diff --git a/cipher/ecdh_es.go b/cipher/ecdh_es.go
index c128e327..093c6467 100644
--- a/cipher/ecdh_es.go
+++ b/cipher/ecdh_es.go
@@ -17,8 +17,10 @@
 package josecipher
 
 import (
+	"bytes"
 	"crypto"
 	"crypto/ecdsa"
+	"crypto/elliptic"
 	"encoding/binary"
 )
 
@@ -44,16 +46,38 @@ func DeriveECDHES(alg string, apuData, apvData []byte, priv *ecdsa.PrivateKey, p
 		panic("public key not on same curve as private key")
 	}
 
-	z, _ := priv.PublicKey.Curve.ScalarMult(pub.X, pub.Y, priv.D.Bytes())
-	reader := NewConcatKDF(crypto.SHA256, z.Bytes(), algID, ptyUInfo, ptyVInfo, supPubInfo, []byte{})
+	z, _ := priv.Curve.ScalarMult(pub.X, pub.Y, priv.D.Bytes())
+	zBytes := z.Bytes()
 
+	// Note that calling z.Bytes() on a big.Int may strip leading zero bytes from
+	// the returned byte array. This can lead to a problem where zBytes will be
+	// shorter than expected which breaks the key derivation. Therefore we must pad
+	// to the full length of the expected coordinate here before calling the KDF.
+	octSize := dSize(priv.Curve)
+	if len(zBytes) != octSize {
+		zBytes = append(bytes.Repeat([]byte{0}, octSize-len(zBytes)), zBytes...)
+	}
+
+	reader := NewConcatKDF(crypto.SHA256, zBytes, algID, ptyUInfo, ptyVInfo, supPubInfo, []byte{})
 	key := make([]byte, size)
 
 	// Read on the KDF will never fail
 	_, _ = reader.Read(key)
+
 	return key
 }
 
+// dSize returns the size in octets for a coordinate on a elliptic curve.
+func dSize(curve elliptic.Curve) int {
+	order := curve.Params().P
+	bitLen := order.BitLen()
+	size := bitLen / 8
+	if bitLen%8 != 0 {
+		size++
+	}
+	return size
+}
+
 func lengthPrefixed(data []byte) []byte {
 	out := make([]byte, len(data)+4)
 	binary.BigEndian.PutUint32(out, uint32(len(data)))
diff --git a/jwe_test.go b/jwe_test.go
index c5c5f969..bba8c326 100644
--- a/jwe_test.go
+++ b/jwe_test.go
@@ -550,6 +550,41 @@ func TestSampleJose4jJWEMessagesECDH(t *testing.T) {
 	}
 }
 
