eciespy 0.1.2

Elliptic Curve Integrated Encryption Scheme for secp256k1 in Python

eciespy

Elliptic Curve Integrated Encryption Scheme for secp256k1 in Python

Install

Install with pip install eciespy under Python version >= 3.5.

Quick Start

>>> from ecies.utils import generate_eth_key
>>> from ecies import encrypt, decrypt
>>> k = generate_eth_key()
>>> prvhex = k.to_hex()
>>> pubhex = k.public_key.to_hex()
>>> data = b'this is a test'
>>> decrypt(prvhex, encrypt(pubhex, data))
b'this is a test'

Or just use a builtin command eciespy in your favorite command line.

API

ecies.encrypt(receiver_pubhex: str, msg: bytes) -> bytes

Parameters:

• receiver_pubhex - Receiver's ethereum public key hex string
• msg - Data to encrypt

Returns: bytes

ecies.decrypt(receiver_prvhex: str, msg: bytes) -> bytes

Parameters:

• receiver_prvhex - Receiver's ethereum private key hex string
• msg - Data to decrypt

Returns: bytes

Command Line Interface

Show help

$ eciespy -h
usage: eciespy [-h] [-e] [-d] [-g] [-k KEY] [-D [DATA]] [-O [OUT]]

Elliptic Curve Integrated Encryption Scheme for secp256k1 in Python

optional arguments:
  -h, --help            show this help message and exit
  -e, --encrypt         encrypt with public key, not compatible with -d
  -d, --decrypt         decrypt with private key, not compatible with -e
  -g, --generate        generate ethereum key pair
  -k KEY, --key KEY     public or private key file
  -D [DATA], --data [DATA]
                        file to encrypt or decrypt, if not specified, it will
                        read from stdin
  -O [OUT], --out [OUT]
                        encrypted or decrypted file, if not specified, it will
                        write to stdout

Generate eth key

$ eciespy -g
Private: 0x95d3c5e483e9b1d4f5fc8e79b2deaf51362980de62dbb082a9a4257eef653d7d
Public: 0x98afe4f150642cd05cc9d2fa36458ce0a58567daeaf5fde7333ba9b403011140a4e28911fcf83ab1f457a30b4959efc4b9306f514a4c3711a16a80e3b47eb58b
Address: 0x47e801184B3a8ea8E6A4A7A4CFEfEcC76809Da72

Encrypt with public key and decrypt with private key

$ echo '0x95d3c5e483e9b1d4f5fc8e79b2deaf51362980de62dbb082a9a4257eef653d7d' > prv
$ echo '0x98afe4f150642cd05cc9d2fa36458ce0a58567daeaf5fde7333ba9b403011140a4e28911fcf83ab1f457a30b4959efc4b9306f514a4c3711a16a80e3b47eb58b' > pub
$ echo 'helloworld' | eciespy -e -k pub | eciespy -d -k prv
helloworld
$ echo 'data to encrypt' > data
$ eciespy -e -k pub -D data -O enc_data
$ eciespy -d -k prv -D enc_data
data to encrypt
$ rm data enc_data

Mechanism

This library combines secp256k1 and AES-256-GCM (powered by coincurve and pycryptodome) to provide an API of encrypting with secp256k1 public key and decrypting with secp256k1's private key. It has two steps:

1. Use ECDH to calculate an AES session key;

   Notice that the server public key is generated every time when ecies.encrypt is invoked, thus, the calculated AES session key varies.

2. Use this AES session key to encrypt/decrypt the data under AES-256-GCM.

Basically the encrypted data will be like this:

+-------------------------------+----------+----------+-----------------+
| 65 Bytes                      | 16 Bytes | 16 Bytes | == data size    |
+-------------------------------+----------+----------+-----------------+
| Server Public Key(Disposable) | Nonce/IV | Tag/MAC  | Encrypted data  |
+-------------------------------+----------+----------+-----------------+
| server_pub                    | nonce    | tag      | encrypted_data  |
+-------------------------------+----------+----------+-----------------+
|           Secp256k1           |              AES-256-GCM              |
+-------------------------------+---------------------------------------+

Secp256k1

So, how do we calculate the ECDH key under secp256k1? If you use library like coincurve, you just simply call k1.ecdh(k2.public_key.format()), then uh-huh, you got it! Let's see how to do it in simple Python snippets:

>>> from coincurve import PrivateKey
>>> k1 = PrivateKey(b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x01')
>>> k2 = PrivateKey(b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x02')
>>> k1.public_key.format(False).hex() # 65 bytes, False means uncompressed key
'0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8'
>>> k2.public_key.format(False).hex() # 65 bytes
'04c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee51ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a'
>>> k1.ecdh(k2.public_key.format()).hex()
'b1c9938f01121e159887ac2c8d393a22e4476ff8212de13fe1939de2a236f0a7'
>>> k2.ecdh(k1.public_key.format()).hex()
'b1c9938f01121e159887ac2c8d393a22e4476ff8212de13fe1939de2a236f0a7'

However, as a hacker like you with strong desire to learn something, you must be curious about the magic under the ground.

