BouncyCastle如何生成ECDH"Keys"？
How Does BouncyCastle Generate ECDH "Keys"?
我有一个使用 BouncyCastle 作为安全提供程序的应用程序，但我想切换到另一个直接使用 OpenSSL (Conscrypt) 的应用程序。我遇到的问题是我正在使用 BouncyCastle 提供的 KeyGenerator 中的 ECDH "Keys"，但在我的其他库中没有类似的 KeyGenerator。
为了比较这两者，我将使用这两种方法和以下输入来解码点 -
为了可读性添加了换行符
BADX_GAXp03z_5p05O1-op61KJAl4j9U2sBnAnJ4p_6GSAIyFGU3lM
oC4aIXw_2qlTnplykArgjvwCWw-2g6L44
使用BouncyCastle方法-
public org.bouncycastle.jce.interfaces.ECPublicKey loadECPublicKeyBC(String encodedPublicKey) throws NoSuchProviderException, NoSuchAlgorithmException, InvalidKeySpecException, IOException {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
KeyFactory keyFactory = KeyFactory.getInstance("ECDH", "BC");
ECParameterSpec ecParameterSpec = ECUtil.getECParameterSpec(openSSLProvider, "prime256v1");
ECPoint ecPoint = ECUtil.decodePoint(decodedPublicKey, ecParameterSpec.getCurve());
ECPublicKeySpec pubSpec = new ECPublicKeySpec(ecPoint, ecParameterSpec);
org.bouncycastle.jce.interfaces.ECPublicKey ecPublicKey = (org.bouncycastle.jce.interfaces.ECPublicKey)keyFactory.generatePublic(pubSpec);
return ecPublicKey;
}
返回的getAlgorithm为EC。
返回的 getFormat 是 X.509.
这个的getEncoded值为-
[48,-126,1,51,48,-127,-20,6,7,42,-122,72,-50,61,2,1,48,
-127,-32,2,1,1,48,44,6,7,42,-122,72,-50,61,1,1,2,33,0,
-1,-1,-1,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,48,68,4,32,-1,-1,-1,-1,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-4,4,32,90,-58,53,-40,-86,58,-109,-25,-77,-21,-67,85,
118,-104,-122,-68,101,29,6,-80,-52,83,-80,-10,59,-50,60,
62,39,-46,96,75,4,65,4,107,23,-47,-14,-31,44,66,71,-8,-68,
-26,-27,99,-92,64,-14,119,3,125,-127,45,-21,51,-96,-12,
-95,57,69,-40,-104,-62,-106,79,-29,66,-30,-2,26,127,-101,
-114,-25,-21,74,124,15,-98,22,43,-50,51,87,107,49,94,-50,
-53,-74,64,104,55,-65,81,-11,2,33,0,-1,-1,-1,-1,0,0,0,0,-1,
-1,-1,-1,-1,-1,-1,-1,-68,-26,-6,-83,-89,23,-98,-124,-13,
-71,-54,-62,-4,99,37,81,2,1,1,3,66,0,4,0,-41,-4,96,23,-89,
77,-13,-1,-102,116,-28,-19,126,-94,-98,-75,40,-112,37,-30,
63,84,-38,-64,103,2,114,120,-89,-2,-122,72,2,50,20,101,55,
-108,-54,2,-31,-94,23,-61,-3,-86,-107,57,-23,-105,41,0,-82,
8,-17,-64,37,-80,-5,104,58,47,-114]
仅使用 BouncyCastle EC 算法（不是 ECDH）我得到-
[48,-126,1,51,48,-127,-20,6,7,42,-122,72,
-50,61,2,1,48,-127,-32,2,1,1,48,44,6,7,42,
-122,72,-50,61,1,1,2,33,0,-1,-1,-1,-1,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,48,68,4,32,-1,-1,-1,-1,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-4,4,32,90,-58,53,-40,
-86,58,-109,-25,-77,-21,-67,85,118,-104,-122,
-68,101,29,6,-80,-52,83,-80,-10,59,-50,60,62,
39,-46,96,75,4,65,4,107,23,-47,-14,-31,44,66,
71,-8,-68,-26,-27,99,-92,64,-14,119,3,125,
