diff --git a/src/crypto/elliptic/elliptic.go b/src/crypto/elliptic/elliptic.go
index f93dc16419f8f9..afedf18df176ac 100644
--- a/src/crypto/elliptic/elliptic.go
+++ b/src/crypto/elliptic/elliptic.go
@@ -71,6 +71,11 @@ func (curve *CurveParams) polynomial(x *big.Int) *big.Int {
 }
 
 func (curve *CurveParams) IsOnCurve(x, y *big.Int) bool {
+	if x.Sign() < 0 || x.Cmp(curve.P) >= 0 ||
+		y.Sign() < 0 || y.Cmp(curve.P) >= 0 {
+		return false
+	}
+
 	// y² = x³ - 3x + b
 	y2 := new(big.Int).Mul(y, y)
 	y2.Mod(y2, curve.P)
diff --git a/src/crypto/elliptic/elliptic_test.go b/src/crypto/elliptic/elliptic_test.go
index e80e7731aaaed0..bb16b0d163e000 100644
--- a/src/crypto/elliptic/elliptic_test.go
+++ b/src/crypto/elliptic/elliptic_test.go
@@ -721,3 +721,84 @@ func testMarshalCompressed(t *testing.T, curve Curve, x, y *big.Int, want []byte
 		t.Errorf("point did not round-trip correctly: got (%v, %v), want (%v, %v)", X, Y, x, y)
 	}
 }
+
+func testAllCurves(t *testing.T, f func(*testing.T, Curve)) {
+	tests := []struct {
+		name  string
+		curve Curve
+	}{
+		{"P256", P256()},
+		{"P256/Params", P256().Params()},
+		{"P224", P224()},
+		{"P224/Params", P224().Params()},
+		{"P384", P384()},
+		{"P384/Params", P384().Params()},
+		{"P521", P521()},
+		{"P521/Params", P521().Params()},
+	}
+	if testing.Short() {
+		tests = tests[:1]
+	}
+	for _, test := range tests {
+		curve := test.curve
+		t.Run(test.name, func(t *testing.T) {
+			t.Parallel()
+			f(t, curve)
+		})
+	}
+}
+
+// TestInvalidCoordinates tests big.Int values that are not valid field elements
+// (negative or bigger than P). They are expected to return false from
+// IsOnCurve, all other behavior is undefined.
+func TestInvalidCoordinates(t *testing.T) {
+	testAllCurves(t, testInvalidCoordinates)
+}
+
+func testInvalidCoordinates(t *testing.T, curve Curve) {
+	checkIsOnCurveFalse := func(name string, x, y *big.Int) {
+		if curve.IsOnCurve(x, y) {
+			t.Errorf("IsOnCurve(%s) unexpectedly returned true", name)
+		}
+	}
+
+	p := curve.Params().P
+	_, x, y, _ := GenerateKey(curve, rand.Reader)
+	xx, yy := new(big.Int), new(big.Int)
+
+	// Check if the sign is getting dropped.
+	xx.Neg(x)
+	checkIsOnCurveFalse("-x, y", xx, y)
+	yy.Neg(y)
+	checkIsOnCurveFalse("x, -y", x, yy)
+
+	// Check if negative values are reduced modulo P.
+	xx.Sub(x, p)
+	checkIsOnCurveFalse("x-P, y", xx, y)
+	yy.Sub(y, p)
+	checkIsOnCurveFalse("x, y-P", x, yy)
+
+	// Check if positive values are reduced modulo P.
+	xx.Add(x, p)
+	checkIsOnCurveFalse("x+P, y", xx, y)
+	yy.Add(y, p)
+	checkIsOnCurveFalse("x, y+P", x, yy)
+
+	// Check if the overflow is dropped.
+	xx.Add(x, new(big.Int).Lsh(big.NewInt(1), 535))
+	checkIsOnCurveFalse("x+2⁵³⁵, y", xx, y)
+	yy.Add(y, new(big.Int).Lsh(big.NewInt(1), 535))
+	checkIsOnCurveFalse("x, y+2⁵³⁵", x, yy)
+
+	// Check if P is treated like zero (if possible).
+	// y^2 = x^3 - 3x + B
+	// y = mod_sqrt(x^3 - 3x + B)
+	// y = mod_sqrt(B) if x = 0
+	// If there is no modsqrt, there is no point with x = 0, can't test x = P.
+	if yy := new(big.Int).ModSqrt(curve.Params().B, p); yy != nil {
+		if !curve.IsOnCurve(big.NewInt(0), yy) {
+			t.Fatal("(0, mod_sqrt(B)) is not on the curve?")
+		}
+		checkIsOnCurveFalse("P, y", p, yy)
+	}
+}
diff --git a/src/crypto/elliptic/p224.go b/src/crypto/elliptic/p224.go
index 8c76021464207f..ff5c8344522da8 100644
--- a/src/crypto/elliptic/p224.go
+++ b/src/crypto/elliptic/p224.go
@@ -48,6 +48,11 @@ func (curve p224Curve) Params() *CurveParams {
 }
 
 func (curve p224Curve) IsOnCurve(bigX, bigY *big.Int) bool {
+	if bigX.Sign() < 0 || bigX.Cmp(curve.P) >= 0 ||
+		bigY.Sign() < 0 || bigY.Cmp(curve.P) >= 0 {
+		return false
+	}
+
 	var x, y p224FieldElement
 	p224FromBig(&x, bigX)
 	p224FromBig(&y, bigY)