DHKE 示例

下面用一个简单的 Python 代码示例演示经典的 Diffie–Hellman 密钥交换（DHKE）算法。

首先，安装 Python 软件包 PyDHE：

pip install pyDHE

接下来，编写 DHKE 示例代码：

import pyDHE

alice = pyDHE.new()
alicePubKey = alice.getPublicKey()
print("Alice public key:", hex(alicePubKey))

bob = pyDHE.new()
bobPubKey = bob.getPublicKey()
print("Bob public key:", hex(bobPubKey))

print("Now exchange the public keys (e.g. through Internet)")

aliceSharedKey = alice.update(bobPubKey)
print("Alice shared key:", hex(aliceSharedKey))

bobSharedKey = bob.update(alicePubKey)
print("Bob shared key:", hex(bobSharedKey))

print("Equal shared keys:", aliceSharedKey == bobSharedKey)

运行上述代码示例：https://repl.it/@nakov/Diffie-Hellman-Key-Exchange-in-Python。

运行上述代码时，它会生成并打印两个 2048 位公钥（分别属于 Alice 和 Bob）。假设 Alice 和 Bob 已经交换了公钥（例如通过互联网互相发送）。Alice 收到 Bob 的公钥后，可以将其与自己的私钥结合来计算共享秘密。同样，Bob 收到 Alice 的公钥后，也可以将其与自己的私钥结合来计算共享秘密。上述示例的输出表明，共享秘密始终是同一个数字（2048 位整数）：

Alice public key: 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
Bob public key: 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
Now exchange the public keys (e.g. through Internet)
Alice shared key: 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
Bob shared key: 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
Equal shared keys: True

请注意，由于密钥生成过程具有随机性，你的输出会有所不同。上述代码使用 RFC 3526（组 14）规定的 2048 位公钥和私钥。可以指定不同的 RFC 3526 组（例如 8192 位密钥对应组 18），以更改 DHKE 密钥长度（从 1536 位到 8192 位）。例如，修改以下两行：

alice = pyDHE.new(group=18)
bob = pyDHE.new(group=18)

运行上述代码示例：https://repl.it/@nakov/DHKE-Example-in-Python。

上述更改会切换到 8192 位密钥，并显著降低计算速度。输出如下：

Alice public key: 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
Bob public key: 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
Now exchange the public keys (e.g. through Internet)
Alice shared key: 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
Bob shared key: 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
Equal shared keys: True

请尽情修改和试验上述代码，以学习 DHKE 协议。