blocks|key|527864|text|查看C#的Bouncy+Castle库，它包含ECDH和ECDSA。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|527865|entityMap|0|LINK|mutability|MUTABLE|url|http://www.bouncycastle.org/csharp/^0|5|D|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

Check out the <a href="http://www.bouncycastle.org/csharp/" rel="noreferrer">Bouncy Castle</a> library for C#, it has ECDH and ECDSA.

blocks|key|4592524|text|.NET框架已经包含了Diffie-Hellman算法，这是一种椭圆曲线加密算法。在System.Security.Cryptography.ECDiffieHellmanCng下查看。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|4592525|entityMap|0|LINK|mutability|MUTABLE|url|http://msdn.microsoft.com/en-us/library/system.security.cryptography.ecdiffiehellmancng.aspx^0|16|1B|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

The .NET Framework already includes Diffie-Hellman, which is an elliptic curve crypto algorithm. Look under <a href="http://msdn.microsoft.com/en-us/library/system.security.cryptography.ecdiffiehellmancng.aspx" rel="noreferrer">System.Security.Cryptography.ECDiffieHellmanCng</a>.

blocks|key|1124787|text|通常使用ECC进行加密的方法是使用“临时性静态Diffie-Hellman”。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1124788|它是这样工作的：|1124789|1124790|获取目标接收者的公钥(可能来自证书)。这是静态密钥。|unordered-list-item|1124791|会生成一个临时的ECDH密钥对。这是临时密钥对。|1124792|使用密钥生成共享对称密钥。|1124793|使用对称密钥对数据进行加密。|1124794|将加密数据与来自临时密钥对的公钥一起传输。|1124795|1124796|接收者现在可以使用临时公钥和他自己的静态私钥来重新创建对称密钥并解密数据。|1124797|您可以在Standards+for+Efficient+Cryptography:+SEC+1:+Elliptic+Curve+Cryptography第5.1.3节中阅读更多内容。|offset|length|1124798|entityMap|0|LINK|mutability|MUTABLE|url|http://www.secg.org/sec1-v2.pdf^0|0|0|0|0|0|0|0|0|0|0|4|20|0|0^^$0|@$1|2|3|4|5|6|7|14|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|15|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|16|8|@]|9|@]|A|$]]|$1|E|3|F|5|G|7|17|8|@]|9|@]|A|$]]|$1|H|3|I|5|G|7|18|8|@]|9|@]|A|$]]|$1|J|3|K|5|G|7|19|8|@]|9|@]|A|$]]|$1|L|3|M|5|G|7|1A|8|@]|9|@]|A|$]]|$1|N|3|O|5|G|7|1B|8|@]|9|@]|A|$]]|$1|P|3|-4|5|6|7|1C|8|@]|9|@]|A|$]]|$1|Q|3|R|5|6|7|1D|8|@]|9|@]|A|$]]|$1|S|3|T|5|6|7|1E|8|@]|9|@$U|1F|V|1G|1|1H]]|A|$]]|$1|W|3|-4|5|6|7|1I|8|@]|9|@]|A|$]]]|X|$Y|$5|Z|10|11|A|$12|13]]]]

The way you usually use ECC for encryption is by using "Ephemeral-Static Diffie-Hellman".

It works this way:

<ul>
<li>Take the intended receivers public key (perhaps from a certificate). This is the static key.</li>
<li>Generate a temporary ECDH keypair. This is the ephemeral keypair.</li>
<li>Use the keys to generate a shared symmetric key.</li>
<li>Encrypt the data with the symmetric key.</li>
<li>Transmit the encrypted data together with the public key from the ephemeral keypair.</li>
</ul>

The receiver can now use the ephemeral public key and his own static private key to recreate the symmetric key and decrypt the data.

You can read more in <a href="http://www.secg.org/sec1-v2.pdf" rel="nofollow noreferrer">Standards for Efficient Cryptography: SEC 1: Elliptic Curve Cryptography</a> section 5.1.3.

blocks|key|4592631|text|看一看SecureBlackBox组件|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|4592632|entityMap|0|LINK|mutability|MUTABLE|url|http://www.eldos.com/sbb/desc-pki-spec.php^0|3|E|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

Have a look at <a href="http://www.eldos.com/sbb/desc-pki-spec.php" rel="nofollow noreferrer">SecureBlackBox</a> components

blocks|key|4592681|text|type|unstyled|depth|inlineStyleRanges|entityRanges|data|4592682|太棒了！我试过了，但找不到如何使用它来加密消息。似乎没有任何“加密”功能|blockquote|4592683|4592684|4592685|这是System.Security.Cryptography.ECDiffieHellmanCng的MSDN示例。|offset|length|style|CODE|4592686|using+System;
using+System.IO;
using+System.Security.Cryptography;
using+System.Text;


class+Alice
{
++++public+static+byte[]+alicePublicKey;

