使用 Python 生成 Java 兼容的 Diffie-Hellman

Question

我正在尝试重写 Python 中的以下代码。原始代码是使用 sjcl 库在 Javascript 中编写的。

// Inputs
var serverPubX = "WIUBDotrk02Rk/apL11jQPbmX0quyaYz2EIkGUlVf7s=";
var serverPubY = "diZ2CbfSUy5Kr82OIfd4Ajusq2K+/kjGZ7ymcqVwn2k=";

// The code
var serverPubXBits = sjcl.codec.base64.toBits(serverPubX);
var serverPubYBits = sjcl.codec.base64.toBits(serverPubY);
var serverPubKeyPointBits = serverPubXBits.concat(serverPubYBits);

var serverPubKey = new sjcl.ecc.elGamal.publicKey(
    sjcl.ecc.curves.c256, serverPubKeyPointBits);

var clientKeys = sjcl.ecc.elGamal.generateKeys(256, 1);

// What I need:
var sharedKey = clientKeys.sec.dhJavaEc(serverPubKey);

我的主要问题是 dhJavaEc 功能。根据 sjcl 文档，它是 Java compatible Diffie-Hellmann function。但是我在 pycryptodome 库中找不到任何等效的东西。

我检查了 dhJavaEc 代码，这是它的作用：

// Looks like it converts the server key to Jacobian and then multiply it by client key
serverPubKey.J.toJac().mult(clientKeys.sec.I, serverPubKey.J).toAffine().x.toBits()

// serverPubKey.J is the X and Y keys concatenated:
sjcl.codec.base64.fromBits(serverPubKey.J.toBits())
"WIUBDotrk02Rk/apL11jQPbmX0quyaYz2EIkGUlVf7t2JnYJt9JTLkqvzY4h93gCO6yrYr7+SMZnvKZypXCfaQ=="

// In my example, clientKeys.sec.I is this:
sjcl.codec.base64.fromBits(clientKeys.sec.I.toBits())
"zIhDVlFUpWQiRP+bjyEIhSLq8rcB8+XInXGhm6JGcVI="

// And the calculated key is:
sjcl.codec.base64.fromBits(sharedKey)
"ZBin/RV1qnfKoIuel+5fzv1y8rn3UZkMPO3pXva3VzQ="

如何使用 Python 生成等效的“sharedKey”？

Answer 1

PyCryptodome目前似乎不支持ECDH，见Future plans. An alternative is the Cryptography library, see Elliptic Curve Key Exchange algorithm.

库期望私钥为 int，public 未压缩格式的密钥为 bytes object。未压缩格式由串联的 x 和 y 坐标组成，前面是 0x04 字节。

sjcl.ecc.curves.c256 定义 secp256r1（又名 prime256v1 又名 NIST P-256 ).

然后在 Python 中使用 密码学 的可能实现是：

from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives.asymmetric import ec
import base64

curve = ec.SECP256R1()

clientKey = 'zIhDVlFUpWQiRP+bjyEIhSLq8rcB8+XInXGhm6JGcVI='
privateKeyInt = int.from_bytes(base64.b64decode(clientKey), byteorder='big', signed=False)
privateKey = ec.derive_private_key(privateKeyInt, curve, default_backend())

serverPubKey = 'WIUBDotrk02Rk/apL11jQPbmX0quyaYz2EIkGUlVf7t2JnYJt9JTLkqvzY4h93gCO6yrYr7+SMZnvKZypXCfaQ=='
publicKeyUncomp = b'\x04' + base64.b64decode(serverPubKey)
publicKey = ec.EllipticCurvePublicKey.from_encoded_point(curve, publicKeyUncomp)

sharedSecret = privateKey.exchange(ec.ECDH(), publicKey)
print(base64.b64encode(sharedSecret).decode('utf8')) # ZBin/RV1qnfKoIuel+5fzv1y8rn3UZkMPO3pXva3VzQ=

生成与 JavaScript 代码相同的共享密钥。

使用 Python 生成 Java 兼容的 Diffie-Hellman

Generate a Java compatible Diffie-Hellman using Python

python

cryptography

elliptic-curve

diffie-hellman

如何使用 Python 生成等效的“sharedKey”？