-127,45,-21,51,-96,-12,-95,57,69,-40,-104,-62,
-106,79,-29,66,-30,-2,26,127,-101,-114,-25,
-21,74,124,15,-98,22,43,-50,51,87,107,49,94,
-50,-53,-74,64,104,55,-65,81,-11,2,33,0,-1,-1,
-1,-1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-68,-26,
-6,-83,-89,23,-98,-124,-13,-71,-54,-62,-4,99,
37,81,2,1,1,3,66,0,4,0,-41,-4,96,23,-89,77,
-13,-1,-102,116,-28,-19,126,-94,-98,-75,40,
-112,37,-30,63,84,-38,-64,103,2,114,120,-89,
-2,-122,72,2,50,20,101,55,-108,-54,2,-31,-94,
23,-61,-3,-86,-107,57,-23,-105,41,0,-82,8,-17,
-64,37,-80,-5,104,58,47,-114]
现在使用 Conscrypt 方法-
public ECPublicKey loadECPublicKey(String encodedPublicKey) throws NoSuchProviderException, NoSuchAlgorithmException, InvalidKeySpecException, IOException {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
KeyFactory keyFactory = KeyFactory.getInstance("EC", "Conscrypt");
ECParameterSpec ecParameterSpec = ECUtil.getECParameterSpec(openSSLProvider, "prime256v1");
ECPoint ecPoint = ECUtil.decodePoint(decodedPublicKey, ecParameterSpec.getCurve());
ECPublicKeySpec pubSpec = new ECPublicKeySpec(ecPoint, ecParameterSpec);
ECPublicKey ecPublicKey = (ECPublicKey)keyFactory.generatePublic(pubSpec);
return ecPublicKey;
}
返回的getAlgorithm为EC。
返回的 getFormat 是 X.509。
这个的getEncoded值为-
[48,89,48,19,6,7,42,-122,72,-50,61,2,1,6,8,42,
-122,72,-50,61,3,1,7,3,66,0,4,0,-41,-4,96,23,
-89,77,-13,-1,-102,116,-28,-19,126,-94,-98,-75,
40,-112,37,-30,63,84,-38,-64,103,2,114,120,-89,
-2,-122,72,2,50,20,101,55,-108,-54,2,-31,-94,23,
-61,-3,-86,-107,57,-23,-105,41,0,-82,8,-17,-64,
37,-80,-5,104,58,47,-114]
忽略两个 EC 生成的密钥之间的差异。 BouncyCastle 在 ECDH KeyGenerator 中有什么作用？
DH 是一个 KeyAgreement，我假设它正在生成一个 EC 密钥并通过 DH KeyAgreement 运行 它-但是当 KeyGenerator 规范中没有指定任何内容时，它初始化为私钥的是什么？
还有。为什么当我将 EC 算法与两个提供商一起使用时，如果两者都使用 prime256v1 规范，我会得到相同算法的不同结果？我假设这些至少是相等的。
编辑：
ECUtil 来自sun.security.util.ECUtil。
对于在我的示例中 BC 和 Java 安全库共享同一个名称的任何 classes（例如 ECPoint）- 它始终是 Java 安全库。只有当 class 以 bouncycastle 路径为前缀（例如 org.bouncycastle.jce.interfaces.ECPublicKey）时，它才是 BC class。 openSSLProvider 是 Conscrypt 库中 OpenSSLProvider 的一个实例。
可以在此处找到该项目。
https://github.com/google/conscrypt
要安装的 pom 在这里-
<dependency>
<groupId>org.conscrypt</groupId>
<artifactId>conscrypt-openjdk-uber</artifactId>
<version>2.1.0</version>
</dependency>
///
import org.conscrypt.OpenSSLProvider;
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import sun.security.util.ECUtil;
Security.addProvider(new BouncyCastleProvider());
Security.addProvider(new OpenSSLProvider());
ECUtil.getECParameterSpec(new OpenSSLProvider, "prime256v1");
编辑编辑：
完整的最小可重现示例-
编辑编辑编辑：
示例现在包括手动加载 public 密钥，而不是使用 KeyFactory。
手动加载 BC public 密钥时，它的编码值与通过密钥工厂加载时 Conscrypt public 密钥的编码值匹配...
