A Simple Drop-In Solution for Full Homomorphic Encryption

Full Homomorphic Encryption (FHE) allows untrusted (e.g. cloud) applications to operate directly on encrypted data, eliminating the need for server-side decryption or trust.

simplefhe is a Python library for FHE that intends to be as easy-to-use as possible. In the simplest case, just a few lines of code are all you need to have working FHE!

Table of Contents

• The Problem
• The Solution
• A More Realistic Example
  • Step 1: Keypair Generation
  • Step 2: Client-Side Encryption
  • Step 3: Server-Side Processing
  • Step 4: Client-Side Decryption
• Installation
• Notes
• Floating Point
• Linear Regression

The Problem

Suppose we have some sensitive data we wish to process on a remote server. The usual approach is to send the data over a secure connection to be processed server-side.

# examples/intro/insecure.py

# The server
def process(x):
    return x**3 - 3*x + 1


# The client
sensitive_data = [-30, -5, 17, 28]
for entry in sensitive_data:
    print(entry, process(entry)) # Bad! We are leaking sensitive information.

The result:

// examples/intro/insecure.out

-30 -26909
-5 -109
17 4863
28 21869

However, this requires trusting the server to keep your data confidential. One rogue admin or database hack is all it takes to expose your sensitive data to the public.

The Solution

A few lines of extra code is all it takes to implement Full Homomorphic Encryption (FHE):

# examples/intro/secure.py

from simplefhe import (
    encrypt, decrypt,
    generate_keypair,
    set_public_key, set_private_key, set_relin_keys,
    display_config
)

# In a real application, the keypair would be generated once,
# and only the public key would be provided to the server.
# A more realistic example is given later.
public_key, private_key, relin_keys = generate_keypair()
set_private_key(private_key)
set_public_key(public_key)
set_relin_keys(relin_keys)
# Don't worry about the relin keys for now.
# They should be shared between the client
# and the server, just like the public keys.

display_config()


# The server
def process(x):
    return x**3 - 3*x + 1


# The client
sensitive_data = [-30, -5, 17, 28]
for entry in sensitive_data:
    encrypted = encrypt(entry) # Encrypt the data...
    result = process(encrypted) # Process the data encrypted on the server...
    print(entry, decrypt(result)) # Decrypt the result on the client.

We obtain the same results, as expected:

// examples/intro/secure.out

===== simplefhe config =====
mode: integer (exact)
min_int: -262143
max_int: 262144
public_key: initialized
private_key: initialized
relin_keys: initialized

-30 -26909
-5 -109
17 4863
28 21869

In this example, we encrypt the data on the client, send only the encrypted data to the server, process the encrypted data server-side, and return the encrypted result to be client-side decrypted. This requires zero trust of the remote server.

A More Realistic Example

Of course, the client and server will generally be separate applications. Here we demonstrate a more realistic pipeline.

Step 1: Keypair Generation

We first generate a fixed pair of keys:

# examples/realistic/1_keygen.py

from simplefhe import generate_keypair

public_key, private_key, relin_keys = generate_keypair()
public_key.save('keys/public.key')
private_key.save('keys/private.key')
relin_keys.save('keys/relin.key')
print('Keypair saved to keys/ directory')

Step 2: Client-Side Encryption

Next, we encrypt our sensitive data on the client. Here we save the encrypted results to disk, but in the real-world these files would be sent over a network to the server.

# examples/realistic/2_encrypt.py

from simplefhe import encrypt, load_public_key, load_relin_keys, display_config

load_public_key('keys/public.key')
load_relin_keys('keys/relin.key')
display_config()


# Encrypt our data (client-side)
sensitive_data = [-30, -5, 17, 28]

for i, entry in enumerate(sensitive_data):
    encrypted = encrypt(entry)
    encrypted.save(f'inputs/{i}.dat')
    print(f'[CLIENT] Input {entry} encrypted to inputs/{i}.dat')


# We may then safely send these files to the server
# over a (possibly insecure) network connection

Output:

// examples/realistic/2_encrypt.out

===== simplefhe config =====
mode: integer (exact)
min_int: -262143
max_int: 262144
public_key: initialized
private_key: initialized
relin_keys: initialized

[CLIENT] Input -30 encrypted to inputs/0.dat
[CLIENT] Input -5 encrypted to inputs/1.dat
[CLIENT] Input 17 encrypted to inputs/2.dat
[CLIENT] Input 28 encrypted to inputs/3.dat

Step 3: Server-Side Processing

We process the encrypted data from the client. The server never has access to the private key, and can never decrypt the client's sensitive data.

