How to use Elliptic Curves Diffie-Hellman with SJC

2019-06-07 10:45发布

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问题:

Using Elliptic-Curves Diffie-Hellman, I want to connect SLCL - JS (documentation) on client and OpenSSL - Ruby (documentation) on server.

I found a similar question here but it wasn't really answered properly and it was also not what I am really looking for since it uses sjcl.ecc.elGamal.generateKeys(384, 10) whereas I am hoping of using sjcl.ecc.curves['c384'] <- NIST

Nevertheless, I still used and modified his code to test because I had problems using sjcl.ecc.curves['c384'] producing a single public point-key, and this is what I came up with.

//Javascript
keypair = sjcl.ecc.elGamal.generateKeys(384, 10);
console.log(keypair.pub._point.toBits()); //Changed from his serialize()

This outputs to

[-1992414123, 638637875, 1917312913, 73389700, -425224557, 743777818, 970253455, 723842951, -1751664279, 982132367, -1949786746, 1067402923, -869929568, 157928816, 1651634060, 1968161300, -216192372, -1858642177, -1345910998, -2128793177, -1325754797, 143080818, 1868787479, -484135391]

Using the output to ruby:

#Ruby
pointArr = [-1992414123, 638637875, 1917312913, 73389700, -425224557, 743777818, 970253455, 723842951, -1751664279, 982132367, -1949786746, 1067402923, -869929568, 157928816, 1651634060, 1968161300, -216192372, -1858642177, -1345910998, -2128793177, -1325754797, 143080818, 1868787479, -484135391]

# ugly bit magic to somehow convert the above array into a proper byte array (in form of a string)
pointStr = [(pointArr.map { |i| (i>=0)?('0'*(8-i.to_s(16).length)+i.to_s(16)):("%08X" % (2**32-1+i+1)) }*'').upcase].pack("H*")

#My modified code
pointInt = pointStr.unpack('B*').first.to_i(2) #Convert BitStr to integer
pointBN = OpenSSL::BN.new(pointInt.to_s, 10) #Int to BigNumber (to be used as param below)

group = OpenSSL::PKey::EC::Group.new('secp384r1') #EC Group to be used

client_pub_point = OpenSSL::PKey::EC::Point.new(group, pointBN)
# ^
# ^ ABOVE'S MY PROBLEM -> OpenSSL::PKey::EC::Point::Error: invalid encoding
# ^

#Server EC: code taken and modified from https://www.ruby-forum.com/topic/3966195 
ec = OpenSSL::PKey::EC.new(group)
ec.generate_key

pub = OpenSSL::PKey::EC.new(group)
pub.public_key = client_pub_point

#Compute Shared Key
shared_key = ec.dh_compute_key(pub.public_key)

puts shared_key.unpack('I>*')

This 'puts' something like below when original code from [(link)] (https://www.ruby-forum.com/topic/3966195) above is used

3747233514
2683763564
475565567
1087119841
857380668
2490387914
3548975947
2348082236
2093543365
1477205987
4289120093
3330807042

That should be it, but just in case here's my test

irb(main):113:0> ec = OpenSSL::PKey::EC.new(group)
=> #<OpenSSL::PKey::EC:0x37f4250>
irb(main):114:0> ec.generate_key
=> #<OpenSSL::PKey::EC:0x37f4250>

irb(main):115:0> pub = OpenSSL::PKey::EC.new(group)
=> #<OpenSSL::PKey::EC:0x374f070>
irb(main):116:0> pub.public_key = ec.public_key
=> #<OpenSSL::PKey::EC::Point:0x37f8090>

irb(main):117:0> pub.public_key.to_bn
=> 7699789176960498967958014210931326569901199635665512831714857096185925821659134057981449113945854620725216613989823482205311316333140754760317456176281271361802541262755346331375041208726203461213190230560617504850860621520632944763
irb(main):119:0> OpenSSL::PKey::EC::Point.new(group, pub.public_key.to_bn)
=> #<OpenSSL::PKey::EC:0x4029f48>

#The ABOVE FORMAT works, unlike the error I got like the following

irb(main):122:0> pointBN
=> 832312614609895991150696681555479456971598284480953722479085426901428295415600048953528780331647571635767075686130334170313461289491500162782258792834115040597490936949579748064005380309022482780162833924377801386781542770068991521
irb(main):123:0> OpenSSL::PKey::EC::Point.new(group, pointBN)
OpenSSL::PKey::EC::Point::Error: invalid encoding

But comparing the working and the not-working just above, it seems that total number of decimal digits are the same, so I think I'm somewhat on the right track, but I just couldn't really work it out.

