Homomorphic encryption using the threshold variant of the DamgardJurik cryptosystem.
Project description
DamgardJurik
An implementation of the threshold variant of the DamgardJurik homomorphic encryption cryptosystem.
Table of Contents
 Installation
 Public and Private Keys
 Key Generation
 Encryption and Decryption
 Homomorphic Operations
Installation
Requires Python 3.6+.
pip install damgardjurik
Alternatively, the code can be cloned and installed locally as follows.
git clone https://github.com/cryptovoting/damgardjurik.git
cd damgardjurik
pip install e .
Note that the e
flag will instruct pip to install the package as "editable". That is, when changes are made to any part of the package during development, those changes will immediately be available systemwide on the activated python environment.
All requirements for this package should be added to setup.py
.
Public and Private Keys
In the threshold variant of DamgardJurik implemented in this repository, a key pair consists of single public key along with a private key that has been split into multiple components using Shamir's secret sharing. The public key encrypts messages while the shares of the private key all contribute a portion of the decryption without ever requiring reconstruction of the private key. Thus, trust is distributed among the holders of the private key shares.
In this implementation, the public key is a PublicKey
object with an encrypt function while the private key shares are PrivateKeyShare
objects with a decrypt function that performs a partial decryption using that share of the private key. A PrivateKeyRing
object holds a set of PrivateKeyShare
s and contains a decrypt function that calls each PrivateKeyShare
's decrypt function and combines the results to obtain the final decryption.
Key Generation
To generate a PublicKey
and the corresponding PrivateKeyRing
, run the following commands:
from damgard_jurik import keygen public_key, private_key_ring = keygen( n_bits=64, s=1, threshold=3, n_shares=3 )
The parameters to keygen
are as follows:
n_bits
: The number of bits of encryption used in the public key and private key shares.s
: The exponent to which the public key parametern
is raised (wheren = p * q
is the product of twon_bits
bit primesp
andq
.). Plaintexts are integers in the spaceZ_n^s = {0, 1, ..., n^s  1}
.threshold
: The minimum number of private key shares needed to decrypt an encrypted message.n_shares
: The number of private key shares to generate.
Encryption and Decryption
Encryption and decryption are implemented as methods of the PublicKey
and PrivateKeyRing
classes, respectively.
For example:
m = 42 c = public_key.encrypt(m) m_prime = private_key_ring.decrypt(c) # m_prime = 42
Plaintexts like m
are simply Python integers while ciphertexts (encrypted plaintexts) like c
are instances of the EncryptedNumber
class. EncryptedNumber
objects contain an encryption of the plaintext along with a reference to the PublicKey
used to encrypt the plaintext.
Additionally, the PublicKey
and PrivateKingRing
classes have a convenience method for encrypting and decrypting lists of integers, as shown below.
m_list = [42, 33, 100] c_list = public_key.encrypt_list(m_list) m_prime_list = private_key_ring.decrypt_list(c_list) # m_prime_list = [42, 33, 100]
Homomorphic Operations
Due to the additively homomorphic nature of the DamgardJurik cryptosystem, ciphertexts can be combined in such a way as to obtain an encryption of the sum of the associated plaintexts. Futhermore, ciphertexts can be combined with unencrypted integers in such a way as to obtain the product of the associated plaintext and the unencrypted integer. For convenience, the EncryptedNumber
class has overridden the +
, 
, *
, and /
operators to implement these operations.
For example:
m_1, m_2 = 42, 33 c_1, c_2 = public_key.encrypt(m_1), public_key.encrypt(m_2) c = c_1 + c_2 m_prime = private_key_ring.decrypt(c) # m_prime = 75 = 42 + 33
m, s = 42, 2 c = public_key.encrypt(m) c_prime = c * s m_prime = private_key_ring.decrypt(c_prime) # m_prime = 84 = 42 * 2
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