import org.bouncycastle.jce.ECNamedCurveTable;
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import org.bouncycastle.jce.provider.JCEECPublicKey;
import org.bouncycastle.jce.spec.ECNamedCurveParameterSpec;
import org.conscrypt.OpenSSLProvider;
import sun.security.util.ECUtil;
import java.io.IOException;
import java.security.*;
import java.security.interfaces.ECPublicKey;
import java.security.spec.ECParameterSpec;
import java.security.spec.ECPoint;
import java.security.spec.ECPublicKeySpec;
import java.security.spec.InvalidKeySpecException;
import java.util.*;
public class Main {
public static void main(String[] args) throws NoSuchAlgorithmException, NoSuchProviderException, InvalidKeySpecException, IOException {
Security.addProvider(new BouncyCastleProvider());
Security.addProvider(new OpenSSLProvider());
String pubKey = "BADX_GAXp03z_5p05O1-op61KJAl4j9U2sBnAnJ4p_6GSAIyFGU3lMoC4aIXw_2qlTnplykArgjvwCWw-2g6L44";
ECPublicKey publicKey = (ECPublicKey)loadPublicKey(pubKey, "Conscrypt");
org.bouncycastle.jce.interfaces.ECPublicKey publicKeyBC = (org.bouncycastle.jce.interfaces.ECPublicKey)loadPublicKey(pubKey, "BC");
org.bouncycastle.jce.interfaces.ECPublicKey publicKeyBC2 = (org.bouncycastle.jce.interfaces.ECPublicKey) loadPublicKeyManually(pubKey);
System.out.println(Arrays.toString(publicKey.getEncoded()));
System.out.println(Arrays.toString(publicKeyBC.getEncoded()));
System.out.println(Arrays.toString(publicKeyBC2.getEncoded()));
}
public static PublicKey loadPublicKey(String encodedPublicKey, String provider) throws NoSuchProviderException, NoSuchAlgorithmException, InvalidKeySpecException, IOException {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
KeyFactory keyFactory = KeyFactory.getInstance("EC", provider);
ECParameterSpec ecParameterSpec = ECUtil.getECParameterSpec(new OpenSSLProvider(), "prime256v1");
ECPoint ecPoint = ECUtil.decodePoint(decodedPublicKey, ecParameterSpec.getCurve());
ECPublicKeySpec pubSpec = new ECPublicKeySpec(ecPoint, ecParameterSpec);
ECPublicKey ecPublicKey = (ECPublicKey)keyFactory.generatePublic(pubSpec);
return ecPublicKey;
}
public static PublicKey loadPublicKeyManually(String encodedPublicKey) {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
ECNamedCurveParameterSpec parameterSpec = ECNamedCurveTable.getParameterSpec("prime256v1");
org.bouncycastle.jce.spec.ECPublicKeySpec ecPublicKeySpec = new org.bouncycastle.jce.spec.ECPublicKeySpec(
parameterSpec.getCurve().decodePoint(decodedPublicKey),
parameterSpec
);
org.bouncycastle.jce.interfaces.ECPublicKey ecPublicKey = new JCEECPublicKey(
"EC",
ecPublicKeySpec
);
return ecPublicKey;
}
}
两个 public 键表示 本质上 等价。两者都是 RFC 5280 中描述的 DER-encoded SubjectPublicKeyInfo 结构的实例。此结构不仅包含 public 密钥，还包含一些描述 public 密钥的算法上下文的元数据。对于其中一种形式，元数据仅声明上下文是“prime256v1”曲线。另一方面，提供了该曲线的所有参数。 public 键本身作为两种形式的最后一部分出现，如您所见，它们是相同的。
