Why is the ECC-DH Symmetric Key Of This Site Diffe

问题:

I am using (this site's) Javascript library and OpenSSL Ruby to compute the symmetric key of Elliptic Curve Diffie Hellman.

However, from my results, OpenSSL Ruby only generated one key unlike that on the site which has X and Y symmetric keys. I am baffled as my OpenSSL symmetric key doesn't match either one of those x and y on the site.

The symmetric(shared secret) keys I got using secp224r1 curve:

Ruby OpenSSL

   13506351678569412185536677668115375188438201041599149052762191980775

Using Site's JS Library

x: 26210366144026557327555572210249241206666031403062020900473236895358
y: 19676808255388748321882118528911150828003358302170965920476006073155

My questions are:

1) Why does OpenSSL Ruby yields only one key while that size yields two keys: x and y (as I've assumed x and y won't be concatenated with each other since the bitsize will be too long when compared to the Ruby symmetric key)

2) Is there a way to convert the two symmetric keys (OpenSSL and JSBN-EC library above) from one another? All my attempts to convert failed.

I've been struggling for a week now implementing Ruby OpenSSL with that JSBN-EC library. I've also tried (SJCL library) but similar results (symmetric keys don't match). Please help.

回答1:

I've managed to work it out now with working symmetric keys on client (JSBN-EC) and on server OpenSSL Ruby

I found out that my problem actually lies in the code itself. After fixing it, I've ended up with a symmetric key on OpenSSL Ruby as follows:

#Ruby: OpenSSL
...
...
symm_key = ec.dh_compute_key(point)
symm_key.unpack('B*').first.to_i(2) #Converts to binary, then to integer
#--> 6922380353406615622038660570577625762884344085425862813095878420328

While on the client side using JSBN-EC

#Javascript: JSBN-EC
...
...
var curve = get_curve();
var P = new ECPointFp(curve,
curve.fromBigInteger(server_pub_key_x),
curve.fromBigInteger(server_pub_key_y));
var a = client_priv_key;
var S = P.multiply(a);

console.log('SYMM_KEY X: '+S.getX().toBigInteger().toString());
//--> 6922380353406615622038660570577625762884344085425862813095878420328
console.log('SYMM_KEY Y: '+S.getY().toBigInteger().toString());
//--> 14426877769799867628378883482085635535383864283889042780773103726343

Therefore from the looks of it, the symmetric key that matches the Ruby OpenSSL value is the X value of the JSBN-EC symmetric key

6922380353406615622038660570577625762884344085425862813095878420328
==
6922380353406615622038660570577625762884344085425862813095878420328

I don't know what the Y value is now for. Looks like I won't need it. Cheers! :)