Java代码实现文件添加数字签名、验证数字签名

Linux下实现加签、验签

1.使用OpenSSL 生成公钥和密钥;

#用 OpenSSL, Linux 上自带,常用命令如下:
#生成 RSA 私钥(传统格式的)
openssl genrsa -out rsa_private_key.pem 1024
#将传统格式的私钥转换成 PKCS#8 格式的(JAVA需要使用的私钥需要经过PKCS#8编码,PHP程序不需要,可以直接略过)
openssl pkcs8 -topk8 -inform PEM -in rsa_private_key.pem -outform PEM -nocrypt
#生成 RSA 公钥
openssl rsa -in rsa_private_key.pem -pubout -out rsa_public_key.pem

2.使用私钥对文件进行加签、并验证

#有明文文件file.txt和RSA密钥rsa_private_key.pem
#使用md5指令指定sha1算法,对file.txt进行签名,生成签名文件sign1.txt
openssl md5 -sha512 -sign rsa_private_key.pem -out data_xinbao.tar.gz.sign data_xinbao.tar.gz
#使用md5指令指定sha1算法,对file.txt进行签名,生成签名文件sign1.txt
openssl dgst -sha512 -sign rsa_private_key.pem -out data_xinbao.tar.gz.sign data_xinbao.tar.gz
#两个签名文件一样,说明两个指令完成相同的功能
diff data_xinbao.tar.gz.sign data_xinbao1.tar.gz.sign
#使用RSA公钥验证签名(verify参数),验证成功
openssl md5 -verify rsa_public_key.pem -sha512 -signature data_xinbao1.tar.gz.sign data_xinbao.tar.gz
openssl dgst -verify rsa_public_key.pem -sha512 -signature data_xinbao.tar.gz.sign data_xinbao.tar.gz

3.查看OpenSSL和帮助

#通过下面命令可以查看openssl的参数说明
$ openssl dgst -
options are
-c              to output the digest with separating colons
-r              to output the digest in coreutils format
-d              to output debug info
-hex            output as hex dump
-binary         output in binary form
-sign   file    sign digest using private key in file
-verify file    verify a signature using public key in file
-prverify file  verify a signature using private key in file
-keyform arg    key file format (PEM or ENGINE)
-out filename   output to filename rather than stdout
-signature file signature to verify
-sigopt nm:v    signature parameter
-hmac key       create hashed MAC with key
-mac algorithm  create MAC (not neccessarily HMAC)
-macopt nm:v    MAC algorithm parameters or key
-engine e       use engine e, possibly a hardware device.
-md4            to use the md4 message digest algorithm
-md5            to use the md5 message digest algorithm
-ripemd160      to use the ripemd160 message digest algorithm
-sha            to use the sha message digest algorithm
-sha1           to use the sha1 message digest algorithm
-sha224         to use the sha224 message digest algorithm
-sha256         to use the sha256 message digest algorithm
-sha384         to use the sha384 message digest algorithm
-sha512         to use the sha512 message digest algorithm
-whirlpool      to use the whirlpool message digest algorithm

4.拿加签的原文件和加签后的文件使用Java代码进行对比;

import javax.crypto.BadPaddingException;
import javax.crypto.Cipher;
import javax.crypto.IllegalBlockSizeException;
import javax.crypto.NoSuchPaddingException;
import java.io.*;
import java.security.*;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.security.spec.InvalidKeySpecException;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.Date;

/**
 * 对文件加签、验签工具类
 * 生成私钥:openssl genrsa -out rsa_private_key.pem 1024
 * 私钥还不能直接被使用,需要进行PKCS#8编码:openssl pkcs8 -topk8 -inform PEM -in rsa_private_key.pem -outform PEM -nocrypt
 * 根据私钥生成公钥:openssl rsa -in rsa_private_key.pem -pubout -out rsa_public_key.pem
 * 使用私钥sha512签名:openssl dgst -sha512 -sign rsa_private_key.pem -out xx.tar.gz.sign xx.tar.gz
 * 使用公钥sha512验签:openssl dgst -verify rsa_public_key.pem -sha512 -signature xx.tar.gz.sign xx.tar.gz
 * @author XIHONGLIE
 * @date 2018-03-27
 */
public class RsaEncrypt {
    /**
     * rsa签名
     * @param data  待签名的字符串
     * @param priKey  rsa私钥字符串
     * @return 签名结果
     * @throws Exception    签名失败则抛出异常
     */
    public byte[] rsaSign(byte[] data, RSAPrivateKey priKey)
            throws SignatureException {
        try {
            Signature signature = Signature.getInstance("SHA512withRSA");
            signature.initSign(priKey);
            signature.update(data);

            byte[] signed = signature.sign();
            return signed;
        } catch (Exception e) {
            throw new SignatureException("RSAcontent = " + data
                    + "; charset = ", e);
        }
    }