您拥有的是相同 public 密钥的总共 3 种不同的表示形式。 base-64 编码字符串只包含一个类型 4（未压缩）椭圆曲线点，根据 SEC 1 第 2.3.3 节编码。您在 sun.security.util.ECUtil class 中找到了一个未记录且不受支持的 API 将其转换为公钥。
我不完全确定你的问题是关于私钥的。对于包括 ECDH 在内的 DH 方案，私钥只是从基础组订单范围中“安全地”选择的一个整数。 public 键然后通过（在椭圆曲线意义上）该整数乘以曲线的基点来计算。结果public键也是曲线上的一个点
我有一个使用 BouncyCastle 作为安全提供程序的应用程序，但我想切换到另一个直接使用 OpenSSL (Conscrypt) 的应用程序。我遇到的问题是我正在使用 BouncyCastle 提供的 KeyGenerator 中的 ECDH "Keys"，但在我的其他库中没有类似的 KeyGenerator。
为了比较这两者，我将使用这两种方法和以下输入来解码点 -
为了可读性添加了换行符
BADX_GAXp03z_5p05O1-op61KJAl4j9U2sBnAnJ4p_6GSAIyFGU3lM
oC4aIXw_2qlTnplykArgjvwCWw-2g6L44
使用BouncyCastle方法-
public org.bouncycastle.jce.interfaces.ECPublicKey loadECPublicKeyBC(String encodedPublicKey) throws NoSuchProviderException, NoSuchAlgorithmException, InvalidKeySpecException, IOException {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
KeyFactory keyFactory = KeyFactory.getInstance("ECDH", "BC");
ECParameterSpec ecParameterSpec = ECUtil.getECParameterSpec(openSSLProvider, "prime256v1");
ECPoint ecPoint = ECUtil.decodePoint(decodedPublicKey, ecParameterSpec.getCurve());
ECPublicKeySpec pubSpec = new ECPublicKeySpec(ecPoint, ecParameterSpec);
org.bouncycastle.jce.interfaces.ECPublicKey ecPublicKey = (org.bouncycastle.jce.interfaces.ECPublicKey)keyFactory.generatePublic(pubSpec);
return ecPublicKey;
}
返回的getAlgorithm为EC。
返回的 getFormat 是 X.509.
这个的getEncoded值为-
[48,-126,1,51,48,-127,-20,6,7,42,-122,72,-50,61,2,1,48,
-127,-32,2,1,1,48,44,6,7,42,-122,72,-50,61,1,1,2,33,0,
-1,-1,-1,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,48,68,4,32,-1,-1,-1,-1,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-4,4,32,90,-58,53,-40,-86,58,-109,-25,-77,-21,-67,85,
118,-104,-122,-68,101,29,6,-80,-52,83,-80,-10,59,-50,60,
62,39,-46,96,75,4,65,4,107,23,-47,-14,-31,44,66,71,-8,-68,
-26,-27,99,-92,64,-14,119,3,125,-127,45,-21,51,-96,-12,
-95,57,69,-40,-104,-62,-106,79,-29,66,-30,-2,26,127,-101,
-114,-25,-21,74,124,15,-98,22,43,-50,51,87,107,49,94,-50,
-53,-74,64,104,55,-65,81,-11,2,33,0,-1,-1,-1,-1,0,0,0,0,-1,
-1,-1,-1,-1,-1,-1,-1,-68,-26,-6,-83,-89,23,-98,-124,-13,
-71,-54,-62,-4,99,37,81,2,1,1,3,66,0,4,0,-41,-4,96,23,-89,
77,-13,-1,-102,116,-28,-19,126,-94,-98,-75,40,-112,37,-30,
63,84,-38,-64,103,2,114,120,-89,-2,-122,72,2,50,20,101,55,
-108,-54,2,-31,-94,23,-61,-3,-86,-107,57,-23,-105,41,0,-82,
8,-17,-64,37,-80,-5,104,58,47,-114]
仅使用 BouncyCastle EC 算法（不是 ECDH）我得到-
[48,-126,1,51,48,-127,-20,6,7,42,-122,72,
-50,61,2,1,48,-127,-32,2,1,1,48,44,6,7,42,
-122,72,-50,61,1,1,2,33,0,-1,-1,-1,-1,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,48,68,4,32,-1,-1,-1,-1,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-4,4,32,90,-58,53,-40,
-86,58,-109,-25,-77,-21,-67,85,118,-104,-122,
-68,101,29,6,-80,-52,83,-80,-10,59,-50,60,62,
