java 如何实现PEM格式的RSA加密和解密

Question

思路是：
1、先用.NET生成XML格式的公钥和密钥

         /// <summary>
        ///在给定路径中生成XML格式的私钥和公钥。
        /// </summary>
        public void GenerateKeys(string path)
        {
            using (var rsa = new RSACryptoServiceProvider(RsaKeySize))
            {
                try
                {
                    // 获取私钥和公钥。
                    var publicKey = rsa.ToXmlString(false);
                    var privateKey = rsa.ToXmlString(true);

                    // 保存到磁盘
                    File.WriteAllText(Path.Combine(path, publicKeyFileName), publicKey);
                    File.WriteAllText(Path.Combine(path, privateKeyFileName), privateKey);

                    MessageBox.Show(string.Format("生成的RSA密钥的路径: {0}\\ [{1}, {2}]", path, publicKeyFileName, privateKeyFileName));
                }
                finally
                {
                    rsa.PersistKeyInCsp = false;
                }
            }
        }

2、再用BouncyCastle将XML的公钥和密钥转成PEM格式的

        /// <summary>
        /// RSA私钥格式转换，.net->java
        /// </summary>
        /// <param name="privateKey">.net生成的私钥</param>
        /// <returns></returns>
        public static string RSAPrivateKeyDotNet2Java(string privateKey)
        {
            XmlDocument doc = new XmlDocument();
            doc.LoadXml(privateKey);
            BigInteger m = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("Modulus")[0].InnerText));
            BigInteger exp = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("Exponent")[0].InnerText));
            BigInteger d = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("D")[0].InnerText));
            BigInteger p = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("P")[0].InnerText));
            BigInteger q = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("Q")[0].InnerText));
            BigInteger dp = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("DP")[0].InnerText));
            BigInteger dq = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("DQ")[0].InnerText));
            BigInteger qinv = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("InverseQ")[0].InnerText));

            RsaPrivateCrtKeyParameters privateKeyParam = new RsaPrivateCrtKeyParameters(m, exp, d, p, q, dp, dq, qinv);

            PrivateKeyInfo privateKeyInfo = PrivateKeyInfoFactory.CreatePrivateKeyInfo(privateKeyParam);
            byte[] serializedPrivateBytes = privateKeyInfo.ToAsn1Object().GetEncoded();
            return Convert.ToBase64String(serializedPrivateBytes);
        }

        /// <summary>
        /// RSA公钥格式转换，.net->java
        /// </summary>
        /// <param name="publicKey">.net生成的公钥</param>
        /// <returns></returns>
        public static string RSAPublicKeyDotNet2Java(string publicKey)
        {
            XmlDocument doc = new XmlDocument();
            doc.LoadXml(publicKey);
            BigInteger m = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("Modulus")[0].InnerText));
            BigInteger p = new BigInteger(1, Convert.FromBase64String(doc.DocumentElement.GetElementsByTagName("Exponent")[0].InnerText));
            RsaKeyParameters pub = new RsaKeyParameters(false, m, p);

            SubjectPublicKeyInfo publicKeyInfo = SubjectPublicKeyInfoFactory.CreateSubjectPublicKeyInfo(pub);
            byte[] serializedPublicBytes = publicKeyInfo.ToAsn1Object().GetDerEncoded();
            return Convert.ToBase64String(serializedPublicBytes);
        } 

3、然后java怎么利用我转换成PEM格式的公钥密钥进行加密和解密，使得跟.NET的一样？