Hi there,

During my recent study of Circom circuits, I have identified three circuits in the Circomlib library that are under-constrained. I am reporting these findings to help other users avoid potential issues and implement possible fixes. I list the counter-examples for each of the affected circuits below:




The BitElementMulAny circuit from escalarmulany.circom:

{'counter_1': ['1', '14672998305363090392983128317648190411747895644754118300922099904584349198871', '10703129564854067807644642570467049369670438847455742959265077605848455102644', '20960083708607970761914303895905599481602869822071550562507451343924354875765', '101406829380884725912470015234854336472166820744246287828719764563795152606', '1', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '0', '20960083708607970761914303895905599481602869822071550562507451343924354875765', '101406829380884725912470015234854336472166820744246287828719764563795152606', '14672998305363090392983128317648190411747895644754118300922099904584349198871', '10703129564854067807644642570467049369670438847455742959265077605848455102644', '0', '0', '5032815389558926975313438970053319662353327241148579973523702641542536081905', '14672998305363090392983128317648190411747895644754118300922099904584349198871', '10703129564854067807644642570467049369670438847455742959265077605848455102644', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1416574969433118380227580706320046397306582246409971937940269504301020238632', '1416574969433118380227580706320046397306582246409971937940269504301020238633', '20960083708607970761914303895905599481602869822071550562507451343924354875765', '101406829380884725912470015234854336472166820744246287828719764563795152606', '1', '0', '0', '20960083708607970761914303895905599481602869822071550562507451343924354875765', '101406829380884725912470015234854336472166820744246287828719764563795152606'], 'counter_2': ['1', '247642465096457776531496957999617871327', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '0', '0', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '0', '16835562930602138819566040090455835269150749916267310882170236538929243188230', '20175654994710418991124453054723803909920014636217041388436765742115957465794', '247642465096457776531496957999617871327', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '0', '0', '10425040324895579544158561735751773411691741085919802341926195217066406856273', '247642465096457776531496957999617871327', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '141117788661410685370609618928219376319', '1416574969433118380227580706320046397306582246409971937940269504301020238633', '0', '0', '0', '0', '0', '16835562930602138819566040090455835269150749916267310882170236538929243188230', '20175654994710418991124453054723803909920014636217041388436765742115957465794']}



The WindowMulFix circuit from escalarmulfix.circom:
{'counter_1': ['1', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '0', '1', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '14672998305363090392983128317648190411747895644754118300922099904584349198871', '10703129564854067807644642570467049369670438847455742959265077605848455102644', '20471667902406156842018825038937228691241782154006062405757934682274788256985', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '14672998305363090392983128317648190411747895644754118300922099904584349198871', '10703129564854067807644642570467049369670438847455742959265077605848455102644', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1416574969433118380227580706320046397306582246409971937940269504301020238632', '1416574969433118380227580706320046397306582246409971937940269504301020238633', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '14672998305363090392983128317648190411747895644754118300922099904584349198871', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '10703129564854067807644642570467049369670438847455742959265077605848455102644', '0', '0', '0', '0', '0', '0', '0', '1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0'], 'counter_2': ['1', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '1', '1', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '247642465096457776531496957999617871327', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '21888242871839275222246405745257275088407246611754623658327594567647589119298', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '0', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '0', '247642465096457776531496957999617871327', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '141117788661410685370609618928219376319', '1416574969433118380227580706320046397306582246409971937940269504301020238633', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '247642465096457776531496957999617871327', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '1974012595152705026653531753491227775885705436547373273072818286542088377183', '0', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '0', '0', '0', '0', '0', '0', '1', '1', '0', '19914230276686570195592873991766047312910301428965118847156882858033337989761', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '0', '0', '1974012595152705026653531753491227775638062971450915496541321328542470505856', '11561163983477874843362127040659415508511356456301887718895675858651956880213', '0', '0', '1974012595152705026653531753491227775638062971450915496541321328542470505856', '11561163983477874843362127040659415508511356456301887718895675858651956880213', '0', '0', '11931127733495990124449968749374251432464677383578161584917008194558566392076', '10327078888361400378884278704597859580037007944114146624802528327923851615404', '9957115138343285097796436995883023656331329481934330535312692950016859974868', '0', '1']}



The Window4 circuit from pedersen.circom:

{"counter_1": ["1", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "1", "1", "0", "1", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "14672998305363090392983128317648190411747895644754118300922099904584349198871", "10703129564854067807644642570467049369670438847455742959265077605848455102644", "20471667902406156842018825038937228691241782154006062405757934682274788256985", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "0", "14672998305363090392983128317648190411747895644754118300922099904584349198871", "10703129564854067807644642570467049369670438847455742959265077605848455102644", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "1416574969433118380227580706320046397306582246409971937940269504301020238632", "1416574969433118380227580706320046397306582246409971937940269504301020238633", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "14672998305363090392983128317648190411747895644754118300922099904584349198871", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "10703129564854067807644642570467049369670438847455742959265077605848455102644", "0", "0", "0", "0", "0", "0", "1", "1", "0", "12698985710210385366329596564156962635862190208206745027849281618042260821688", "10703129564854067807644642570467049369670438847455742959265077605848455102644", "0", "0", "9189257161628889855916809181100312452686174192209289315848922568533547673929", "11185113306985207414601763174790225718877925552960291384433126580727353392973", "0", "0", "9189257161628889855916809181100312452686174192209289315848922568533547673929", "11185113306985207414601763174790225718877925552960291384433126580727353392973", "0", "0", "4715883167019805295186691321765166755416566162819787765609406954567489224003", "10703129564854067807644642570467049369670438847455742959265077605848455102644", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "1"], "counter_2": ["1", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "0", "1", "1", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "247642465096457776531496957999617871327", "10327078888361400378884278704597859580037007944114146624802528327923851615404", "21888242871839275222246405745257275088407246611754623658327594567647589119298", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "0", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "0", "247642465096457776531496957999617871327", "10327078888361400378884278704597859580037007944114146624802528327923851615404", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "141117788661410685370609618928219376319", "1416574969433118380227580706320046397306582246409971937940269504301020238633", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "247642465096457776531496957999617871327", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "1974012595152705026653531753491227775885705436547373273072818286542088377183", "0", "10327078888361400378884278704597859580037007944114146624802528327923851615404", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "9957115138343285097796436995883023656331329481934330535312692950016859974868", "0", "0"]}