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问题：

从模和指数重建RSA私钥失败

钱选
2023-03-14

我试图从模数&私有/公共指数重建一个RSA keypair。对公钥的转换是正确的，但对私钥的转换在比较编码的私钥时失败。

当使用此重建私有/公共键盘进行加密时，它工作（！）在Java中，但是在PHP中使用rebuild keypair时，解密部分失败（加密工作），所以在我看来，rebuild私钥与“原始”私钥是不同的。

仅供参考：使用“原始”keypair在PHP中一切都很好。

所以我的问题是：如何从（BigInteger）模和私有指数中检索“原始”私钥？

编辑：在结尾处查看我的最终编辑

Rebuilding of a RSA PrivateKey from modulus & exponent
privateKey equals rebuild: false
publicKey equals rebuild: true

import java.math.BigInteger;
import java.security.*;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.security.spec.InvalidKeySpecException;
import java.security.spec.RSAPrivateKeySpec;
import java.security.spec.RSAPublicKeySpec;
import java.util.Arrays;

public class RebuildRSAPrivateKey {
    public static void main(String[] args) throws NoSuchAlgorithmException, InvalidKeySpecException {
        System.out.println("Rebuilding of a RSA PrivateKey from modulus & exponent");
        // rsa key generation
        KeyPairGenerator kpGen = KeyPairGenerator.getInstance("RSA");
        //kpGen.initialize(2048, new SecureRandom());
        kpGen.initialize(2048, new SecureRandom());
        KeyPair keyPair = kpGen.generateKeyPair();
        // private key
        PrivateKey privateKey = keyPair.getPrivate();
        // get modulus & exponent
        RSAPrivateKey rsaPrivateKey = (RSAPrivateKey) privateKey;
        BigInteger modulus = rsaPrivateKey.getModulus();
        BigInteger privateExponent = rsaPrivateKey.getPrivateExponent();
        // rebuild the private key
        KeyFactory keyFactory = KeyFactory.getInstance("RSA");
        RSAPrivateKeySpec rsaPrivateKeySpec = new RSAPrivateKeySpec(modulus, privateExponent);
        PrivateKey privateKeyRebuild = keyFactory.generatePrivate(rsaPrivateKeySpec);
        System.out.println("privateKey equals rebuild: " + Arrays.equals(privateKey.getEncoded(), privateKeyRebuild.getEncoded()));
        // public key
        PublicKey publicKey = keyPair.getPublic();
        // get modulus & exponent
        RSAPublicKey rsaPublicKey = (RSAPublicKey) publicKey;
        BigInteger modulusPub = rsaPublicKey.getModulus();
        BigInteger publicExponent = rsaPublicKey.getPublicExponent();
        // rebuild the public key
        KeyFactory keyFactoryPub = KeyFactory.getInstance("RSA");
        RSAPublicKeySpec rsaPublicKeySpec = new RSAPublicKeySpec(modulusPub, publicExponent);
        PublicKey publicKeyRebuild = keyFactory.generatePublic(rsaPublicKeySpec);
        System.out.println("publicKey equals rebuild: " + Arrays.equals(publicKey.getEncoded(), publicKeyRebuild.getEncoded()));
    }
}

编辑：下面的程序将显示，从编码密钥派生的RSA私有/公共keypair可以得到恢复，加密和解密工作在Java和PHP中。密钥是不安全的RSA512位密钥和Base64解码。

