Java 生成 DH 公钥大小与文档中的示例大小不同

Question

我的一份文档说

Generate the private and public keys using the Diffie-Hellman parameters (‘p’ and ‘g’). The result is ‘Pub_key’and ‘Priv_key’ (1024-bit/128 bytes).

其中 P 和 G 通过以下方式给出:

Diffie-Hellman-Parameters: (1024 bit) Prime (p): e5:16:e4:3e:54:57:b2:f6:6f:6c:a3:67:b3:35:ea: d8:31:99:39:fa:4d:f6:c1:b7:f8:6e:73:e9:22:a6: d1:93:93:25:5e:41:90:96:66:81:74:e3:5c:81:8a: 66:11:7f:79:9e:86:66:c8:05:0e:e4:36:f9:80:13: 51:60:6c:55:d4:5f:ab:a0:3f:39:e2:92:3b:a9:26: a9:cd:75:d4:bd:bc:a9:de:78:b6:2a:9b:84:7a:78: 1c:69:2c:06:3e:aa:cb:43:a3:96:f0:1d:12:1d:04: 27:55:d0:b7:c0:b2:df:a8:b4:98:a5:7e:4d:90:c3: 0c:a0:49:a7:ac:2b:7f:73

generator (g): 5 (0x5)

文档提供的有关公钥的示例数据如下:

85:f0:4d:d0:03:45:64:2a:d1:2b:65:bd:1a:7c:38:72:8b:ff:0b:8e:28:1d:db: 6a:c4:f2:73:9e:82:a0:21:45:da:ab:f2:3d:17:3c:93:39:13:b1:f8:44:05:97: 10:e9:12:55:91:56:9d:e4:27:ea:e1:d2:69:ac:cb:fa:33:05:06:9d:eb:76:22: d1:da:3a:d9:82:0d:11:bd:24:fd:cc:e5:38:1d:2d:f9:9b:da:31:43:94:73:8d: fc:be:21:0e:ae:24:7b:13:03:e7:92:97:ff:74:6c:d9:19:e1:89:f6:a5:77:6e: 6e:cc:24:c8:90:0d:e0:f3:8f:15:90:72:de

但是，当我尝试使用 Java 使用参数生成 DH 公钥时，我得到如下内容:

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

如您所见，它更长......

这是我的编码部分

import java.math.BigInteger;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import javax.crypto.KeyAgreement;
import javax.crypto.spec.DHParameterSpec;

public class DHKeyAgreement {

  // The 1024 bit Diffie-Hellman modulus values used by SKIP
  private static final byte skip1024ModulusBytes[] = {(byte) 0xe5, (byte) 0x16, (byte) 0xe4,
      (byte) 0x3e, (byte) 0x54, (byte) 0x57, (byte) 0xb2, (byte) 0xf6, (byte) 0x6f, (byte) 0x6c,
      (byte) 0xa3, (byte) 0x67, (byte) 0xb3, (byte) 0x35, (byte) 0xea, (byte) 0xd8, (byte) 0x31,
      (byte) 0x99, (byte) 0x39, (byte) 0xfa, (byte) 0x4d, (byte) 0xf6, (byte) 0xc1, (byte) 0xb7,
      (byte) 0xf8, (byte) 0x6e, (byte) 0x73, (byte) 0xe9, (byte) 0x22, (byte) 0xa6, (byte) 0xd1,
      (byte) 0x93, (byte) 0x93, (byte) 0x25, (byte) 0x5e, (byte) 0x41, (byte) 0x90, (byte) 0x96,
      (byte) 0x66, (byte) 0x81, (byte) 0x74, (byte) 0xe3, (byte) 0x5c, (byte) 0x81, (byte) 0x8a,
      (byte) 0x66, (byte) 0x11, (byte) 0x7f, (byte) 0x79, (byte) 0x9e, (byte) 0x86, (byte) 0x66,
      (byte) 0xc8, (byte) 0x05, (byte) 0x0e, (byte) 0xe4, (byte) 0x36, (byte) 0xf9, (byte) 0x80,
      (byte) 0x13, (byte) 0x51, (byte) 0x60, (byte) 0x6c, (byte) 0x55, (byte) 0xd4, (byte) 0x5f,
      (byte) 0xab, (byte) 0xa0, (byte) 0x3f, (byte) 0x39, (byte) 0xe2, (byte) 0x92, (byte) 0x3b,
      (byte) 0xa9, (byte) 0x26, (byte) 0xa9, (byte) 0xcd, (byte) 0x75, (byte) 0xd4, (byte) 0xbd,
      (byte) 0xbc, (byte) 0xa9, (byte) 0xde, (byte) 0x78, (byte) 0xb6, (byte) 0x2a, (byte) 0x9b,
      (byte) 0x84, (byte) 0x7a, (byte) 0x78, (byte) 0x1c, (byte) 0x69, (byte) 0x2c, (byte) 0x06,
      (byte) 0x3e, (byte) 0xaa, (byte) 0xcb, (byte) 0x43, (byte) 0xa3, (byte) 0x96, (byte) 0xf0,
      (byte) 0x1d, (byte) 0x12, (byte) 0x1d, (byte) 0x04, (byte) 0x27, (byte) 0x55, (byte) 0xd0,
      (byte) 0xb7, (byte) 0xc0, (byte) 0xb2, (byte) 0xdf, (byte) 0xa8, (byte) 0xb4, (byte) 0x98,
      (byte) 0xa5, (byte) 0x7e, (byte) 0x4d, (byte) 0x90, (byte) 0xc3, (byte) 0x0c, (byte) 0xa0,
      (byte) 0x49, (byte) 0xa7, (byte) 0xac, (byte) 0x2b, (byte) 0x7f, (byte) 0x73};


