eciespy 0.2.0

Elliptic Curve Integrated Encryption Scheme for secp256k1 in Python

eciespy

Elliptic Curve Integrated Encryption Scheme for secp256k1 in Python.

Other language versions:

• TypeScript
• Rust
• Golang (from community)

You can also check a flask web backend demo here.

Install

Install with pip install eciespy under Python 3.5+.

Quick Start

>>> from ecies.utils import generate_eth_key, generate_key
>>> from ecies import encrypt, decrypt
>>> eth_k = generate_eth_key()
>>> prvhex = eth_k.to_hex()
>>> pubhex = eth_k.public_key.to_hex()
>>> data = b'this is a test'
>>> decrypt(prvhex, encrypt(pubhex, data))
b'this is a test'
>>> secp_k = generate_key()
>>> prvhex = secp_k.to_hex()
>>> pubhex = secp_k.public_key.format(True).hex()
>>> 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_pk: Union[str, bytes], msg: bytes) -> bytes

Parameters:

• receiver_pk - Receiver's public key (hex str or bytes)
• msg - Data to encrypt

Returns: bytes

ecies.decrypt(receiver_sk: Union[str, bytes], msg: bytes) -> bytes

Parameters:

• receiver_sk - Receiver's private key (hex str or bytes)
• 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, exclusive with -d
  -d, --decrypt         decrypt with private key, exclusive 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 and implementation details

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 parts generally:

1. Use ECDH to exchange an AES session key;

   Notice that the sender public key is generated every time when ecies.encrypt is invoked, thus, the 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    |
+-------------------------------+----------+----------+-----------------+
| Sender Public Key (ephemeral) | Nonce/IV | Tag/MAC  | Encrypted data  |
+-------------------------------+----------+----------+-----------------+
| sender_pk                     | nonce    | tag      | encrypted_data  |
+-------------------------------+----------+----------+-----------------+
|           Secp256k1           |              AES-256-GCM              |
+-------------------------------+---------------------------------------+

Secp256k1

Glance at ecdh

So, how do we calculate the ECDH key under secp256k1? If you use a library like coincurve, you might 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'

Calculate your ecdh key manually

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'

Warning: NEVER use small integers as private keys on any production systems or storing any valuable assets.

Warning: ALWAYS use safe methods like os.urandom to generate private keys.

Math on ecdh

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, it can be 1 for k1 here, and (x, y) here is an extremely large number pair like (89565891926547004231252920425935692360644145829622209833684329913297188986597, 12158399299693830322967808612713398636155367887041628176798871954788371653930).

Warning: 1 * (x, y) == (x, y) is always true, since 1 is the identity element for multiplication.

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 (easy to multiply, hard to divide).

Compressed and uncompressed keys

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 in a compressed or uncompressed format.

• Compressed format (x coordinate only)

>>> 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 ((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'

The format is depicted by the image below from the bitcoin book.

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:

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. It's better to use the compressed format, since you can always get x from x or (x, y) without any calculation.

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

You may want to ask, what if no hash? Briefly, hash can:

1. Make the shared key's length fixed;
2. Make it safer since hash functions 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'
>>> iv = 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=iv)
>>> decipher.decrypt_and_verify(data, tag)
b'helloworld'

Strictly speaking, nonce != iv, but this is a little bit off topic, if you are curious, you can check the comment in utils.py.

Release Notes

0.2.0

• API change: ecies.encrypt and ecies.decrypt now can take both hex str and raw bytes
• Bump dependency versions
• Update documentation

0.1.1 ~ 0.1.9

• Bump dependency versions
• Update documentation
• Switch to Circle CI
• Change license to MIT

0.1.0

• First beta version release