39,-46,96,75,4,65,4,107,23,-47,-14,-31,44,66,
71,-8,-68,-26,-27,99,-92,64,-14,119,3,125,
-127,45,-21,51,-96,-12,-95,57,69,-40,-104,-62,
-106,79,-29,66,-30,-2,26,127,-101,-114,-25,
-21,74,124,15,-98,22,43,-50,51,87,107,49,94,
-50,-53,-74,64,104,55,-65,81,-11,2,33,0,-1,-1,
-1,-1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-68,-26,
-6,-83,-89,23,-98,-124,-13,-71,-54,-62,-4,99,
37,81,2,1,1,3,66,0,4,0,-41,-4,96,23,-89,77,
-13,-1,-102,116,-28,-19,126,-94,-98,-75,40,
-112,37,-30,63,84,-38,-64,103,2,114,120,-89,
-2,-122,72,2,50,20,101,55,-108,-54,2,-31,-94,
23,-61,-3,-86,-107,57,-23,-105,41,0,-82,8,-17,
-64,37,-80,-5,104,58,47,-114]
现在使用 Conscrypt 方法-
public ECPublicKey loadECPublicKey(String encodedPublicKey) throws NoSuchProviderException, NoSuchAlgorithmException, InvalidKeySpecException, IOException {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
KeyFactory keyFactory = KeyFactory.getInstance("EC", "Conscrypt");
ECParameterSpec ecParameterSpec = ECUtil.getECParameterSpec(openSSLProvider, "prime256v1");
ECPoint ecPoint = ECUtil.decodePoint(decodedPublicKey, ecParameterSpec.getCurve());
ECPublicKeySpec pubSpec = new ECPublicKeySpec(ecPoint, ecParameterSpec);
ECPublicKey ecPublicKey = (ECPublicKey)keyFactory.generatePublic(pubSpec);
return ecPublicKey;
}
返回的getAlgorithm为EC。
返回的 getFormat 是 X.509。
这个的getEncoded值为-
[48,89,48,19,6,7,42,-122,72,-50,61,2,1,6,8,42,
-122,72,-50,61,3,1,7,3,66,0,4,0,-41,-4,96,23,
-89,77,-13,-1,-102,116,-28,-19,126,-94,-98,-75,
40,-112,37,-30,63,84,-38,-64,103,2,114,120,-89,
-2,-122,72,2,50,20,101,55,-108,-54,2,-31,-94,23,
-61,-3,-86,-107,57,-23,-105,41,0,-82,8,-17,-64,
37,-80,-5,104,58,47,-114]
忽略两个 EC 生成的密钥之间的差异。 BouncyCastle 在 ECDH KeyGenerator 中有什么作用？
DH 是一个 KeyAgreement，我假设它正在生成一个 EC 密钥并通过 DH KeyAgreement 运行 它-但是当 KeyGenerator 规范中没有指定任何内容时，它初始化为私钥的是什么？
还有。为什么当我将 EC 算法与两个提供商一起使用时，如果两者都使用 prime256v1 规范，我会得到相同算法的不同结果？我假设这些至少是相等的。
编辑：
ECUtil 来自sun.security.util.ECUtil。
对于在我的示例中 BC 和 Java 安全库共享同一个名称的任何 classes（例如 ECPoint）- 它始终是 Java 安全库。只有当 class 以 bouncycastle 路径为前缀（例如 org.bouncycastle.jce.interfaces.ECPublicKey）时，它才是 BC class。 openSSLProvider 是 Conscrypt 库中 OpenSSLProvider 的一个实例。
可以在此处找到该项目。
https://github.com/google/conscrypt
要安装的 pom 在这里-
<dependency>
<groupId>org.conscrypt</groupId>
<artifactId>conscrypt-openjdk-uber</artifactId>
<version>2.1.0</version>
</dependency>
///
import org.conscrypt.OpenSSLProvider;
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import sun.security.util.ECUtil;
Security.addProvider(new BouncyCastleProvider());
Security.addProvider(new OpenSSLProvider());
ECUtil.getECParameterSpec(new OpenSSLProvider, "prime256v1");
编辑编辑：
完整的最小可重现示例-
编辑编辑编辑：
示例现在包括手动加载 public 密钥，而不是使用 KeyFactory。
手动加载 BC public 密钥时，它的编码值与通过密钥工厂加载时 Conscrypt public 密钥的编码值匹配...
