Elliptic Curves in python

DiffieHellman, Elfgamal, ECDSA & STS with elliptic curve in python

WARNING This was a school project do not use it for actual security purpose.

Description

General

That software provide a python package with elliptic curves and security primitives class :

• Diffie Hellman : diffiehellman.py
• ElGamal : elgamal.py
• ECDSA : ECDSA.py
• STS : STS.py
• Elliptic Curves : elliptic.py and point.py
• Some tools : tools.py, ectools.py, stools.py

In more there is four front-end for an immediate usage :

• Diffie Hellman : dh
• ElGamal : elgamal
• ECDSA : ecdsa
• STS : sts

Program architecture

Tools used by primitives Class and front-end :

• EllipticCurve : The elliptic curve class
• Point ; The point class
• ectools.py : Mathematic function for elliptic curve
• tools.py :
  • tools : Read curve, I/O files
  • key : I/O functions for the keys
  • message Easy to use socket functions
• stools : STS and DH tools for secret exchange using socket

File system :

• curves/ :
  • There are 17 256bits curves and 18 512bits curves. All front-end and class manage the two sizes of curve
  • The curve are taken from http://galg.acrypta.com/. Therefore these are not the usual curves recommended by the NIST
  • We use Weierstrass curves
  • See curves/README.md for more information
• keys/
  • As the curve are not the classic NSA's curves, the key format contains the curve itself.
  • See keys/README.md for more information about keys format
• sample/
  • Default directory for plain text, signed and encrypted files
  • See sample/README.md for more information

Requirements

That software run with Python 2.x and 3.x.

For AES function and the secure random generator you need the python library Crypto avaible here

If you want to install the pakage ecurve : sudo python setup install

Usages

All the following command are showed with all their options. But some options are not mandatory as described

Diffie Hellman (DH) : dh

Create connection with a computer and start DH protocol :

dh --curve <curve.gp> --output <sharedsecret> --port <port> --host <hostname>

The first computer connected have to create the server with --server

dh --curve <curve.gp> --output <sharedsecret> --port <port> --server

Get the help :

dh --help

Default options :

• <curve.gp> : curves/w256-001.gp
• <sharedsecret> : keys/dh.shared
• <port> : 12800
• <localhost> : 12800

Elgamal : elgamal

This front-end provide an easy to use command for encrypt a file with elgamal. The front-end reads the file as a binary file but writes the cipher as a text file. As an asymetric security primitives, Elgamal is used for encryption of short message like keys. Do not use it for encrypt big file.

Generate an elgamal key pair : <key> as private and <key.pub> as public key

elgamal --keygen --curve <curves.gp> --output <key>

Encrypt a file :

elgamal --crypt --key <key.pub> --input <file> --output <file.elgamal>

Decrypt a file :

elgamal --decrypt -key <key> --input <file.elgamal> --output <file.decoded>

Get the help :

elgamal --help

Default options :

• <curve.gp> : curves/w256-001.gp
• <key.pub> : keys/elgamal.pub Public key
• <key> : keys/elgamal Private key
• <file> : sample/text Plain text file
• <file.elgamal> : sample/text.elgamal Encrypted file
• <file.decoded> : sample/text.decoded File decrypted

ECDSA : ecdsa

ecdsa reads your file as a binary file with a buffer. Therefore, you can sign any file you want.

Generate an ECDSA key pair : <key> as private and <key.pub> as public key

ecdsa --keygen --curve <curves.gp> --output <key>

Sign a file :

ecdsa --sign --key <key> --input <file> --output <file.signed>

Verify the signature : the signed have to be named <file.signed>

ecdsa --verif --key <key.pub> --input <file> 

Get the help :

ecdsa --help

Default options :

• <curve.gp> : curves/w256-001.gp
• <key.pub> : keys/ecdsa.pub Public key
• <key> : keys/ecdsa Private key
• <file> : sample/text Plain text file
• <file.signed> : sample/text.signed The signed of the file (You still need the file itsel)

Sation To Station (STS) : sts

Requirements :

• You need to generate first an ECDSA key pair with the same curve you will use for STS
• <key> is your ECDSA private key
• <key.pub> is your ECDSA public key

Create connection with a computer and start STS protocol :

sts --curve <curve.gp> --key <key> --output <sharedsecret> --port <port> --host <hostname>

The first computer connected have to create the server with --server

sts --curve <curve.gp> --key <key> --output <sharedsecret> --port <port> --server

Get the help :

sts --help

Default options :

• <curve.gp> : curves/w256-001.gp
• <key> : keys/ecdsa and keys/ecdsa.pub We need the both private and public key
• <sharedsecret> : keys/sts.shared
• <port> : 12800
• <localhost> : 12800

Security purpose

We provide elliptic curve for level 7 and 8.

Authors

• Alexandre PUJOL [email protected]
• Maxime CHEMIN [email protected]