P-521(Web Crypto-Api)/secp521r1(NodeJS Crypto)的ECDH生成一个略有不同的

Question

我已经从NodeJS 生成了一个带有ECDH的公钥和私钥对

function _genPrivateKey(curveName = "secp384r1", encoding = "hex") {
const private_0 = crypto.createECDH(curveName);
private_0.generateKeys();
return private_0.getPrivateKey().toString(encoding);
}

BOB私钥

9d0c809d692c83c7d8d1355205dd78e679066fd9c15d12cdea3e1103b041873765264351e8939083b876d89d423301d8486a956da455ddbdc4a91ef60af7dd2325

BOB公钥

[hex] 
0400d7a342e89f501e1cd8224e2463ef1ad057c9b64bf45c1d3627cc1f06c055c80f75c2013c27b63dc984b467ecfc5202cf9a126ef1f1487e92b9acfb52abaeb7022e01f4259918ca34f442214a31d1bad329f9be1c67ce98af6621f622e44887264e856ee8c664a51e56f24008c932ee1cb5514c02d03ba27f6b6a1cd0aa0f8eac261250
[jwk] {
key_ops: [ 'deriveKey' ],
ext: true,
kty: 'EC',
x:'ANejQuifUB4c2CJOJGPvGtBXybZL9FwdNifMHwbAVcgPdcIBPCe2PcmEtGfs_FICz5oSbvHxSH6Suaz7UquutwIu',
y:'AfQlmRjKNPRCIUox0brTKfm-HGfOmK9mIfYi5EiHJk6FbujGZKUeVvJACMky7hy1UUwC0Duif2tqHNCqD46sJhJQ',
crv: 'P-521'
}

以及来自具有web Crypto API的网页的Alice的密钥

const generateAlicesKeyPair = window.crypto.subtle.generateKey({
name: "ECDH",
namedCurve: "P-521"
},
false,
["deriveBits"]
);

ALICE公钥

04000eefa90c3de22e79e6742f807806a603059d16afaa9f1bc69f420050aae100d0006e6510fe17a8f6767fe1e69bada039175ef5a375e30af4085e4315cf7527655f00ed9a39552a5f9170cc7626c1f4584d0e6de17870e336bcc5b6e251e3ea2c7cd9633e1afe2f9aee5f9a7445d38218c20695cc7ba2a462b67ce39a060e6464133609

---

当我试图推导shared key时，发生了一件奇怪的事情，密钥的末尾有不同的位。

NodeJS:

function _getSharedSecret(privateKey, publicKey, curveName = "secp521r1", encoding = "hex") {
const private_0 = crypto.createECDH(curveName);
private_0.setPrivateKey(privateKey, encoding);
const _sharedSecret = private_0.computeSecret(publicKey, encoding);
return _sharedSecret
};

Web加密API

const sharedSecret = await window.crypto.subtle.deriveBits({
name: "ECDH",
namedCurve: "P-521",
public: publicKey
},
privateKey, 
521
);

结果：

//NodeJS: 
0089b99212c9348a6fd3aa78225a773a90ef45f57bbd10dc86d8e52fa26662c550b56d2368ee358ab240ceec10191b6cdd7d09bb0a8763ea48a487a5676ebdf7af[eb]
//WebCryptoAPI:
0089b99212c9348a6fd3aa78225a773a90ef45f57bbd10dc86d8e52fa26662c550b56d2368ee358ab240ceec10191b6cdd7d09bb0a8763ea48a487a5676ebdf7af[80]

这种情况仅发生在p-521/secp521r1曲线上，而不发生在
p-256/secp256r1-384/secp384r1曲线上

Answer 1

使用第三个库(Python，Cryptography库(进行检查表明NodeJS结果是正确的(即以0xEB结尾的结果(。

p-521的X和Y坐标由66个字节表示(521位＝65个字节+1位((此处为s(。共享秘密是曲线点的X坐标(此处为s(，因此也具有66字节＝528位。此值将在deriveBits()中的WebCrypto API实现中指定为共享机密的长度。

如果指定521位，则仅考虑最高位(为0xEB设置(，其余位将设置为0，从而得到值0x80。

以下代码说明了这一点(请注意，该脚本不是在Firefox下运行的，这可能是一个错误(：

(async () => {
await getSharedSecret(521);
await getSharedSecret(528);
})();
async function getSharedSecret(bits) {
var bobPrivateKeyJwk = {   
kty: "EC",
crv: "P-521",
x:'ANejQuifUB4c2CJOJGPvGtBXybZL9FwdNifMHwbAVcgPdcIBPCe2PcmEtGfs_FICz5oSbvHxSH6Suaz7UquutwIu',
y:'AfQlmRjKNPRCIUox0brTKfm-HGfOmK9mIfYi5EiHJk6FbujGZKUeVvJACMky7hy1UUwC0Duif2tqHNCqD46sJhJQ',
d: "AJ0MgJ1pLIPH2NE1UgXdeOZ5Bm_ZwV0Szeo-EQOwQYc3ZSZDUeiTkIO4dtidQjMB2EhqlW2kVd29xKke9gr33SMl",
ext: true,
}
var alicePublicKeyBuffer = typedArray('04000eefa90c3de22e79e6742f807806a603059d16afaa9f1bc69f420050aae100d0006e6510fe17a8f6767fe1e69bada039175ef5a375e30af4085e4315cf7527655f00ed9a39552a5f9170cc7626c1f4584d0e6de17870e336bcc5b6e251e3ea2c7cd9633e1afe2f9aee5f9a7445d38218c20695cc7ba2a462b67ce39a060e6464133609');    
var privateKey = await window.crypto.subtle.importKey(
"jwk", 
bobPrivateKeyJwk,
{ name: "ECDH", namedCurve: "P-521" },
true, 
["deriveKey", "deriveBits"] 
);
var publicKey = await window.crypto.subtle.importKey(
"raw", 
alicePublicKeyBuffer.buffer,
{ name: "ECDH", namedCurve: "P-521"},
true, 
[] 
);
var sharedSecret = await window.crypto.subtle.deriveBits(
{ name: "ECDH", namedCurve: "P-521", public: publicKey },
privateKey, 
bits 
);
console.log("Bob's shared secret:n", buf2hex(sharedSecret).replace(/(.{48})/g,'$1n'));
}; 
function typedArray(hex) {
return new Uint8Array(hex.match(/[da-f]{2}/gi).map(function (h) { // from: https://stackoverflow.com/a/43131635
return parseInt(h, 16)
}))
}
function buf2hex(buffer) {
return Array.prototype.map.call(new Uint8Array(buffer), x => ('00' + x.toString(16)).slice(-2)).join(''); // from: https://stackoverflow.com/a/40031979/9014097 
}

对于曲线p-256和p-384，问题不会发生，因为素数字段已经是8的倍数(分别为32字节和48字节(。