import org.bouncycastle.jce.ECNamedCurveTable;
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import org.bouncycastle.jce.provider.JCEECPublicKey;
import org.bouncycastle.jce.spec.ECNamedCurveParameterSpec;
import org.conscrypt.OpenSSLProvider;
import sun.security.util.ECUtil;
import java.io.IOException;
import java.security.*;
import java.security.interfaces.ECPublicKey;
import java.security.spec.ECParameterSpec;
import java.security.spec.ECPoint;
import java.security.spec.ECPublicKeySpec;
import java.security.spec.InvalidKeySpecException;
import java.util.*;
public class Main {
public static void main(String[] args) throws NoSuchAlgorithmException, NoSuchProviderException, InvalidKeySpecException, IOException {
Security.addProvider(new BouncyCastleProvider());
Security.addProvider(new OpenSSLProvider());
String pubKey = "BADX_GAXp03z_5p05O1-op61KJAl4j9U2sBnAnJ4p_6GSAIyFGU3lMoC4aIXw_2qlTnplykArgjvwCWw-2g6L44";
ECPublicKey publicKey = (ECPublicKey)loadPublicKey(pubKey, "Conscrypt");
org.bouncycastle.jce.interfaces.ECPublicKey publicKeyBC = (org.bouncycastle.jce.interfaces.ECPublicKey)loadPublicKey(pubKey, "BC");
org.bouncycastle.jce.interfaces.ECPublicKey publicKeyBC2 = (org.bouncycastle.jce.interfaces.ECPublicKey) loadPublicKeyManually(pubKey);
System.out.println(Arrays.toString(publicKey.getEncoded()));
System.out.println(Arrays.toString(publicKeyBC.getEncoded()));
System.out.println(Arrays.toString(publicKeyBC2.getEncoded()));
}
public static PublicKey loadPublicKey(String encodedPublicKey, String provider) throws NoSuchProviderException, NoSuchAlgorithmException, InvalidKeySpecException, IOException {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
KeyFactory keyFactory = KeyFactory.getInstance("EC", provider);
ECParameterSpec ecParameterSpec = ECUtil.getECParameterSpec(new OpenSSLProvider(), "prime256v1");
ECPoint ecPoint = ECUtil.decodePoint(decodedPublicKey, ecParameterSpec.getCurve());
ECPublicKeySpec pubSpec = new ECPublicKeySpec(ecPoint, ecParameterSpec);
ECPublicKey ecPublicKey = (ECPublicKey)keyFactory.generatePublic(pubSpec);
return ecPublicKey;
}
public static PublicKey loadPublicKeyManually(String encodedPublicKey) {
Base64.Decoder base64Decoder = Base64.getUrlDecoder();
byte[] decodedPublicKey = base64Decoder.decode(encodedPublicKey);
ECNamedCurveParameterSpec parameterSpec = ECNamedCurveTable.getParameterSpec("prime256v1");
org.bouncycastle.jce.spec.ECPublicKeySpec ecPublicKeySpec = new org.bouncycastle.jce.spec.ECPublicKeySpec(
parameterSpec.getCurve().decodePoint(decodedPublicKey),
parameterSpec
);
org.bouncycastle.jce.interfaces.ECPublicKey ecPublicKey = new JCEECPublicKey(
"EC",
ecPublicKeySpec
);
return ecPublicKey;
}
}
两个 public 键表示 本质上 等价。两者都是 RFC 5280 中描述的 DER-encoded SubjectPublicKeyInfo 结构的实例。此结构不仅包含 public 密钥，还包含一些描述 public 密钥的算法上下文的元数据。对于其中一种形式，元数据仅声明上下文是“prime256v1”曲线。另一方面，提供了该曲线的所有参数。 public 键本身作为两种形式的最后一部分出现，如您所见，它们是相同的。
您拥有的是相同 public 密钥的总共 3 种不同的表示形式。 base-64 编码字符串只包含一个类型 4（未压缩）椭圆曲线点，根据 SEC 1 第 2.3.3 节编码。您在 sun.security.util.ECUtil class 中找到了一个未记录且不受支持的 API 将其转换为公钥。
我不完全确定你的问题是关于私钥的。对于包括 ECDH 在内的 DH 方案，私钥只是从基础组订单范围中“安全地”选择的一个整数。 public 键然后通过（在椭圆曲线意义上）该整数乘以曲线的基点来计算。结果public键也是曲线上的一个点