使用 Java 中的模数和指数的 RSA 加密

Question

我目前正在 Java 上进行 RSA 加密，我必须使用私有和 public 模数进行加密。我目前有以下内容：

private void createPublicKey() throws NoSuchAlgorithmException, InvalidKeySpecException {
        String publicModulus = "d2c34017ef94f8ab6696dae66e3c0d1ad186bbd9ce4461b68d7cd017c15bda174045bfef36fbf048" +
                "73cfd6d09e3806af3949f99c3e09d6d3c37f6398d8c63f9a3e39b78a187809822e8bcf912f4c44a8" +
                "92fe6a65a477ddea9582738317317286a2610ba30b6b090c3b8c61ffb64207229b3f01afe928a960" +
                "c5a44c24b26f5f91";

        BigInteger keyInt = new BigInteger(publicModulus, 16);
        BigInteger exponentInt = new BigInteger("10001", 16);
        RSAPublicKeySpec keySpeck = new RSAPublicKeySpec(keyInt, exponentInt);
        KeyFactory keyFactory = KeyFactory.getInstance("RSA");
        publicKey = keyFactory.generatePublic(keySpeck);

    }

private void createPrivateKey() throws NoSuchAlgorithmException, InvalidKeySpecException {
        String privateModulus = "6c97ab6369cf00dd174bacd7c37e6f661d04e5af10670d4d88d30148ec188e63227b8dac0c517cf9" +
                "67aa73cd23684c9165dc269f091bfab33b6c5c7db95b54130e348255c30aaaac1c7f09ef701e0d6f" +
                "6dc142d2e4ed78466cc104e28d50be7adf3863afc021dbdd8b5f0b968b7cd965242c7d8d4b32ee84" +
                "0fac3cad134344c1";
        BigInteger privateModulusInt = new BigInteger(privateModulus, 16);
        BigInteger exponentInt = new BigInteger("10001", 16);
        RSAPrivateKeySpec privateKeySpec = new RSAPrivateKeySpec(privateModulusInt, exponentInt);
        KeyFactory factory = KeyFactory.getInstance("RSA");
        privateKey = factory.generatePrivate(privateKeySpec);
    }

在主要方法中，我有以下内容：

        createPrivateKey();
        createPublicKey();

        String data = "12";

        Cipher cipher1 = Cipher.getInstance("RSA/ECB/NoPadding");
        cipher1.init(Cipher.ENCRYPT_MODE, publicKey);
        byte[] encryptedData = cipher1.doFinal(data.getBytes());

        Cipher cipher2 = Cipher.getInstance("RSA/ECB/NoPadding");
        cipher2.init(Cipher.DECRYPT_MODE,privateKey);
        byte[] decryptedData = cipher2.doFinal(encryptedData);
        System.out.println(new String(decryptedData));

在控制台中，我得到以下信息：��.7��p;%kV��9y��xa��ɼ{ 而不是 "12" 如果我使 String data = "12345"; ，然后我得到：javax.crypto.BadPaddingException: Message is larger than modulus

首先为什么加解密不行？为什么我不回来 "12"。其次，为什么我的数据不能大于 2 个字符？

请注意，我使用以下 website 来获取模数和指数值。

Answer 1

创建私钥时出错。您正在提供 public 指数而不是私有指数，并且（如评论@dave_thomsom_085）私有指数而不是模数

将createPrivateKey()改为

private static PrivateKey createPrivateKey() throws NoSuchAlgorithmException, InvalidKeySpecException {
        String publicModulus = "d2c34017ef94f8ab6696dae66e3c0d1ad186bbd9ce4461b68d7cd017c15bda174045bfef36fbf048" +
                "73cfd6d09e3806af3949f99c3e09d6d3c37f6398d8c63f9a3e39b78a187809822e8bcf912f4c44a8" +
                "92fe6a65a477ddea9582738317317286a2610ba30b6b090c3b8c61ffb64207229b3f01afe928a960" +
                "c5a44c24b26f5f91";
        String privateExponent = "6c97ab6369cf00dd174bacd7c37e6f661d04e5af10670d4d88d30148ec188e63227b8dac0c517cf9" +
                "67aa73cd23684c9165dc269f091bfab33b6c5c7db95b54130e348255c30aaaac1c7f09ef701e0d6f" +
                "6dc142d2e4ed78466cc104e28d50be7adf3863afc021dbdd8b5f0b968b7cd965242c7d8d4b32ee84" +
                "0fac3cad134344c1";
        BigInteger privateExponenInt = new BigInteger(privateExponent, 16);
        BigInteger keyInt = new BigInteger(publicModulus, 16);
        RSAPrivateKeySpec privateKeySpec = new RSAPrivateKeySpec(keyInt, privateExponenInt);
        KeyFactory factory = KeyFactory.getInstance("RSA");
        return factory.generatePrivate(privateKeySpec);
    }

此外，出于安全原因，您不应使用没有填充的原始 RSA。使用 RSA/ECB/PKCS1Padding 或新的 OAEP 填充 RSA/ECB/OAEPWithSHA1AndMGF1Padding

根据this answer you can encrypt with PKCS1Padding data up to 11 bytes less than the key size. and using OAEP，它必须小于密钥模数的大小 – 41

然后，使用您的 1024 位密钥：

PKCS1: (1024 bits / 8) - 11 = 117 bytes
OAEP：(1024 bits / 8) - 42 = 86 bytes

也建议直接使用CRT而不是private exponent

RSAPrivateCrtKeySpec privateKeySpec = 
    new RSAPrivateCrtKeySpec(modulus, publicExponent, privateExponent, primeP, primeQ, primeExpP, primeExpQ, crtCoefficient);

使用 Java 中的模数和指数的 RSA 加密

RSA Encryption using modulus and exponent in Java

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