src/crypto/elliptic/elliptic.go      |  5 +++++
 src/crypto/elliptic/elliptic_test.go | 55 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 src/crypto/elliptic/p224.go          |  5 +++++
 src/crypto/elliptic/p521.go          |  5 +++++

diff --git a/src/crypto/elliptic/elliptic.go b/src/crypto/elliptic/elliptic.go
index f072960bfeddf83ce69d6a6ec1c701b99a2a6d9b..b84339ec1c2cfee5b438a9ff9c522e0e26ea29d6 100644
--- a/src/crypto/elliptic/elliptic.go
+++ b/src/crypto/elliptic/elliptic.go
@@ -86,6 +86,11 @@ 	if specific, ok := matchesSpecificCurve(curve, p224, p521); ok {
 		return specific.IsOnCurve(x, y)
 	}
 
+	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 183861a54b52fe2678f9165b171a38b471e9b40f..3fe53c5f3328c37c82c6cca80d0260a903594df1 100644
--- a/src/crypto/elliptic/elliptic_test.go
+++ b/src/crypto/elliptic/elliptic_test.go
@@ -174,6 +174,61 @@ 		}
 	}
 }
 
+// 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)
+	}
+}
+
 func TestMarshalCompressed(t *testing.T) {
 	t.Run("P-256/03", func(t *testing.T) {
 		data, _ := hex.DecodeString("031e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
diff --git a/src/crypto/elliptic/p224.go b/src/crypto/elliptic/p224.go
index 8c76021464207f4f78a1bd0a7bc3d7d8e7bbb20e..ff5c8344522da8cc5abfe31055df3edf0c349543 100644
--- a/src/crypto/elliptic/p224.go
+++ b/src/crypto/elliptic/p224.go
@@ -48,6 +48,11 @@ 	return curve.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)
diff --git a/src/crypto/elliptic/p521.go b/src/crypto/elliptic/p521.go
index 3d355943ec7fae1545ea804c20a9e63b398dcf47..587991e31bf7660a1f595a19470040c509cfd88e 100644
--- a/src/crypto/elliptic/p521.go
+++ b/src/crypto/elliptic/p521.go
@@ -32,6 +32,11 @@ 	return curve.CurveParams
 }
 
 func (curve p521Curve) 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
+	}
+
 	x1 := bigIntToFiatP521(x)
 	y1 := bigIntToFiatP521(y)
 	b := bigIntToFiatP521(curve.B) // TODO: precompute this value.