    /**
     * rsa验签
     * @param data  被签名的内容
     * @param sign   签名后的结果
     * @param pubKey   rsa公钥
     * @return 验签结果
     * @throws SignatureException 验签失败,则抛异常
     */
    public boolean verify(byte[] data, byte[] sign, RSAPublicKey pubKey)
            throws SignatureException {
        try {
            Signature signature = Signature.getInstance("SHA512withRSA");
            signature.initVerify(pubKey);
            signature.update(data);
            return signature.verify(sign);

        } catch (Exception e) {
            e.printStackTrace();
            throw new SignatureException("RSA验证签名[content = " + data
                    + "; charset = " + "; signature = " + sign + "]发生异常!", e);
        }
    }

    /**
     * 私钥
     */
    private RSAPrivateKey privateKey;

    /**
     * 公钥
     */
    private RSAPublicKey publicKey;

    /**
     * 字节数据转字符串专用集合
     */
    private static final char[] HEX_CHAR = { '0', '1', '2', '3', '4', '5', '6',
            '7', '8', '9', 'a', 'b', 'c', 'd', 'e', 'f' };

    /**
     * 获取私钥
     * @return 当前的私钥对象
     */
    public RSAPrivateKey getPrivateKey() {
        return privateKey;
    }

    /**
     * 获取公钥
     * @return 当前的公钥对象
     */
    public RSAPublicKey getPublicKey() {
        return publicKey;
    }

    /**
     * 随机生成密钥对
     */
    public void genKeyPair() {
        KeyPairGenerator keyPairGen = null;
        try {
            keyPairGen = KeyPairGenerator.getInstance("RSA");
        } catch (NoSuchAlgorithmException e) {
            e.printStackTrace();
        }
        keyPairGen.initialize(1024, new SecureRandom());
        KeyPair keyPair = keyPairGen.generateKeyPair();
        this.privateKey = (RSAPrivateKey) keyPair.getPrivate();
        this.publicKey = (RSAPublicKey) keyPair.getPublic();
    }

    /**
     * 从.pem文件中取得私钥
     * @param filePath 文件路径
     * @return 私钥
     */
    public String getPrivateKeyFromFile(String filePath){
        String strPrivateKey = "";
        try {
            BufferedReader privateKey = new BufferedReader(new FileReader(filePath));
            String line = "";
            while((line = privateKey.readLine()) != null){
                strPrivateKey += line;
            }
            privateKey.close();
            strPrivateKey = strPrivateKey.replace("-----BEGIN PRIVATE KEY-----","").replace("-----END PRIVATE KEY-----","");
        }catch (Exception e){
            e.printStackTrace();
        }
        return strPrivateKey;
    }

    /**
     * 从.pem文件中取得公钥
     * @param filePath 文件路径
     * @return 公钥
     */
    public String getPublicKeyFromFile(String filePath){
        String strPublicKey = "";
        try {
            BufferedReader publicKey = new BufferedReader(new FileReader(filePath));
            String line = "";
            while((line = publicKey.readLine()) != null){
                strPublicKey += line;
            }
            publicKey.close();
            strPublicKey = strPublicKey.replace("-----BEGIN PUBLIC KEY-----","").replace("-----END PUBLIC KEY-----","");
        }catch (Exception e){
            e.printStackTrace();
        }
        return strPublicKey;
    }

    /**
     * 从字符串中加载公钥
     * @param publicKeyStr 公钥数据字符串
     * @throws Exception 加载公钥时产生的异常
     */
    public void loadPublicKey(String publicKeyStr) throws Exception {
        try {
            byte[] buffer = Base64Utils.decode(publicKeyStr);
            KeyFactory keyFactory = KeyFactory.getInstance("RSA");
            X509EncodedKeySpec keySpec = new X509EncodedKeySpec(buffer);
            this.publicKey = (RSAPublicKey) keyFactory.generatePublic(keySpec);
        } catch (NoSuchAlgorithmException e) {
            throw new Exception("无此算法");
        } catch (InvalidKeySpecException e) {
            throw new Exception("公钥非法");
        }catch (NullPointerException e) {
            throw new Exception("公钥数据为空");
        }
    }

