为什么双方的秘密不一样？

Question

我正在尝试理解diffie hellman密钥交换是如何工作的，并编写了一个简单的node.js程序来进行测试：

var crypto = require("crypto");

//create a public & private key for alice
var Alice = crypto.createDiffieHellman(512);
Alice.generateKeys();

//create a public & private key for bob
var Bob = crypto.createDiffieHellman(512);
Bob.generateKeys();

//let bob and alice compute the shared secret
console.log(Alice.computeSecret(Bob.getPublicKey()).toString("hex"));
console.log(Bob.computeSecret(Alice.getPublicKey()).toString("hex"));

如果我理解this维基百科文章中的正确图形，那么这两个秘密应该是相同的。但他们永远不会，为什么？

Answer 1

啊，我已经找到了解决方案：

var crypto = require("crypto");

var prime = crypto.createDiffieHellman(512).getPrime();

//create a public & private key for alice
var Alice = crypto.createDiffieHellman(prime);
Alice.generateKeys();

//create a public & private key for bob
var Bob = crypto.createDiffieHellman(prime);
Bob.generateKeys();

//let bob and alice compute the shared secret
console.log(Alice.computeSecret(Bob.getPublicKey()).toString("hex"));
console.log(Bob.computeSecret(Alice.getPublicKey()).toString("hex"));