shellcode33/elliptic-curves-algorithms

Elliptic curves algorithms written in Python

Elliptic Curves Cryptography

Simple Python module implementing Diffie Hellman, El Gamal and DSA algorithms using elliptic curves. These algorithms don't guarentee authentication, a MITM attack could be performed in order to hijack the public key.

Just stating the obvious here : those scripts are for educational purposes only, do not use it in anything serious.

Diffie Hellman

You can run the server then the client to see the generated secret key is the same on both sides.

shellcode@laptop:/home/shellcode/Crypto/Elliptic-Curves-Algorithms/demo  git:(master*) $ ./server_dh.py 
Waiting for client...
Client connected.
-------------------------------------
1: y² = x³ + 1x + 3
2: y² = x³ + 109454571331697278617670725030735128145969349647868738157201323556196022393856x + 107744541122042688792155207242782455150382764043089114141096634497567301547839
Which curve do you want to use ? [default 1] : 2
DH remote parameter:  (97138913127608459681135738238509448998881853099266326240818802819815727419427, 81448349606468118554919636307944551532799340194696086176081536871720747880178)
sha1(secret_key) = 0dcbd6505d31db24dc58da473788560c4e2c0c0a

shellcode@laptop:/home/shellcode/Crypto/Elliptic-Curves-Algorithms/demo  git:(master*) $ ./client_dh.py 
-------------------------------------
1: y² = x³ + 1x + 3
2: y² = x³ + 109454571331697278617670725030735128145969349647868738157201323556196022393856x + 107744541122042688792155207242782455150382764043089114141096634497567301547839
Which curve do you want to use ? [default 1] : 2
Received parameter:  (101031615897151406461415691397072605734385577084318901325540546750227921865334, 27542374492052082156151997086209450249676378539960817158152497875354487990941)
sha1(secret_key) = 0dcbd6505d31db24dc58da473788560c4e2c0c0a

El Gamal

This algorithm enables you to exchange encrypted messages asymetrically :

shellcode@laptop:/home/shellcode/Crypto/Elliptic-Curves-Algorithms/demo  git:(master*) $ ./server_eg.py 
Waiting for client...
Client connected.
-------------------------------------
1: y² = x³ + 1x + 3
2: y² = x³ + 109454571331697278617670725030735128145969349647868738157201323556196022393856x + 107744541122042688792155207242782455150382764043089114141096634497567301547839
Which curve do you want to use ? [default 1] : 2
Sending public key to client...
Cipher received: ((36773955846380952537541287416321290092702887872322771572617991430614752831531, 44933767436387503989913507543382489164051634957543418839767485102168306626167), (70407540337237980970268132682638014818491496697688582317136440105096786225421, 61756750508062620281767048328228541891853280587433946972746014997795360954962))
Received: (82638672503301278923015998535776227331280144783487139112686874194432446389503, 43992510890276411535679659957604584722077886330284298232193264058442323471611)

shellcode@laptop:/home/shellcode/Crypto/Elliptic-Curves-Algorithms/demo  git:(master*) $ ./client_eg.py 
-------------------------------------
1: y² = x³ + 1x + 3
2: y² = x³ + 109454571331697278617670725030735128145969349647868738157201323556196022393856x + 107744541122042688792155207242782455150382764043089114141096634497567301547839
Which curve do you want to use ? [default 1] : 2
Server's public key received.
Sending encrypted message to server...

DSA

This algorithm enables you to sign messages in order to check integrity, to be sure the message is from a legitimate emitter.

shellcode@laptop:/home/shellcode/Crypto/Elliptic-Curves-Algorithms/demo  git:(master*) $ ./server_dsa.py 
-------------------------------------
1: y² = x³ + 1x + 3
2: y² = x³ + 109454571331697278617670725030735128145969349647868738157201323556196022393856x + 107744541122042688792155207242782455150382764043089114141096634497567301547839
Which curve do you want to use ? [default 1] : 2
Waiting for client...
Client connected.
Public key is sent.
Signature is sent.

shellcode@laptop:/home/shellcode/Crypto/Elliptic-Curves-Algorithms/demo  git:(master*) $ ./client_dsa.py 
-------------------------------------
1: y² = x³ + 1x + 3
2: y² = x³ + 109454571331697278617670725030735128145969349647868738157201323556196022393856x + 107744541122042688792155207242782455150382764043089114141096634497567301547839
Which curve do you want to use ? [default 1] : 2
Received public key:  (15021019540827427930960423889714676004813071951062158447139104086683546669408, 79401835124672877735276056892375637840864613443911033730883544544473821748130)
Received signature: (10784918051478807134560271922891148593921688428015743990310288453562865141549, 4240444791637007411409401138864890210082751360370998026778984045081195792678)
Is the signature valid : True

More

You can add more elliptic curves inside the EllipticCurve class :