From 434bd2dcc6bc3d1ce5489dd5643ed70d47430efb Mon Sep 17 00:00:00 2001
From: Shramee Srivastav <shramee.srivastav@gmail.com>
Date: Sun, 12 Apr 2026 19:06:19 +0530
Subject: [PATCH] feat(emulated): checkZero mulcheck in hint

closes consensys/gnark#1748
---
 std/math/emulated/field_mul.go | 17 +++++++++++++----
 1 file changed, 13 insertions(+), 4 deletions(-)

diff --git a/std/math/emulated/field_mul.go b/std/math/emulated/field_mul.go
index a434090194..5557f3cb70 100644
--- a/std/math/emulated/field_mul.go
+++ b/std/math/emulated/field_mul.go
@@ -534,8 +534,12 @@ func (f *Field[T]) callMulHint(a, b *Element[T], isMulMod bool, customMod *Eleme
 	if customMod != nil {
 		modulusLimbs = customMod.Limbs
 	}
-	hintInputs := make([]frontend.Variable, 0, 4+len(modulusLimbs)+len(a.Limbs)+len(b.Limbs))
-	hintInputs = append(hintInputs, nbBits, nbLimbs, len(a.Limbs), nbQuoLimbs)
+	isCheckZero := 0
+	if !isMulMod {
+		isCheckZero = 1
+	}
+	hintInputs := make([]frontend.Variable, 0, 5+len(modulusLimbs)+len(a.Limbs)+len(b.Limbs))
+	hintInputs = append(hintInputs, nbBits, nbLimbs, len(a.Limbs), nbQuoLimbs, isCheckZero)
 	hintInputs = append(hintInputs, modulusLimbs...)
 	hintInputs = append(hintInputs, a.Limbs...)
 	hintInputs = append(hintInputs, b.Limbs...)
@@ -566,8 +570,9 @@ func mulHint(field *big.Int, inputs, outputs []*big.Int) error {
 	nbLimbs := int(inputs[1].Int64())
 	nbALen := int(inputs[2].Int64())
 	nbQuoLen := int(inputs[3].Int64())
-	nbBLen := len(inputs) - 4 - nbLimbs - nbALen
-	ptr := 4
+	isCheckZero := inputs[4].Int64() == 1
+	nbBLen := len(inputs) - 5 - nbLimbs - nbALen
+	ptr := 5
 	plimbs := inputs[ptr : ptr+nbLimbs]
 	ptr += nbLimbs
 	alimbs := inputs[ptr : ptr+nbALen]
@@ -611,6 +616,10 @@ func mulHint(field *big.Int, inputs, outputs []*big.Int) error {
 	if p.Sign() != 0 {
 		quo.QuoRem(ab, p, rem)
 	}
+	if isCheckZero && rem.Sign() != 0 {
+		// we expect the remainder to be zero
+		return fmt.Errorf("unexpected non-zero remainder for checkZero")
+	}
 	if err := limbs.Decompose(quo, uint(nbBits), quoLimbs); err != nil {
 		return fmt.Errorf("decompose quo: %w", err)
 	}