++++public+static+void+Main(string[]+args)
++++{
++++++++using+(ECDiffieHellmanCng+alice+=+new+ECDiffieHellmanCng())
++++++++{

++++++++++++alice.KeyDerivationFunction+=+ECDiffieHellmanKeyDerivationFunction.Hash;
++++++++++++alice.HashAlgorithm+=+CngAlgorithm.Sha256;
++++++++++++alicePublicKey+=+alice.PublicKey.ToByteArray();
++++++++++++Bob+bob+=+new+Bob();
++++++++++++CngKey+k+=+CngKey.Import(bob.bobPublicKey,+CngKeyBlobFormat.EccPublicBlob);
++++++++++++byte[]+aliceKey+=+alice.DeriveKeyMaterial(CngKey.Import(bob.bobPublicKey,+CngKeyBlobFormat.EccPublicBlob));
++++++++++++byte[]+encryptedMessage+=+null;
++++++++++++byte[]+iv+=+null;
++++++++++++Send(aliceKey,+"Secret+message",+out+encryptedMessage,+out+iv);
++++++++++++bob.Receive(encryptedMessage,+iv);
++++++++}

++++}

++++private+static+void+Send(byte[]+key,+string+secretMessage,+out+byte[]+encryptedMessage,+out+byte[]+iv)
++++{
++++++++using+(Aes+aes+=+new+AesCryptoServiceProvider())
++++++++{
++++++++++++aes.Key+=+key;
++++++++++++iv+=+aes.IV;

++++++++++++//+Encrypt+the+message+
++++++++++++using+(MemoryStream+ciphertext+=+new+MemoryStream())
++++++++++++using+(CryptoStream+cs+=+new+CryptoStream(ciphertext,+aes.CreateEncryptor(),+CryptoStreamMode.Write))
++++++++++++{
++++++++++++++++byte[]+plaintextMessage+=+Encoding.UTF8.GetBytes(secretMessage);
++++++++++++++++cs.Write(plaintextMessage,+0,+plaintextMessage.Length);
++++++++++++++++cs.Close();
++++++++++++++++encryptedMessage+=+ciphertext.ToArray();
++++++++++++}
++++++++}
++++}

}
public+class+Bob+
{
++++public+byte[]+bobPublicKey;
++++private+byte[]+bobKey;
++++public+Bob()
++++{
++++++++using+(ECDiffieHellmanCng+bob+=+new+ECDiffieHellmanCng())
++++++++{

++++++++++++bob.KeyDerivationFunction+=+ECDiffieHellmanKeyDerivationFunction.Hash;
++++++++++++bob.HashAlgorithm+=+CngAlgorithm.Sha256;
++++++++++++bobPublicKey+=+bob.PublicKey.ToByteArray();
++++++++++++bobKey+=+bob.DeriveKeyMaterial(CngKey.Import(Alice.alicePublicKey,+CngKeyBlobFormat.EccPublicBlob));

++++++++}
++++}

++++public+void+Receive(byte[]+encryptedMessage,+byte[]+iv)
++++{

++++++++using+(Aes+aes+=+new+AesCryptoServiceProvider())
++++++++{
++++++++++++aes.Key+=+bobKey;
++++++++++++aes.IV+=+iv;
++++++++++++//+Decrypt+the+message+
++++++++++++using+(MemoryStream+plaintext+=+new+MemoryStream())
++++++++++++{
++++++++++++++++using+(CryptoStream+cs+=+new+CryptoStream(plaintext,+aes.CreateDecryptor(),+CryptoStreamMode.Write))
++++++++++++++++{
++++++++++++++++++++cs.Write(encryptedMessage,+0,+encryptedMessage.Length);
++++++++++++++++++++cs.Close();
++++++++++++++++++++string+message+=+Encoding.UTF8.GetString(plaintext.ToArray());
++++++++++++++++++++Console.WriteLine(message);
++++++++++++++++}
++++++++++++}
++++++++}
++++}

}|code-block|syntax|javascript|4592687|entityMap|0|LINK|mutability|MUTABLE|url|http://msdn.microsoft.com/en-us/library/system.security.cryptography.ecdiffiehellmancng.aspx^0|0|0|0|0|2|1B|2|1B|0|0|0^^$0|@$1|2|3|-4|4|5|6|Y|7|@]|8|@]|9|$]]|$1|A|3|B|4|C|6|Z|7|@]|8|@]|9|$]]|$1|D|3|-4|4|5|6|10|7|@]|8|@]|9|$]]|$1|E|3|-4|4|5|6|11|7|@]|8|@]|9|$]]|$1|F|3|G|4|5|6|12|7|@$H|13|I|14|J|K]]|8|@$H|15|I|16|1|17]]|9|$]]|$1|L|3|M|4|N|6|18|7|@]|8|@]|9|$O|P]]|$1|Q|3|-4|4|5|6|19|7|@]|8|@]|9|$]]]|R|$S|$4|T|U|V|9|$W|X]]]]