+func TestPrecomputedECDHMessagesFromJose4j(t *testing.T) {
+	data := []struct{ key, message string }{
+		{
+			`{"kty":"EC","x":"fXx-DfOsmecjKh3VrLZFsF98Z1nutsL4UdFTdgA8S7Y","y":"LGzyJY99aqKk52UIExcNFSTs0S7HnNzQ-DRWBTHDad4","crv":"P-256","d":"OeVCWbXuFuJ9U16q7bhLNoKPLLnK-yTx95grzfvQ2l4"}`,
+			`eyJlbmMiOiJBMjU2Q0JDLUhTNTEyIiwiYWxnIjoiRUNESC1FUyIsImVwayI6eyJrdHkiOiJFQyIsIngiOiJ3ZlRHNVFHZkItNHUxanVUUEN1aTNESXhFTV82ZUs5ZEk5TXNZckpxWDRnIiwieSI6Ik8yanlRbHQ2TXFGTGtqMWFCWW1aNXZJWHFVRHh6Ulk3dER0WmdZUUVNa0kiLCJjcnYiOiJQLTI1NiJ9fQ..mk4wQzGSSeZ8uSgEYTIetA.fCw3-TosL4p0D5fEXw0bEA.9mPsdmGTVoVexXqEOdN5VUKk-ZNtfOtUfbdjVHoko_o`,
+		},
+		{
+			`{"kty":"EC","x":"nBr92fh2JsEjIF1LR5PKICBeHNIBe0xb7nlBrrU3WoWgfJYfXve1jxC-5VT5EPLt","y":"sUAxL3L5lJdzFUSR9EHLniuBhEbvXfPa_3OiR6Du0_GOlFXXIi4UmbNpk10_Thfq","crv":"P-384","d":"0f0NnWg__Qgqjj3fl2gAlsID4Ni41FR88cmZPVgb6ch-ZShuVJRjoxymCuzVP7Gi"}`,
+			`eyJlbmMiOiJBMTkyQ0JDLUhTMzg0IiwiYWxnIjoiRUNESC1FUyIsImVwayI6eyJrdHkiOiJFQyIsIngiOiJsX3hXdzIyb1NfOWZGbV96amNzYkstd3R3d0RHSlRQLUxnNFVBWDI3WWF1b1YwNml2emwtcm1ra2h6ci11SDBmIiwieSI6IloyYmVnbzBqeE9nY0YtNVp4SFNBOU5jZDVCOW8wUE1pSVlRbm9sWkNQTHA3YndPd1RLUEZaaFZVUlFPSjdoeUciLCJjcnYiOiJQLTM4NCJ9fQ..jSWP7pfa4KcpqKWZ1x8awg.osb-5641Ej1Uon_f3U8bNw.KUQWwb35Gxq3YQ34_AVkebugx4rxq1lO`,
+		},
+		{
+			`{"kty":"EC","x":"AH3rqSYjKue50ThW0qq_qQ76cNtqWrc7hU6kZR6akxy8iTf8ugcpqnbgbi98AgSwIqgJZDBMCk-8eoiGaf3R_kDD","y":"AeafPdJjHLf6pK5V7iyMsL3-6MShpHS6jXQ8m-Bcbp06yxAMn6TJbdkacvj45dy_pdh1s6XZwoxRxNETg_gj-hq9","crv":"P-521","d":"AB2tm9vgGe2BaxZmJQ016GY-U7NV_EWhrPsLDC5l9tAM9DGEwI2cT2HcO20Z6CQndw0ZhqLZ6MEvS8siL-SCxIl2"}`,
+			`eyJlbmMiOiJBMjU2Q0JDLUhTNTEyIiwiYWxnIjoiRUNESC1FUyIsImVwayI6eyJrdHkiOiJFQyIsIngiOiJBQ1RLMlVPSjJ6SVk3U1U4T0xkaG1QQmE4ZUVpd2JrX09UMXE0MHBsRlRwQmJKUXg3YWdqWG9LYml2NS1OTXB6eXZySm1rblM3SjNRUWlUeFgwWmtjemhEIiwieSI6IkFXeTZCR1dkZld2ekVNeGIxQklCQnZmRDJ4bEh6Rjk2YzVVRVQ4SFBUS0RSeUJyMnQ4T2dTX1J2MnNoUmxGbXlqUWpyX25uQk94akcxVTZNWDNlZ2VETzciLCJjcnYiOiJQLTUyMSJ9fQ..EWqSGntxbO_Y_6JRjFkCgg.DGjDNjAYdsnYTpUFJi1gEI4YtNd7gBPMjD3CDH047RAwZKTme6Ah_ztzxSfVg5kG.yGm5jn2LtbFXaK_yf0b0932sI2O77j2gwmL1Y09YC_Y`,
+		},
+	}
+
+	for i, vector := range data {
+		var jwk JSONWebKey
+		err := jwk.UnmarshalJSON([]byte(vector.key))
+		if err != nil {
+			t.Fatal(i, err)
+		}
+
+		parsed, err := ParseEncrypted(vector.message)
+		if err != nil {
+			t.Fatal(i, err)
+		}
+
+		_, err = parsed.Decrypt(jwk)
+		if err != nil {
+			t.Fatal(i, err)
+		}
+	}
+}
+
 func TestSampleAESCBCHMACMessagesFromNodeJose(t *testing.T) {
 	samples := []struct {
 		key        []byte
diff --git a/jwk.go b/jwk.go
index 6cb8adb8..936a0202 100644
--- a/jwk.go
+++ b/jwk.go
@@ -357,11 +357,11 @@ func (key rawJSONWebKey) ecPublicKey() (*ecdsa.PublicKey, error) {
 	// the curve specified in the "crv" parameter.
 	// https://tools.ietf.org/html/rfc7518#section-6.2.1.2
 	if curveSize(curve) != len(key.X.data) {
-		return nil, fmt.Errorf("square/go-jose: invalid EC private key, wrong length for x")
+		return nil, fmt.Errorf("square/go-jose: invalid EC public key, wrong length for x")
 	}
 
 	if curveSize(curve) != len(key.Y.data) {
-		return nil, fmt.Errorf("square/go-jose: invalid EC private key, wrong length for y")
+		return nil, fmt.Errorf("square/go-jose: invalid EC public key, wrong length for y")
 	}
 
 	x := key.X.bigInt()