# examples/realistic/3_process.py

from simplefhe import load_public_key, load_relin_keys, display_config, load_encrypted_value


# The private key never leaves the client.
load_public_key('keys/public.key')
load_relin_keys('keys/relin.key')
display_config()

# Process values on server.
def f(x): return x**3 - 3*x + 1

for i in range(4):
    # Load encrypted value sent from client
    value = load_encrypted_value(f'inputs/{i}.dat')

    # simplefhe seamlessly translates all arithmetic to
    # FHE encrypted operations.
    # We never gain access to the unencrypted information.
    result = f(value) 

    # Send encrypted result back to client
    result.save(f'outputs/{i}.dat')
    print(f'[SERVER] Processed entry {i}: inputs/{i}.dat -> outputs/{i}.dat')

Output:

// examples/realistic/3_process.out

===== simplefhe config =====
mode: integer (exact)
min_int: -262143
max_int: 262144
public_key: initialized
private_key: initialized
relin_keys: initialized

[SERVER] Processed entry 0: inputs/0.dat -> outputs/0.dat
[SERVER] Processed entry 1: inputs/1.dat -> outputs/1.dat
[SERVER] Processed entry 2: inputs/2.dat -> outputs/2.dat
[SERVER] Processed entry 3: inputs/3.dat -> outputs/3.dat

Step 4: Client-Side Decryption

Finally, the encrypted results are sent back to the client, where they are decrypted. The private key never needs to leave the client.

# examples/realistic/4_decrypt.py

from simplefhe import (
    load_private_key, load_relin_keys,
    display_config,
    decrypt, load_encrypted_value
)

# Note: this is the only step at which the private key is used!
load_private_key('keys/private.key')
load_relin_keys('keys/relin.key')
display_config()


# Decrypt results from the server (client-side)
sensitive_data = [-30, -5, 17, 28]

for i, entry in enumerate(sensitive_data):
    encrypted = load_encrypted_value(f'outputs/{i}.dat')
    result = decrypt(encrypted)
    print(f'[CLIENT] Result for {entry}: {result}')

As expected, we obtain the correct results:

// examples/realistic/4_decrypt.out

===== simplefhe config =====
mode: integer (exact)
min_int: -262143
max_int: 262144
public_key: missing
private_key: missing
relin_keys: missing

[CLIENT] Result for -30: -26909
[CLIENT] Result for -5: -109
[CLIENT] Result for 17: 4863
[CLIENT] Result for 28: 21869

Installation

simplefhe depends on SEAL-Python and all its prerequisites. After installing SEAL-Python, the simplefhe library is just a pip install away: pip3 install simplefhe

Notes

• To enable floating point computations (results will be approximate):

from simplefhe import initialize
initialize('float')

This must be done before any other simplefhe code (keygen, encryption/decryption, etc.) is executed. A full example is shown later.

• To increase the maximum range of allowable integers:

from simplefhe import initialize

MAX_INT = pow(2, 25)
initialize('int', max_int=MAX_INT)

Integers in the range [-MAX_INT + 1, MAX_INT] inclusive are representable.

• Comparison operations (<, =, >) are not supported on encrypted data. If they were, it would be pretty easy to figure out what the plaintext is! As a side effect, it's not really possible to branch based on encrypted data.
• There is some randomness in the encryption process: the same value, encrypted with the same key, will yield different ciphertexts. This prevents a simple plaintext enumeration attack.

Floating Point

The following code shows a full floating point demo:

# examples/float_demo.py

from simplefhe import (
    encrypt, decrypt,
    generate_keypair,
    set_public_key, set_private_key, set_relin_keys,
    initialize, display_config
)

initialize('float')

public_key, private_key, relin_key = generate_keypair()
set_private_key(private_key)
set_public_key(public_key)
set_relin_keys(relin_key)

display_config()


# The server
def process(x):
    return x**3 - 3.1*x + 5.3


# The client
sensitive_data = [-3.2, 0.1, 5.3, 50.6]
for entry in sensitive_data:
    insecure_result = process(entry)
    secure_result = decrypt(process(encrypt(entry)))
    print(
        f'{entry:8.1f}',
        '|',
        f'{insecure_result:12.2f}',
        f'{secure_result:12.2f}'
    )

The results are approximate, and will change slightly on each run:

// examples/float_demo.out

===== simplefhe config =====
mode: float (approximate)
public_key: initialized
private_key: initialized
relin_keys: initialized

    -3.2 |       -17.55       -17.55
     0.1 |         4.99         4.99
     5.3 |       137.75       137.75
    50.6 |    129402.66    129402.76

Linear Regression

See here for a working server-side linear regression example.