然后从模和私有/公共指数导出相同的密钥，en-/解密在Java中工作，但在PHP中不工作。

这就是为什么我想从模数和指数中获得“原始”RSA密钥，谢谢你的好心帮助。

Java程序的结果：

Rebuilding of a RSA PrivateKey from modulus & exponent v4
privateKey Original Base64: MIIBVgIBADANBgkqhkiG9w0BAQEFAASCAUAwggE8AgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIDAQABAkEAkDpf4gNRrms+W/mpSshyKsoDTbh9+d5ePP601QlQI79lrsjdy2GLgk4RV1XmwYinM9Sk8G+ssyXTYHdby6A2wQIhAPcRtl6tub6PFiIE1jcuIkib/HzAdRYHZx3ZdzRTYDetAiEA4uv43xpGl5N8yG27Kv0DkRoOlr4Ch6oM24hLVw7ClhcCIFgdRAo+MQlqJH2bdf6WAHoez4x6YwepOjhmD2Jk/eK9AiEAtHgI6J5EEB56+gfS+CBa6tZ3Tcl1x6ElMp8Vk/ooJScCIQDUa3LUkcc58yjJYq8ZNQC/86+HIzd5MldTwg5buR1lpw==
privateKey Rebuild  Base64: MIIBVgIBADANBgkqhkiG9w0BAQEFAASCAUAwggE8AgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIDAQABAkEAkDpf4gNRrms+W/mpSshyKsoDTbh9+d5ePP601QlQI79lrsjdy2GLgk4RV1XmwYinM9Sk8G+ssyXTYHdby6A2wQIhAPcRtl6tub6PFiIE1jcuIkib/HzAdRYHZx3ZdzRTYDetAiEA4uv43xpGl5N8yG27Kv0DkRoOlr4Ch6oM24hLVw7ClhcCIFgdRAo+MQlqJH2bdf6WAHoez4x6YwepOjhmD2Jk/eK9AiEAtHgI6J5EEB56+gfS+CBa6tZ3Tcl1x6ElMp8Vk/ooJScCIQDUa3LUkcc58yjJYq8ZNQC/86+HIzd5MldTwg5buR1lpw==
publicKey           Base64: MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==

generate private & public key via modulus and private/public exponent
privateKey Modulus  Base64: MIGzAgEAMA0GCSqGSIb3DQEBAQUABIGeMIGbAgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIBAAJBAJA6X+IDUa5rPlv5qUrIcirKA024ffneXjz+tNUJUCO/Za7I3cthi4JOEVdV5sGIpzPUpPBvrLMl02B3W8ugNsECAQACAQACAQACAQACAQA=
publicKey  Modulus  Base64: MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==

en-/decryption with original keys
ciphertext Original   : fvFPRZ5B2GMgv9aXQjyQsxnRHK2wotfXlLV+zGea1E3nsZC6RMn+LQMOe9yvZ8IcaG2F/8wWv2NkNmBX4wuxaw==
decryptedtext Original: this is the message to encrypt

en-/decryption with keys from modulus & exponent
ciphertext Modulus    : o0tB4xQIwQRFDSsWj1WgWHexXnJOp9jeBymFPJvy+xZBvfJay2yR0XZEy+0VwaedxdTf9CoyKVvgCbn2HCohSQ==
decryptedtext Modulus : this is the message to encrypt

PHP程序的结果：

php version: 7.4.6 openssl version: OpenSSL 1.1.1g 21 Apr 2020
plaintext: this is the message to encrypt
rsa encryption with original keys
priBase64:MIIBVgIBADANBgkqhkiG9w0BAQEFAASCAUAwggE8AgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIDAQABAkEAkDpf4gNRrms+W/mpSshyKsoDTbh9+d5ePP601QlQI79lrsjdy2GLgk4RV1XmwYinM9Sk8G+ssyXTYHdby6A2wQIhAPcRtl6tub6PFiIE1jcuIkib/HzAdRYHZx3ZdzRTYDetAiEA4uv43xpGl5N8yG27Kv0DkRoOlr4Ch6oM24hLVw7ClhcCIFgdRAo+MQlqJH2bdf6WAHoez4x6YwepOjhmD2Jk/eK9AiEAtHgI6J5EEB56+gfS+CBa6tZ3Tcl1x6ElMp8Vk/ooJScCIQDUa3LUkcc58yjJYq8ZNQC/86+HIzd5MldTwg5buR1lpw==
pubBase64:MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==
ciphertext Base64:WmvVwqf2EHQc0yb6L4pVJ0/23pNW4QsBun3SNvYE8p/sEk+1GQSYxYpbY/mLbSGF2Lb1P5g5er+z7dWxHmodNA==
decryptedtext: this is the message to encrypt

rsa encryption with keys created via modulus & exponents
priBase64:MIGzAgEAMA0GCSqGSIb3DQEBAQUABIGeMIGbAgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIBAAJBAJA6X+IDUa5rPlv5qUrIcirKA024ffneXjz+tNUJUCO/Za7I3cthi4JOEVdV5sGIpzPUpPBvrLMl02B3W8ugNsECAQACAQACAQACAQACAQA=
pubBase64:MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==
ciphertext Base64:kqn8aZpvfpPzr3u2NBX/XmnlFweEvOm+Qu4l2wiUSQCjA0hutQ10mbLaO55oCox7GixvMgb3VtoDBJ8hfW1zbQ==
Cannot Decrypt error:0407109F:rsa routines:RSA_padding_check_PKCS1_type_2:pkcs decoding error
decryptedtext:

