilla <iavecilla@fi.uba.ar>
Co-authored-by: Iván Litteri <ilitteri@fi.uba.ar>

* Add function utils to check elements in curve and twisted curve

* Add conditional for g2 from affine

* Add tests for conjugate in fp12 and fp2

* Fix miller loop errors

* Add pair function

* Add pairing test from eth tests

* Correct NAF representation

* Change exponentiation impl to be able to test it correctly

* Correct point doubling and miller loop

* Add test for point doubling and line evaluation

* add addition tests

* Add tests for frobenius

* Add line evaluation test after point addition

* Add point doubling and adding functions for projective coordinates

* Fix in miller loop function

* Add test refactors with new functions

* Fix constant for fp12

* Add functions for g2 in projective and affine

* Fix NAF representation

* add eth tests

* add tests names

* add expt

* change final_exp

* fix fp6 square

* Delete test generator for pairing in python

* Delete unnecesary comments

* Delete unused exponentiation function

* Delete unused import and old todo

* Improve naming of doubling and addition steps in miller loop

* Add implementation for exponentiation by t for fp12

---------

Co-authored-by: Joaquin Carletti <joaquin.carletti@lambdaclass.com>
Co-authored-by: Iván Litteri <ilitteri@fi.uba.ar>

* Add function utils to check elements in curve and twisted curve

* Add conditional for g2 from affine

* Add tests for conjugate in fp12 and fp2

* Fix miller loop errors

* Add pair function

* Add pairing test from eth tests

* Correct NAF representation

* Change exponentiation impl to be able to test it correctly

* Correct point doubling and miller loop

* Add test for point doubling and line evaluation

* add addition tests

* Add tests for frobenius

* Add line evaluation test after point addition

* Add point doubling and adding functions for projective coordinates

* Fix in miller loop function

* Add test refactors with new functions

* Fix constant for fp12

* Add functions for g2 in projective and affine

* Fix NAF representation

* add eth tests

* add tests names

* add expt

* change final_exp

* fix fp6 square

* Delete test generator for pairing in python

* Delete unnecesary comments

* Delete unused exponentiation function

* Delete unused import and old todo

* Improve naming of doubling and addition steps in miller loop

* add final exponentiation

* Update precompiles/Playground.yul

Co-authored-by: Ivan Litteri <67517699+ilitteri@users.noreply.github.com>

---------

Co-authored-by: IAvecilla <iavecilla@fi.uba.ar>
Co-authored-by: Ivan Litteri <67517699+ilitteri@users.noreply.github.com>

* Add function utils to check elements in curve and twisted curve

* Add conditional for g2 from affine

* Add tests for conjugate in fp12 and fp2

* Fix miller loop errors

* Add pair function

* Add pairing test from eth tests

* Correct NAF representation

* Change exponentiation impl to be able to test it correctly

* Correct point doubling and miller loop

* Add test for point doubling and line evaluation

* add addition tests

* Add tests for frobenius

* Add line evaluation test after point addition

* Add point doubling and adding functions for projective coordinates

* Fix in miller loop function

* Add test refactors with new functions

* Fix constant for fp12

* Add functions for g2 in projective and affine

* Fix NAF representation

* add eth tests

* add tests names

* add expt

* change final_exp

* fix fp6 square

* Delete test generator for pairing in python

* Delete unnecesary comments

* Delete unused exponentiation function

* Delete unused import and old todo

* Improve naming of doubling and addition steps in miller loop

* Add implementation for point doubling step of the miller loop

* Fix fp2 neg function parameters

* Fix typo in parameters to return

* Add precomputation for inverse of two

---------

Co-authored-by: Joaquin Carletti <joaquin.carletti@lambdaclass.com>

* Add basic functionality for G2 Twist

* Rename neg to g2Neg

* Add ecpairing official tests

* Change tests path for test generator script

---------

Co-authored-by: IAvecilla <nachoavecilla@gmail.com>