For those who might run into this kind of problem, these are my reference codes (1) (2) (3) (4) (5)

I'm stuck on this for two days now and there seems to be not much written about this on the net, and I couldn't find any other JS library that supports elliptic curve. Any help would be much appreciated.

回答1:

#Server EC: code taken and modified from https://www.ruby-forum.com/topic/3966195 ec = OpenSSL::PKey::EC.new(group) ec.generate_key ...

Usually, we just call EC_KEY_new_by_curve_name with the NID of a well known curve. The NIDs would include:

  • NID_secp160k1
  • NID_secp192k1
  • NID_secp224k1
  • NID_secp256k1
  • NID_secp384r1
  • NID_secp521r1
  • other primary field curves
  • other binary field curves

I think the complete list of them is available in the OpenSSL sources, obj_mac.h:

#define SN_secp112r1        "secp112r1"
#define NID_secp112r1       704
#define OBJ_secp112r1       OBJ_secg_ellipticCurve,6L

#define SN_secp112r2        "secp112r2"
#define NID_secp112r2       705
#define OBJ_secp112r2       OBJ_secg_ellipticCurve,7L

#define SN_secp128r1        "secp128r1"
#define NID_secp128r1       706
#define OBJ_secp128r1       OBJ_secg_ellipticCurve,28L

#define SN_secp128r2        "secp128r2"
#define NID_secp128r2       707
#define OBJ_secp128r2       OBJ_secg_ellipticCurve,29L

#define SN_secp160k1        "secp160k1"
#define NID_secp160k1       708
#define OBJ_secp160k1       OBJ_secg_ellipticCurve,9L

#define SN_secp160r1        "secp160r1"
#define NID_secp160r1       709
#define OBJ_secp160r1       OBJ_secg_ellipticCurve,8L

#define SN_secp160r2        "secp160r2"
#define NID_secp160r2       710
#define OBJ_secp160r2       OBJ_secg_ellipticCurve,30L

#define SN_secp192k1        "secp192k1"
#define NID_secp192k1       711
#define OBJ_secp192k1       OBJ_secg_ellipticCurve,31L

#define SN_secp224k1        "secp224k1"
#define NID_secp224k1       712
#define OBJ_secp224k1       OBJ_secg_ellipticCurve,32L

#define SN_secp224r1        "secp224r1"
#define NID_secp224r1       713
#define OBJ_secp224r1       OBJ_secg_ellipticCurve,33L

#define SN_secp256k1        "secp256k1"
#define NID_secp256k1       714
#define OBJ_secp256k1       OBJ_secg_ellipticCurve,10L

#define SN_secp384r1        "secp384r1"
#define NID_secp384r1       715
#define OBJ_secp384r1       OBJ_secg_ellipticCurve,34L

#define SN_secp521r1        "secp521r1"
#define NID_secp521r1       716
#define OBJ_secp521r1       OBJ_secg_ellipticCurve,35L

#define SN_sect113r1        "sect113r1"
#define NID_sect113r1       717
#define OBJ_sect113r1       OBJ_secg_ellipticCurve,4L

#define SN_sect113r2        "sect113r2"
#define NID_sect113r2       718
#define OBJ_sect113r2       OBJ_secg_ellipticCurve,5L

#define SN_sect131r1        "sect131r1"
#define NID_sect131r1       719
#define OBJ_sect131r1       OBJ_secg_ellipticCurve,22L

#define SN_sect131r2        "sect131r2"
#define NID_sect131r2       720
#define OBJ_sect131r2       OBJ_secg_ellipticCurve,23L

#define SN_sect163k1        "sect163k1"
#define NID_sect163k1       721
#define OBJ_sect163k1       OBJ_secg_ellipticCurve,1L