    /**
     * 加载私钥
     * @param privateKeyStr 私钥文件名
     * @return 是否成功
     * @throws Exception
     */
    public void loadPrivateKey(String privateKeyStr) throws Exception {
        try {
            byte[] buffer = Base64Utils.decode(privateKeyStr);
            PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(buffer);
            KeyFactory keyFactory = KeyFactory.getInstance("RSA");
            this.privateKey = (RSAPrivateKey) keyFactory.generatePrivate(keySpec);
        } catch (NoSuchAlgorithmException e) {
            throw new Exception("无此算法");
        } catch (InvalidKeySpecException e) {
            throw new Exception("私钥非法");
        } catch (NullPointerException e) {
            throw new Exception("私钥数据为空");
        }
    }

    /**
     * 加密过程
     * @param publicKey 公钥
     * @param plainTextData 明文数据
     * @return
     * @throws Exception 加密过程中的异常信息
     */
    public byte[] encrypt(RSAPublicKey publicKey, byte[] plainTextData)
            throws Exception {
        if (publicKey == null) {
            throw new Exception("加密公钥为空, 请设置");
        }
        Cipher cipher = null;
        try {
            cipher = Cipher.getInstance("RSA");
            cipher.init(Cipher.ENCRYPT_MODE, publicKey);
            byte[] output = cipher.doFinal(plainTextData);
            return output;
        } catch (NoSuchAlgorithmException e) {
            throw new Exception("无此加密算法");
        } catch (NoSuchPaddingException e) {
            e.printStackTrace();
            return null;
        } catch (InvalidKeyException e) {
            throw new Exception("加密公钥非法,请检查");
        } catch (IllegalBlockSizeException e) {
            throw new Exception("明文长度非法");
        } catch (BadPaddingException e) {
            throw new Exception("明文数据已损坏");
        }
    }

    /**
     * 解密过程
     * @param privateKey 私钥
     * @param cipherData 密文数据
     * @return 明文
     * @throws Exception   解密过程中的异常信息
     */
    public byte[] decrypt(RSAPrivateKey privateKey, byte[] cipherData)
            throws Exception {
        if (privateKey == null) {
            throw new Exception("解密私钥为空, 请设置");
        }
        Cipher cipher = null;
        try {
            cipher = Cipher.getInstance("RSA");
            cipher.init(Cipher.DECRYPT_MODE, privateKey);
            byte[] output = cipher.doFinal(cipherData);
            return output;
        } catch (NoSuchAlgorithmException e) {
            throw new Exception("无此解密算法");
        } catch (NoSuchPaddingException e) {
            e.printStackTrace();
            return null;
        } catch (InvalidKeyException e) {
            throw new Exception("解密私钥非法,请检查");
        } catch (IllegalBlockSizeException e) {
            throw new Exception("密文长度非法");
        } catch (BadPaddingException e) {
            throw new Exception("密文数据已损坏");
        }
    }

    /**
     * 字节数据转十六进制字符串
     * @param data  输入数据
     * @return 十六进制内容
     */
    public static String byteArrayToString(byte[] data) {
        StringBuilder stringBuilder = new StringBuilder();
        for (int i = 0; i < data.length; i++) {
            // 取出字节的高四位 作为索引得到相应的十六进制标识符 注意无符号右移
            stringBuilder.append(HEX_CHAR[(data[i] & 0xf0) >>> 4]);
            // 取出字节的低四位 作为索引得到相应的十六进制标识符
            stringBuilder.append(HEX_CHAR[(data[i] & 0x0f)]);
            if (i < data.length - 1) {
                stringBuilder.append(' ');
            }
        }
        return stringBuilder.toString();
    }

    /**
     * btye转换hex函数
     * @param byteArray
     * @return
     */
    public static String byteToHex(byte[] byteArray) {
        StringBuffer strBuff = new StringBuffer();
        for (int i = 0; i < byteArray.length; i++) {
            if (Integer.toHexString(0xFF & byteArray[i]).length() == 1) {
                strBuff.append("0").append(
                        Integer.toHexString(0xFF & byteArray[i]));
            } else {
                strBuff.append(Integer.toHexString(0xFF & byteArray[i]));
            }
        }
        return strBuff.toString();
    }