decrypt error: error:0909006C:PEM routines:get_name:no start line

源代码Java：

import javax.crypto.BadPaddingException;
import javax.crypto.Cipher;
import javax.crypto.IllegalBlockSizeException;
import javax.crypto.NoSuchPaddingException;
import java.io.IOException;
import java.math.BigInteger;
import java.security.*;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.security.spec.*;
import java.util.Base64;

public class RebuildRSAPrivateKey4 {
    public static void main(String[] args) throws NoSuchAlgorithmException, InvalidKeySpecException, IllegalBlockSizeException, InvalidKeyException, BadPaddingException, NoSuchPaddingException, IOException {
        System.out.println("Rebuilding of a RSA PrivateKey from modulus & exponent v4");
        // rsa key generation
        KeyPairGenerator kpGen = KeyPairGenerator.getInstance("RSA");
        //kpGen.initialize(2048, new SecureRandom());
        kpGen.initialize(512, new SecureRandom()); // don't use 512 bit keys as they are insecure !!
        KeyPair keyPair = kpGen.generateKeyPair();

        // privateKey   Base64: MIIBVgIBADANBgkqhkiG9w0BAQEFAASCAUAwggE8AgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIDAQABAkEAkDpf4gNRrms+W/mpSshyKsoDTbh9+d5ePP601QlQI79lrsjdy2GLgk4RV1XmwYinM9Sk8G+ssyXTYHdby6A2wQIhAPcRtl6tub6PFiIE1jcuIkib/HzAdRYHZx3ZdzRTYDetAiEA4uv43xpGl5N8yG27Kv0DkRoOlr4Ch6oM24hLVw7ClhcCIFgdRAo+MQlqJH2bdf6WAHoez4x6YwepOjhmD2Jk/eK9AiEAtHgI6J5EEB56+gfS+CBa6tZ3Tcl1x6ElMp8Vk/ooJScCIQDUa3LUkcc58yjJYq8ZNQC/86+HIzd5MldTwg5buR1lpw==
        // publicKey    Base64: MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==
        String privateKeyBase64 = "MIIBVgIBADANBgkqhkiG9w0BAQEFAASCAUAwggE8AgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIDAQABAkEAkDpf4gNRrms+W/mpSshyKsoDTbh9+d5ePP601QlQI79lrsjdy2GLgk4RV1XmwYinM9Sk8G+ssyXTYHdby6A2wQIhAPcRtl6tub6PFiIE1jcuIkib/HzAdRYHZx3ZdzRTYDetAiEA4uv43xpGl5N8yG27Kv0DkRoOlr4Ch6oM24hLVw7ClhcCIFgdRAo+MQlqJH2bdf6WAHoez4x6YwepOjhmD2Jk/eK9AiEAtHgI6J5EEB56+gfS+CBa6tZ3Tcl1x6ElMp8Vk/ooJScCIQDUa3LUkcc58yjJYq8ZNQC/86+HIzd5MldTwg5buR1lpw==";
        String publicKeyBase64 = "MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==";
        KeyFactory keyFactory = KeyFactory.getInstance("RSA");
        PKCS8EncodedKeySpec privateKeySpec = new PKCS8EncodedKeySpec(Base64.getDecoder().decode(privateKeyBase64));
        PrivateKey privateKey = keyFactory.generatePrivate(privateKeySpec);
        X509EncodedKeySpec publicKeySpec = new X509EncodedKeySpec(Base64.getDecoder().decode(publicKeyBase64));
        PublicKey publicKey = keyFactory.generatePublic(publicKeySpec);
        System.out.println("privateKey Original Base64: " + privateKeyBase64);
        System.out.println("privateKey Rebuild  Base64: " + Base64.getEncoder().encodeToString(privateKey.getEncoded()));
        System.out.println("publicKey           Base64: " + publicKeyBase64);
        // get modulus & private exponent via RSAPrivateKey
        RSAPrivateKey rsaPrivateKey = (RSAPrivateKey) privateKey;
        BigInteger modulus = rsaPrivateKey.getModulus();
        BigInteger privateExponent = rsaPrivateKey.getPrivateExponent();
        // rebuild the private key
        RSAPrivateKeySpec rsaPrivateKeySpec = new RSAPrivateKeySpec(modulus, privateExponent);
        PrivateKey privateKeyModulusExponent = keyFactory.generatePrivate(rsaPrivateKeySpec);
        // public key
        RSAPublicKey rsaPublicKey = (RSAPublicKey) publicKey;
        BigInteger modulusPub = rsaPublicKey.getModulus();
        BigInteger publicExponent = rsaPublicKey.getPublicExponent();
        // rebuild the public key
        RSAPublicKeySpec rsaPublicKeySpec = new RSAPublicKeySpec(modulusPub, publicExponent);
        PublicKey publicKeyModulusExponent = keyFactory.generatePublic(rsaPublicKeySpec);
        System.out.println("\ngenerate private & public key via modulus and private/public exponent");
        System.out.println("privateKey Modulus  Base64: " + Base64.getEncoder().encodeToString(privateKeyModulusExponent.getEncoded()));
        System.out.println("publicKey  Modulus  Base64: " + Base64.getEncoder().encodeToString(publicKeyModulusExponent.getEncoded()));
        System.out.println("\nen-/decryption with original keys");
        String plaintext = "this is the message to encrypt";
        String ciphertextOriginal = encrypt(publicKey, plaintext);
        String decryptedtextOriginal = decrypt(privateKey, ciphertextOriginal);
        System.out.println("ciphertext Original   : " + ciphertextOriginal);
        System.out.println("decryptedtext Original: " + decryptedtextOriginal);
        System.out.println("\nen-/decryption with keys from modulus & exponent");
        String ciphertextModulus = encrypt(publicKeyModulusExponent, plaintext);
        String decryptedtextModulus = decrypt(privateKeyModulusExponent, ciphertextOriginal);
        System.out.println("ciphertext Modulus    : " + ciphertextModulus);
        System.out.println("decryptedtext Modulus : " + decryptedtextModulus);
    }

