diff --git a/lib/elliptic/curve/edwards.js b/lib/elliptic/curve/edwards.js
index 75c1666..a9889d9 100644
--- a/lib/elliptic/curve/edwards.js
+++ b/lib/elliptic/curve/edwards.js
@@ -57,7 +57,11 @@ EdwardsCurve.prototype.pointFromX = function pointFromX(x, odd) {
   var rhs = this.c2.redSub(this.a.redMul(x2));
   var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));
 
-  var y = rhs.redMul(lhs.redInvm()).redSqrt();
+  var y2 = rhs.redMul(lhs.redInvm());
+  var y = y2.redSqrt();
+  if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
+    throw new Error('invalid point');
+
   var isOdd = y.fromRed().isOdd();
   if (odd && !isOdd || !odd && isOdd)
     y = y.redNeg();
diff --git a/lib/elliptic/curve/short.js b/lib/elliptic/curve/short.js
index 53c40d3..dfe25d0 100644
--- a/lib/elliptic/curve/short.js
+++ b/lib/elliptic/curve/short.js
@@ -192,6 +192,8 @@ ShortCurve.prototype.pointFromX = function pointFromX(x, odd) {
 
   var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);
   var y = y2.redSqrt();
+  if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
+    throw new Error('invalid point');
 
   // XXX Is there any way to tell if the number is odd without converting it
   // to non-red form?
diff --git a/lib/elliptic/ec/index.js b/lib/elliptic/ec/index.js
index 0a950cc..02deffa 100644
--- a/lib/elliptic/ec/index.js
+++ b/lib/elliptic/ec/index.js
@@ -208,7 +208,12 @@ EC.prototype.getKeyRecoveryParam = function(e, signature, Q, enc) {
     return signature.recoveryParam;
 
   for (var i = 0; i < 4; i++) {
-    var Qprime = this.recoverPubKey(e, signature, i);
+    var Qprime;
+    try {
+      Qprime = this.recoverPubKey(e, signature, i);
+    } catch (e) {
+      continue;
+    }
 
     if (Qprime.eq(Q))
       return i;
diff --git a/lib/elliptic/ec/signature.js b/lib/elliptic/ec/signature.js
index 9f8776f..09d7213 100644
--- a/lib/elliptic/ec/signature.js
+++ b/lib/elliptic/ec/signature.js
@@ -16,7 +16,7 @@ function Signature(options, enc) {
   assert(options.r && options.s, 'Signature without r or s');
   this.r = new BN(options.r, 16);
   this.s = new BN(options.s, 16);
-  if (options.recoveryParam !== null)
+  if (options.recoveryParam)
     this.recoveryParam = options.recoveryParam;
   else
     this.recoveryParam = null;
diff --git a/test/ecdsa-test.js b/test/ecdsa-test.js
index 53bbe7f..b573ff0 100644
--- a/test/ecdsa-test.js
+++ b/test/ecdsa-test.js
@@ -367,4 +367,19 @@ describe('ECDSA', function() {
     var r =  ec.recoverPubKey(msg, signature, recid);
     assert(key.getPublic().eq(r), 'the keys should match');
   });
+
+  it('should fail to recover key when no quadratic residue available',
+     function() {
+    var ec = new elliptic.ec('secp256k1');
+
+    var message =
+        'f75c6b18a72fabc0f0b888c3da58e004f0af1fe14f7ca5d8c897fe164925d5e9';
+
+    assert.throws(function() {
+      ecdsa.recoverPubKey(message, {
+        r: 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140',
+        s: '8887321be575c8095f789dd4c743dfe42c1820f9231f98a962b210e3ac2452a3',
+      }, 0);
+    });
+  });
 });