使用Java中的模數和指數的RSA加密

Question

我目前正在使用Java進行RSA加密，我必須使用私有和公共模數進行加密。 我目前有以下內容：

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，我有以下內容：

        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，我得到以下結果： .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

首先為什么加密和解密不起作用？ 為什么我沒有回到"12" 。 其次，為什么我的數據不能大於2個字符？

注意我使用以下網站獲取模數和指數值。

Answer 1

創建私鑰時出錯。 您提供公共指數而不是私有和（如評論@ dave_thomsom_085）私有指數而不是模數

使用更改createPrivateKey()

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，出於安全原因，您不應使用原始RSA而不使用填充。 使用RSA/ECB/PKCS1Padding或新的OAEP填充RSA/ECB/OAEPWithSHA1AndMGF1Padding

根據這個答案，您可以使用PKCS1Padding數據加密，最多比密鑰大小少11個字節。 並且使用OAEP它必須小於鍵模數的大小 - 41

然后，使用您的1024位密鑰：

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

還建議直接使用CRT而不是私有指數

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