    private static String encrypt(PublicKey publicKey, String plaintext) throws NoSuchAlgorithmException, NoSuchPaddingException, InvalidKeyException, IOException, BadPaddingException, IllegalBlockSizeException {
        String ciphertext = "";
        Cipher cipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");
        cipher.init(Cipher.ENCRYPT_MODE, publicKey);
        byte[] ciphertextByte = cipher.doFinal(plaintext.getBytes("UTF8"));
        ciphertext = Base64.getEncoder().encodeToString(ciphertextByte).replaceAll("\\r|\\n", "");
        return ciphertext;
    }

    private static String decrypt(PrivateKey privateKey, String ciphertext) throws NoSuchAlgorithmException, NoSuchPaddingException, InvalidKeyException, BadPaddingException, IllegalBlockSizeException {
        Cipher cipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");
        cipher.init(Cipher.DECRYPT_MODE, privateKey);
        byte[] ciphertextByte = Base64.getDecoder().decode(ciphertext);
        byte[] decryptedtextByte = cipher.doFinal(ciphertextByte);
        return new String(decryptedtextByte);
    }
    private static String bytesToHex(byte[] bytes) {
        StringBuffer result = new StringBuffer();
        for (byte b : bytes) result.append(Integer.toString((b & 0xff) + 0x100, 16).substring(1));
        return result.toString();
    }

}

<?php

function encrypt($publicKeyBase64, $plaintext){
    $pub = base64_decode($publicKeyBase64);
    // public key conversion der to pem
    $pubPem = chunk_split(base64_encode($pub), 64, "\n");
    $pubPem = "-----BEGIN PUBLIC KEY-----\n" . $pubPem . "-----END PUBLIC KEY-----\n";
    $ublicKey = "";
    $publicKey = openssl_get_publickey($pubPem);
    if (!$publicKey) {
        echo "Cannot get public key" . "<br>";
    }
    $ciphertext = "";
    openssl_public_encrypt($plaintext, $ciphertext, $publicKey);
    if (!empty($ciphertext)) {
        openssl_free_key($publicKey);
        //echo "Encryption OK!" . "<br>";
    } else {
        echo "Cannot Encrypt" . "<br>";
    }
    $ciphertextBase64 = base64_encode($ciphertext);
    return $ciphertextBase64;
}