In one sentence, the secp256k1's ECDH key of k1 and k2 is nothing but sha256(k2.public_key.multiply(k1).

>>> k1.to_int()
1
>>> shared_pub = k2.public_key.multiply(bytes.fromhex(k1.to_hex()))
>>> shared_pub.point()
(89565891926547004231252920425935692360644145829622209833684329913297188986597,
 12158399299693830322967808612713398636155367887041628176798871954788371653930)
>>> import hashlib
>>> h = hashlib.sha256()
>>> h.update(shared_pub.format())
>>> h.hexdigest()  # here you got the ecdh key same as above!
'b1c9938f01121e159887ac2c8d393a22e4476ff8212de13fe1939de2a236f0a7'

Let's discuss in details. The word multiply here means multiplying a point of a public key on elliptic curve (like (x, y)) with a scalar (like k). Here k is the integer format of a private key, for instance, a simple 1 as k1, and (x, y) here is an extremely large number pair like (89565891926547004231252920425935692360644145829622209833684329913297188986597, 12158399299693830322967808612713398636155367887041628176798871954788371653930).

Mathematically, the elliptic curve cryptography is based on the fact that you can easily multiply point A (aka base point, or public key in ECDH) and scalar k (aka private key) to get another point B (aka public key), but it's almost impossible to calculate A from B reversely.

A point multiplying a scalar can be regarded that this point adds itself multiple times, and the point B can be converted to a readable public key (compressed or uncompressed format).

• Compressed format (only use x coordinate)

>>> point = (89565891926547004231252920425935692360644145829622209833684329913297188986597, 12158399299693830322967808612713398636155367887041628176798871954788371653930)
>>> prefix = '02' if point[1] % 2 == 0 else '03'
>>> compressed_key_hex = prefix + hex(point[0])[2:]
>>> compressed_key = bytes.fromhex(compressed_key_hex)
>>> compressed_key.hex()
'02c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5'

• Uncompressed format (use (x, y) coordinate)

>>> uncompressed_key_hex = '04' + hex(point[0])[2:] + hex(point[1])[2:]
>>> uncompressed_key = bytes.fromhex(uncompressed_key_hex)
>>> uncompressed_key.hex()
'04c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee51ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a'

If you want to convert the compressed format to uncompressed, basically, you need to calculate y from x by solving the equation using Cipolla's Algorithm: $$ y^2=(x^3 + 7) \bmod p,\ where\ p=2^{256}-2^{32}-2^{9}-2^{8}-2^{7}-2^{6}-2^{4}-1 $$ You can check the bitcoin wiki and this thread on bitcointalk.org for more details.

Then, the shared key between k1 and k2 is the sha256 hash of the compressed key.

>>> h = hashlib.sha256()
>>> h.update(compressed_key)
>>> h.hexdigest()
'b1c9938f01121e159887ac2c8d393a22e4476ff8212de13fe1939de2a236f0a7'

You may want to ask, what if no hash? Briefly, hash can make it safer since hash function can remove "weak bits" in the original computed key. Check the introduction section of this paper for more details.

AES

Now we have the shared key, and we can use the nonce and tag to decrypt. This is quite straight, and the example derives from pycryptodome's documentation.

>>> from Cryptodome.Cipher import AES
>>> key = b'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00'
>>> nonce = b'\xf3\xe1\xba\x81\r,\x89\x00\xb1\x13\x12\xb7\xc7%V_'
>>> tag = b'\xec;q\xe1|\x11\xdb\xe3\x14\x84\xda\x94P\xed\xcfl'
>>> data = b'\x02\xd2\xff\xed\x93\xb8V\xf1H\xb9'
>>> decipher = AES.new(key, AES.MODE_GCM, nonce=nonce)
>>> decipher.decrypt_and_verify(data, tag)
b'helloworld'

Release Notes

0.1.2

• Support Python 3.7 build
• Minor fix on documentation

0.1.1

• Update documentation

0.1.0

• First beta version release