    /**
     * 以字节为单位读取文件,常用于读二进制文件,如图片、声音、影像等文件。
     */
    public static byte[] readFileByBytes(String fileName) {
        File file = new File(fileName);
        InputStream in = null;
        byte[] txt = new byte[(int) file.length()];
        try {
            // 一次读一个字节
            in = new FileInputStream(file);
            int tempbyte;
            int i = 0;
            while ((tempbyte = in.read()) != -1) {
                txt[i] = (byte) tempbyte;
                i++;
            }
            in.close();
            return txt;
        } catch (IOException e) {
            e.printStackTrace();
            return txt;
        }
    }

    /**
     * Main 测试方法
     * @param args
     */
    public static void main(String[] args) {
        RsaEncrypt rsaEncrypt = new RsaEncrypt();
        try {
            String publicKey = "MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDPTrsUJ26WDSEQwKuAJhQ6XTNHKl1/+bWeyKRQKb0jeCyuiChMxN/qYSgg2BvS2bP51Rb5P9/UE1Rxm5drr3RYNMDvQoXBuA+rHiUX3wkdXmWSaktVbfe5C95N5FCF2jyLMIuWmrMk6Wo3r5MXrCb54A6zU7SzO/r7F0VkpBh9KwIDAQAB";
            rsaEncrypt.loadPublicKey(publicKey);
            System.out.println("加载公钥成功");
        } catch (Exception e) {
            System.err.println(e.getMessage());
            System.err.println("加载公钥失败");
        }
        // 加载私钥
        try {
            String privateKey = "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";
            rsaEncrypt.loadPrivateKey(privateKey);
            System.out.println("加载私钥成功");
        } catch (Exception e) {
            System.err.println(e.getMessage());
            System.err.println("加载私钥失败");
        }
        // 测试字符串
        String encryptStr = "12321dsfasf1321312fsfdsafsdafasfsadf";
        try {
            System.out.println(new Date());
            // 加密
            byte[] cipher = rsaEncrypt.encrypt(rsaEncrypt.getPublicKey(),
                    encryptStr.getBytes());
            // 解密
            byte[] plainText = rsaEncrypt.decrypt(rsaEncrypt.getPrivateKey(),
                    cipher);
            System.out.println(new Date());
            System.out.println(new String(plainText));
            byte[] content = readFileByBytes("/data/zhnx/IN/data_xinbao.tar.gz");
            // 签名验证
            byte[] signbyte = rsaEncrypt.rsaSign(content, rsaEncrypt.getPrivateKey());
            System.out.println("签名-----:" + byteToHex(signbyte));
            ByteUtil.saveFile(signbyte,"/data/zhnx/IN/","data_xinbao1.tar.gz.sign");
            Boolean isok = rsaEncrypt.verify(content, signbyte, rsaEncrypt.getPublicKey());
            System.out.println("验证:" + isok);

            // 读取验证文件
            byte[] read = readFileByBytes("/data/zhnx/IN/data_xinbao.tar.gz.sign");
            System.out.println("读取签名文件:" + byteToHex(read));
            Boolean isfok = rsaEncrypt.verify(content, read, rsaEncrypt.getPublicKey());
            System.out.println("文件验证2:" + isfok);

        } catch (Exception e) {
            System.err.println(e.getMessage());
        }
    }
}
import java.io.UnsupportedEncodingException;

/**
 * Base64 加密解密工具类
 * @author XIHONGLEI
 * @date 2018-03-27
 */
public class Base64Utils {
    private static char[] base64EncodeChars = new char[]
            {'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T',
                    'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm',
                    'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', '0', '1', '2', '3', '4', '5',
                    '6', '7', '8', '9', '+', '/'};
    private static byte[] base64DecodeChars = new byte[]
            {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
                    -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 62, -1, -1, -1, 63, 52, 53,
                    54, 55, 56, 57, 58, 59, 60, 61, -1, -1, -1, -1, -1, -1, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
                    12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, -1, -1, -1, -1, -1, -1, 26, 27, 28, 29,
                    30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, -1, -1,
                    -1, -1, -1};