function decrypt($privateKeyBase64, $ciphertext){
    $pri = base64_decode($privateKeyBase64);
    // private key conversion der to pem
    $priPem = chunk_split(base64_encode($pri), 64, "\n");
    $priPem = "-----BEGIN PRIVATE KEY-----\n" . $priPem . "-----END PRIVATE KEY-----\n";
    $privateKey = openssl_get_privatekey($priPem);
    $Crypted = openssl_private_decrypt($ciphertext, $decryptedtext, $privateKey);
    if (!$Crypted) {
        echo 'Cannot Decrypt ' . openssl_error_string() . '<br>';
    } else {
        openssl_free_key($privateKey);
        //echo "decryptedtext: " . $decryptedtext . "<br>";
    }
    return $decryptedtext;
}

echo 'php version: ' . PHP_VERSION . ' openssl version: ' . OPENSSL_VERSION_TEXT . '<br>';
$plaintext = "this is the message to encrypt";
echo "plaintext: " . $plaintext . "<br>";

// RSA 512 keys from Java GenerateKeysSo.java
echo 'rsa encryption with original keys' . '<br>';
$priBase64 = "MIIBVgIBADANBgkqhkiG9w0BAQEFAASCAUAwggE8AgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIDAQABAkEAkDpf4gNRrms+W/mpSshyKsoDTbh9+d5ePP601QlQI79lrsjdy2GLgk4RV1XmwYinM9Sk8G+ssyXTYHdby6A2wQIhAPcRtl6tub6PFiIE1jcuIkib/HzAdRYHZx3ZdzRTYDetAiEA4uv43xpGl5N8yG27Kv0DkRoOlr4Ch6oM24hLVw7ClhcCIFgdRAo+MQlqJH2bdf6WAHoez4x6YwepOjhmD2Jk/eK9AiEAtHgI6J5EEB56+gfS+CBa6tZ3Tcl1x6ElMp8Vk/ooJScCIQDUa3LUkcc58yjJYq8ZNQC/86+HIzd5MldTwg5buR1lpw==";
$pubBase64 = "MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==";
echo 'priBase64:' . $priBase64 . '<br>';
echo 'pubBase64:' . $pubBase64 . '<br>';
$ciphertextBase64 = encrypt($pubBase64, $plaintext);
echo 'ciphertext Base64:' . $ciphertextBase64 . '<br>';
$ciphertext = base64_decode($ciphertextBase64);
$decryptedtext = decrypt($priBase64, $ciphertext);
echo "decryptedtext: " . $decryptedtext . "<br><br>";

// keys created via modulus & exponent
$priBase64 = "MIGzAgEAMA0GCSqGSIb3DQEBAQUABIGeMIGbAgEAAkEA2wFgcni89ijJ/uijQkzCGF4JiUB1+mEJ48u4Lk0vxB7ym3/FCvOEnN2H7FLUzsGvXRhFriLBiSJlg2tOhV5eiwIBAAJBAJA6X+IDUa5rPlv5qUrIcirKA024ffneXjz+tNUJUCO/Za7I3cthi4JOEVdV5sGIpzPUpPBvrLMl02B3W8ugNsECAQACAQACAQACAQACAQA=";
$pubBase64 = "MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBANsBYHJ4vPYoyf7oo0JMwhheCYlAdfphCePLuC5NL8Qe8pt/xQrzhJzdh+xS1M7Br10YRa4iwYkiZYNrToVeXosCAwEAAQ==";
echo 'rsa encryption with keys created via modulus & exponents' . '<br>';
echo 'priBase64:' . $priBase64 . '<br>';
echo 'pubBase64:' . $pubBase64 . '<br>';
$ciphertextBase64 = encrypt($pubBase64, $plaintext);
echo 'ciphertext Base64:' . $ciphertextBase64 . '<br>';
$ciphertext = base64_decode($ciphertextBase64);
$decryptedtext = decrypt($priBase64, $ciphertext);
echo "decryptedtext: " . $decryptedtext . "<br><br>";
echo 'decrypt error: error:0909006C:PEM routines:get_name:no start line' . '<br>';
?>