  // The SKIP 1024 bit modulus
  private static final BigInteger skip1024Modulus = new BigInteger(1, skip1024ModulusBytes);

  // The base used with the SKIP 1024 bit modulus
  private static final BigInteger skip1024Base = BigInteger.valueOf(5);

  public static void main(String[] args) throws Exception {
    DHParameterSpec dhSkipParamSpec;
    dhSkipParamSpec = new DHParameterSpec(skip1024Modulus, skip1024Base);
    System.out.println("ALICE: Generate DH keypair ...");
    KeyPairGenerator aliceKpairGen = KeyPairGenerator.getInstance("DH");
    aliceKpairGen.initialize(dhSkipParamSpec);
    KeyPair aliceKpair = aliceKpairGen.generateKeyPair();
    System.out.println("ALICE: Initialization ...");
    KeyAgreement aliceKeyAgree = KeyAgreement.getInstance("DH");
    aliceKeyAgree.init(aliceKpair.getPrivate());

    // Alice encodes her public key, and sends it over to Bob.
    byte[] alicePubKeyEnc = aliceKpair.getPublic().getEncoded();
    byte[] alicePrivKeyEnc = aliceKpair.getPrivate().getEncoded();


    System.out.println("ALICE public key: " + toHexString(alicePubKeyEnc));
    System.out.println("Alice private key: " + toHexString(alicePrivKeyEnc));

  }

  /*
   * Converts a byte to hex digit and writes to the supplied buffer
   */
  private static void byte2hex(byte b, StringBuffer buf) {
    char[] hexChars =
        {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F'};
    int high = ((b & 0xf0) >> 4);
    int low = (b & 0x0f);
    buf.append(hexChars[high]);
    buf.append(hexChars[low]);
  }

  /*
   * Converts a byte array to hex string
   */
  private static String toHexString(byte[] block) {
    StringBuffer buf = new StringBuffer();

    int len = block.length;

    for (int i = 0; i < len; i++) {
      byte2hex(block[i], buf);
      if (i < len - 1) {
        buf.append(":");
      }
    }
    return buf.toString();
  }
}

是我理解错误还是文档有误？

Answer 1

您看到的作为 aliceKpair.getPublic().getEncoded() 结果的最终十六进制字符串是 ASN.1 DER 编码字符串。您拥有的公钥的十六进制字符串(已删除 :)是

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

遵循以下格式。 ASN.1 格式用于以独立于平台的方式序列化和反序列化数据结构。

SEQUENCE (2 elem)
  SEQUENCE (2 elem)
    OBJECT IDENTIFIER 1.2.840.113549.1.3.1 dhKeyAgreement (PKCS #3)
    SEQUENCE (3 elem)
      INTEGER (1024 bit) 160872061717711572653317052595503399048868038241656045229773297825253…
      INTEGER 5
      INTEGER 512
  BIT STRING (1 elem)
    INTEGER (1024 bit) 119156181916892940910396680345482295722468357006826527903397802475513…

3 元素序列包含素数 (p) 作为结构的第一个元素，生成元 (g) 作为第二个元素。在 JDK 中，每个 PublicKey 类型(EC/DH/​​RSA 等)都包含相应的 getEncoded() 实现，该实现创建 ASN.1 编码的 DER 字符串。 Here's such an implementation来自 JDK 的 DHPublicKey。 DHPrivateKey 也将有类似的实现。

就您而言，中的素数值为 1024 位，这就是您要查找的值，而您感兴趣的公钥值是 1024 位 BIT STRING 值。

您提供的示例公钥是 256 个字符的十六进制编码，即 128 字节数组，即 1024 位值。这是编码公钥结构中 3 元素序列的第一个值。