    public static String encode(byte[] data) {
        StringBuffer sb = new StringBuffer();
        int len = data.length;
        int i = 0;
        int b1, b2, b3;
        while (i < len) {
            b1 = data[i++] & 0xff;
            if (i == len) {
                sb.append(base64EncodeChars[b1 >>> 2]);
                sb.append(base64EncodeChars[(b1 & 0x3) << 4]);
                sb.append("==");
                break;
            }
            b2 = data[i++] & 0xff;
            if (i == len) {
                sb.append(base64EncodeChars[b1 >>> 2]);
                sb.append(base64EncodeChars[((b1 & 0x03) << 4) | ((b2 & 0xf0) >>> 4)]);
                sb.append(base64EncodeChars[(b2 & 0x0f) << 2]);
                sb.append("=");
                break;
            }
            b3 = data[i++] & 0xff;
            sb.append(base64EncodeChars[b1 >>> 2]);
            sb.append(base64EncodeChars[((b1 & 0x03) << 4) | ((b2 & 0xf0) >>> 4)]);
            sb.append(base64EncodeChars[((b2 & 0x0f) << 2) | ((b3 & 0xc0) >>> 6)]);
            sb.append(base64EncodeChars[b3 & 0x3f]);
        }
        return sb.toString();
    }

    public static byte[] decode(String str) {
        try {
            return decodePrivate(str);
        } catch (UnsupportedEncodingException e) {
            e.printStackTrace();
        }
        return new byte[]
                {};
    }

    private static byte[] decodePrivate(String str) throws UnsupportedEncodingException {
        StringBuffer sb = new StringBuffer();
        byte[] data = null;
        data = str.getBytes("US-ASCII");
        int len = data.length;
        int i = 0;
        int b1, b2, b3, b4;
        while (i < len) {
            do {
                b1 = base64DecodeChars[data[i++]];
            } while (i < len && b1 == -1);
            if (b1 == -1) {
                break;

            }
            do {
                b2 = base64DecodeChars[data[i++]];
            } while (i < len && b2 == -1);
            if (b2 == -1) {
                break;
            }
            sb.append((char) ((b1 << 2) | ((b2 & 0x30) >>> 4)));

            do {
                b3 = data[i++];
                if (b3 == 61) {
                    return sb.toString().getBytes("iso8859-1");
                }
                b3 = base64DecodeChars[b3];
            } while (i < len && b3 == -1);
            if (b3 == -1) {
                break;
            }
            sb.append((char) (((b2 & 0x0f) << 4) | ((b3 & 0x3c) >>> 2)));
            do {
                b4 = data[i++];
                if (b4 == 61) {
                    return sb.toString().getBytes("iso8859-1");
                }
                b4 = base64DecodeChars[b4];
            } while (i < len && b4 == -1);
            if (b4 == -1) {
                break;
            }
            sb.append((char) (((b3 & 0x03) << 6) | b4));
        }
        return sb.toString().getBytes("iso8859-1");
    }
}

注:私钥必须是通过pkcs8 进行编码以后的;

 

import java.io.*;

/**
 * byte数组工具类实现byte[]与文件之间的相互转换
 * @author XIHONGLEI
 * @Date 2018-03-26
 */
public class ByteUtil {
    /**
     * 获得指定文件的byte数组
     */
    public static byte[] getBytes(String filePath){
        byte[] buffer = null;
        try {
            File file = new File(filePath);
            FileInputStream fis = new FileInputStream(file);
            ByteArrayOutputStream bos = new ByteArrayOutputStream(1000);
            byte[] b = new byte[1000];
            int n;
            while ((n = fis.read(b)) != -1) {
                bos.write(b, 0, n);
            }
            fis.close();
            bos.close();
            buffer = bos.toByteArray();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return buffer;
    }

    /**
     * 根据byte数组,生成文件
     */
    public static void saveFile(byte[] bfile, String filePath,String fileName) {
        BufferedOutputStream bos = null;
        FileOutputStream fos = null;
        File file = null;
        try {
            File dir = new File(filePath);
            //判断文件目录是否存在
            if(!dir.exists()&&dir.isDirectory()){
                dir.mkdirs();
            }
            file = new File(filePath+"\\"+fileName);
            fos = new FileOutputStream(file);
            bos = new BufferedOutputStream(fos);
            bos.write(bfile);
        } catch (Exception e) {
            e.printStackTrace();
        } finally {
            if (bos != null) {
                try {
                    bos.close();
                } catch (IOException e1) {
                    e1.printStackTrace();
                }
            }
            if (fos != null) {
                try {
                    fos.close();
                } catch (IOException e1) {
                    e1.printStackTrace();
                }
            }
        }
    }
}

 

 

 

5.验证结果:

Java代码实现文件添加数字签名、验证数字签名_第1张图片

 

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