#define SN_sect163r1        "sect163r1"
#define NID_sect163r1       722
#define OBJ_sect163r1       OBJ_secg_ellipticCurve,2L

#define SN_sect163r2        "sect163r2"
#define NID_sect163r2       723
#define OBJ_sect163r2       OBJ_secg_ellipticCurve,15L

#define SN_sect193r1        "sect193r1"
#define NID_sect193r1       724
#define OBJ_sect193r1       OBJ_secg_ellipticCurve,24L

#define SN_sect193r2        "sect193r2"
#define NID_sect193r2       725
#define OBJ_sect193r2       OBJ_secg_ellipticCurve,25L

#define SN_sect233k1        "sect233k1"
#define NID_sect233k1       726
#define OBJ_sect233k1       OBJ_secg_ellipticCurve,26L

#define SN_sect233r1        "sect233r1"
#define NID_sect233r1       727
#define OBJ_sect233r1       OBJ_secg_ellipticCurve,27L

#define SN_sect239k1        "sect239k1"
#define NID_sect239k1       728
#define OBJ_sect239k1       OBJ_secg_ellipticCurve,3L

#define SN_sect283k1        "sect283k1"
#define NID_sect283k1       729
#define OBJ_sect283k1       OBJ_secg_ellipticCurve,16L

#define SN_sect283r1        "sect283r1"
#define NID_sect283r1       730
#define OBJ_sect283r1       OBJ_secg_ellipticCurve,17L

#define SN_sect409k1        "sect409k1"
#define NID_sect409k1       731
#define OBJ_sect409k1       OBJ_secg_ellipticCurve,36L

#define SN_sect409r1        "sect409r1"
#define NID_sect409r1       732
#define OBJ_sect409r1       OBJ_secg_ellipticCurve,37L

#define SN_sect571k1        "sect571k1"
#define NID_sect571k1       733
#define OBJ_sect571k1       OBJ_secg_ellipticCurve,38L

#define SN_sect571r1        "sect571r1"
#define NID_sect571r1       734
#define OBJ_sect571r1       OBJ_secg_ellipticCurve,39L
...

#Compute Shared Key shared_key = ec.dh_compute_key(pub.public_key)

There's an example of ECDH on the OpenSSL wiki. I believe Matt Caswell provided it. You can find it at Elliptic Curve Diffie Hellman.

I think the OpenSSL wiki example was also copy/pasted once here: ECDH secrets generated by BouncyCastle Java API and by OpenSSL are different.

I don't know SJCL or Ruby, so I can't help you.

sjcl.ecc.curves['c384'] <- NIST

I believe you would want NID_secp384r1 for this, but I don't know Ruby so take it at face value. For a list of named curves to NIDs, see OpenSSL: openssl/ CHANGES openssl/apps/ ecparam.c openssl/crypto....

If you are going to save the key to disk and possibly use it later in a certificate (for example, ECDSA signing), then you will want to set the OPENSSL_EC_NAMED_CURVE flag. The flag simply saves the group parameters by name (for example, ASN1 OID: prime256v1) rather than listing all the domain parameters in ASN1 objects (field type, primary or binary field, base point, etc).

You do that with:

EC_KEY_set_asn1_flag(key, OPENSSL_EC_NAMED_CURVE);

If you don't set the flag, then you will encounter "no shared ciphers" error when negotiating suites. Here are the symptoms on the client and server:

  • Client (s_client):

    • 139925962778272:error:14094410:SSL routines:SSL3_READ_BYTES:sslv3 alert handshake failure:s3_pkt.c:1256:SSL alert number 40
    • 139925962778272:error:1409E0E5:SSL routines:SSL3_WRITE_BYTES:ssl handshake failure:s3_pkt.c:596:

  • Server (s_server):

    • 140339533272744:error:1408A0C1:SSL routines:SSL3_GET_CLIENT_HELLO:no shared cipher:s3_srvr.c:1353:


回答2:

I've finally solved this problem! :)

I used a different Javascript library. If you're looking on solving similar problem like this, please refer to the other question of mine (link)



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