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 一个比较简单的实现:一个三个类KeyGenerater生成公钥私钥对，Signaturer类使用私钥签名，SignProvider用公钥验证。公钥和私钥使用Base64加密Base64这个类也在博客里面

public class KeyGenerater {
 private byte[] priKey;
 private byte[] pubKey;

 public void generater() {
  try {
   java.security.KeyPairGenerator keygen = java.security.KeyPairGenerator
     .getInstance("RSA");
   SecureRandom secrand = new SecureRandom();
   secrand.setSeed("syj".getBytes()); // 初始化随机产生器
   keygen.initialize(1024, secrand);
   KeyPair keys = keygen.genKeyPair();

   PublicKey pubkey = keys.getPublic();
   PrivateKey prikey = keys.getPrivate();

   pubKey = Base64.encodeToByte(pubkey.getEncoded());
   priKey = Base64.encodeToByte(prikey.getEncoded());

   System.out.println("pubKey = " + new String(pubKey));
   System.out.println("priKey = " + new String(priKey));
  } catch (java.lang.Exception e) {
   System.out.println("生成密钥对失败");
   e.printStackTrace();
  }
 }

 public byte[] getPriKey() {
  return priKey;
 }

 public byte[] getPubKey() {
  return pubKey;
 }
}

public class Signaturer {
 /**
  * 
  * Description:数字签名
  * 
  * @param priKeyText
  * @param plainText
  * @return
  * @author 孙钰佳
  * @since：2007-12-27 上午10:51:48
  */
 public static byte[] sign(byte[] priKeyText, String plainText) {
  try {
   PKCS8EncodedKeySpec priPKCS8 = new PKCS8EncodedKeySpec(Base64
     .decode(priKeyText));
   KeyFactory keyf = KeyFactory.getInstance("RSA");
   PrivateKey prikey = keyf.generatePrivate(priPKCS8);

   // 用私钥对信息生成数字签名
   java.security.Signature signet = java.security.Signature
     .getInstance("MD5withRSA");
   signet.initSign(prikey);
   signet.update(plainText.getBytes());
   byte[] signed = Base64.encodeToByte(signet.sign());
   return signed;
  } catch (java.lang.Exception e) {
   System.out.println("签名失败");
   e.printStackTrace();
  }
  return null;
 }
}

public class SignProvider {
 private SignProvider() {

 }

 /**
  * 
  * Description:校验数字签名,此方法不会抛出任务异常,成功返回true,失败返回false,要求全部参数不能为空
  * 
  * @param pubKeyText
  *            公钥,base64编码
  * @param plainText
  *            明文
  * @param signTest
  *            数字签名的密文,base64编码
  * @return 校验成功返回true 失败返回false
  * @author 孙钰佳
  * @since：2007-12-27 上午09:33:55
  */
 public static boolean verify(byte[] pubKeyText, String plainText,
   byte[] signText) {
  try {
   // 解密由base64编码的公钥,并构造X509EncodedKeySpec对象
   java.security.spec.X509EncodedKeySpec bobPubKeySpec = new java.security.spec.X509EncodedKeySpec(
     Base64.decode(pubKeyText));
   // RSA对称加密算法
   java.security.KeyFactory keyFactory = java.security.KeyFactory
     .getInstance("RSA");
   // 取公钥匙对象
   java.security.PublicKey pubKey = keyFactory
     .generatePublic(bobPubKeySpec);
   // 解密由base64编码的数字签名
   byte[] signed = Base64.decode(signText);
   java.security.Signature signatureChecker = java.security.Signature
     .getInstance("MD5withRSA");
   signatureChecker.initVerify(pubKey);
   signatureChecker.update(plainText.getBytes());
   // 验证签名是否正常
   if (signatureChecker.verify(signed))
    return true;
   else
    return false;
  } catch (Throwable e) {
   System.out.println("校验签名失败");
   e.printStackTrace();
   return false;
  }
 }
}