最终编辑解决方案及结论

如果我们想使用RSA私有-公共keypair进行加密（以及签名？）在Java以外的其他系统中，私钥保存在意大利是很重要的。如果我们试图从已编码的表单（通过PKCS8EncodedKeySpec)，重新构建私钥，那么肯定会丢失一些数据。这些重建私钥将无法工作（这里在PHP/OpenSSL中）。

如果我们需要从编码形式(Byte[])重建私钥，则需要通过一种名为“CreateCrtKey”的方法来增强私钥--这种方法是由James K.Polk总统编写的，所有学分都归他所有。由于链接有时会过期，我在下面将自己的答案标记为接受答案，因为createCrtKey-method在那里有文档。

感谢@James K.Polk、@Topaco和@Michalk总统指引我走向正确的方向。

共有1个答案

朱祺
2023-03-14

执行RSA解密操作所需的最小信息是模n和解密指数d。有一个优化可以应用于RSA解密，它涉及中国剩余定理，通过对RSA素数分别进行幂运算，然后组合生成最终值，因此在RSA私钥语法和根据它建模的JavaRSAPrivateCrtkey接口中有一些额外的字段用于此目的。

现在这里提出的问题是：两个RSAPrivateCrtKey实例何时相等？我认为，当它们在RSA算法中的作用相同时，它们是相等的。您要求的是一个更狭义的定义，即当它们的编码形式相等时，它们也相等。这个定义的问题在于它过于特定于实现。目前，当“sun”提供程序生成密钥对时，它总是将素数p和q排序为pq。但我喜欢另一种方式，其中p<q。RSAPrivateCrtKey接口不关心这两种情况，因为它不进行检查。接口的Javadocs不指定顺序。只需颠倒p.compareto(q)>0中的比较，就可以更改我的代码以生成与当前“Sun”实现相同的编码形式。然而，默认的实现可以在将来改变以匹配我的偏好，如果我接管世界的计划成功了，它也会改变。Javadocs是规范，只要它符合Javadocs，实现就可以改变。

下面，我提供了一个等式函数的实现，其中我试图结合符合规范的最广泛的等式概念。也就是说，keyequals返回true的任意两个RSAPrivateCRTKey实例在RSA算法中使用时应该产生相同的结果，如果返回false，则至少应该有一个值产生不同的结果。

public static boolean keyEquals(RSAPrivateCrtKey k1, RSAPrivateCrtKey k2) {

    final BigInteger ZERO = BigInteger.ZERO;

    boolean result = true;

    result = result && isConsistent(k1) && isConsistent(k2);
    result = result && k1.getModulus().equals(k2.getModulus());
    BigInteger lambda = computeCarmichaelLambda(k1.getPrimeP(), k1.getPrimeQ());

    result = result && k1.getPublicExponent().subtract(k2.getPublicExponent()).mod(lambda).equals(ZERO);
    result = result && k1.getPrivateExponent().subtract(k2.getPrivateExponent()).mod(lambda).equals(ZERO);

    return result;
}

private static boolean isConsistent(RSAPrivateCrtKey k1) {
    final BigInteger ZERO = BigInteger.ZERO;
    final BigInteger ONE = BigInteger.ONE;

    BigInteger n = k1.getModulus();
    BigInteger p = k1.getPrimeP();
    BigInteger q = k1.getPrimeQ();
    BigInteger e = k1.getPublicExponent();
    BigInteger d = k1.getPrivateExponent();

    boolean result = true;

    result = p.multiply(q).equals(n);
    BigInteger lambda = computeCarmichaelLambda(p, q);
    result = result && e.multiply(d).mod(lambda).equals(ONE);
    result = result && d.subtract(key.getPrimeExponentP()).mod(p.subtract(ONE)).equals(ZERO);
    result = result && d.subtract(key.getPrimeExponentQ()).mod(q.subtract(ONE)).equals(ZERO);
    result = result && q.multiply(k1.getCrtCoefficient()).mod(p).equals(ONE);
    return result;
}

private static BigInteger computeCarmichaelLambda(BigInteger p, BigInteger q) {
    return lcm(p.subtract(BigInteger.ONE), q.subtract(BigInteger.ONE));
}

private static BigInteger lcm(BigInteger x, BigInteger y) {
    return x.multiply(y).divide(x.gcd(y));
}
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