<blockquote>
 Great! I tried it but cant find how to use it to encrypt a message.
 Doesn't seem to have any "Encrypt" function
</blockquote>

This the MSDN sample for <a href="http://msdn.microsoft.com/en-us/library/system.security.cryptography.ecdiffiehellmancng.aspx" rel="nofollow"><code>System.Security.Cryptography.ECDiffieHellmanCng</code></a>.

<pre><code>using System;
using System.IO;
using System.Security.Cryptography;
using System.Text;


class Alice
{
 public static byte[] alicePublicKey;

 public static void Main(string[] args)
 {
 using (ECDiffieHellmanCng alice = new ECDiffieHellmanCng())
 {

 alice.KeyDerivationFunction = ECDiffieHellmanKeyDerivationFunction.Hash;
 alice.HashAlgorithm = CngAlgorithm.Sha256;
 alicePublicKey = alice.PublicKey.ToByteArray();
 Bob bob = new Bob();
 CngKey k = CngKey.Import(bob.bobPublicKey, CngKeyBlobFormat.EccPublicBlob);
 byte[] aliceKey = alice.DeriveKeyMaterial(CngKey.Import(bob.bobPublicKey, CngKeyBlobFormat.EccPublicBlob));
 byte[] encryptedMessage = null;
 byte[] iv = null;
 Send(aliceKey, "Secret message", out encryptedMessage, out iv);
 bob.Receive(encryptedMessage, iv);
 }

 }

 private static void Send(byte[] key, string secretMessage, out byte[] encryptedMessage, out byte[] iv)
 {
 using (Aes aes = new AesCryptoServiceProvider())
 {
 aes.Key = key;
 iv = aes.IV;

 // Encrypt the message 
 using (MemoryStream ciphertext = new MemoryStream())
 using (CryptoStream cs = new CryptoStream(ciphertext, aes.CreateEncryptor(), CryptoStreamMode.Write))
 {
 byte[] plaintextMessage = Encoding.UTF8.GetBytes(secretMessage);
 cs.Write(plaintextMessage, 0, plaintextMessage.Length);
 cs.Close();
 encryptedMessage = ciphertext.ToArray();
 }
 }
 }

}
public class Bob 
{
 public byte[] bobPublicKey;
 private byte[] bobKey;
 public Bob()
 {
 using (ECDiffieHellmanCng bob = new ECDiffieHellmanCng())
 {

 bob.KeyDerivationFunction = ECDiffieHellmanKeyDerivationFunction.Hash;
 bob.HashAlgorithm = CngAlgorithm.Sha256;
 bobPublicKey = bob.PublicKey.ToByteArray();
 bobKey = bob.DeriveKeyMaterial(CngKey.Import(Alice.alicePublicKey, CngKeyBlobFormat.EccPublicBlob));

 }
 }

 public void Receive(byte[] encryptedMessage, byte[] iv)
 {

 using (Aes aes = new AesCryptoServiceProvider())
 {
 aes.Key = bobKey;
 aes.IV = iv;
 // Decrypt the message 
 using (MemoryStream plaintext = new MemoryStream())
 {
 using (CryptoStream cs = new CryptoStream(plaintext, aes.CreateDecryptor(), CryptoStreamMode.Write))
 {
 cs.Write(encryptedMessage, 0, encryptedMessage.Length);
 cs.Close();
 string message = Encoding.UTF8.GetString(plaintext.ToArray());
 Console.WriteLine(message);
 }
 }
 }
 }

}
</code></pre>

Please can you suggest any implementation of elliptical curve cryptography to be used on .NET platform?

Also if you have used them, can you tell me the recommended curves that should be used?

[EDIT]

As @FatCat mentioned, its implementation is available in .NET framework 3.5 but that is only available on windows vista. Can you please suggest another way/library to use it?

.NET implementation (libraries) of elliptic curve cryptography

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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你能推荐一些在.NET平台上使用的椭圆曲线密码的实现吗？另外，如果你用过它们，你能告诉我应该使用的推荐曲线吗？编辑正如@FatCat提到的，它的实现在.NET Framework3.5中可用，但只在windows vista上可用。你能推荐另一种方式/库来使用它吗？

问椭圆曲线密码算法的.NET实现(库)
EN

回答 5

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