Homomorphic Encryption and Secure MPC

Advanced Privacy Enhancing Technologies (PETs) allow computation on data without exposing the raw data itself.

Fully Homomorphic Encryption (FHE)

FHE allows computations to be performed on encrypted data. The result is encrypted and can only be decrypted by the owner of the secret key.

Implementation with TenSEAL

TenSEAL is a library for performing homomorphic encryption operations on tensors, built on Microsoft SEAL.

import tenseal as ts

# Setup TenSEAL context
context = ts.context(
    ts.SCHEME_TYPE.CKKS,
    poly_modulus_degree=8192,
    coeff_mod_bit_sizes=[60, 40, 40, 60]
)
context.generate_galois_keys()
context.global_scale = 2**40

# Data Owner: Encrypts data
secret_data = [5.5, 10.2, 3.3]
encrypted_vector = ts.ckks_vector(context, secret_data)

# Cloud Provider / Processor: Performs computation on encrypted data
# Multiply encrypted data by 2
multiplier = [2.0, 2.0, 2.0]
encrypted_result = encrypted_vector * multiplier

# Data Owner: Decrypts the result
decrypted_result = encrypted_result.decrypt()
print(f"Original Data: {secret_data}")
print(f"Decrypted Computation Result: {decrypted_result}")
# Output: [11.0, 20.4, 6.6]

Secure Multi-Party Computation (SMPC)

SMPC allows multiple parties to jointly compute a function over their inputs while keeping those inputs private. No single party learns the others' inputs.

Private Set Intersection (PSI)

A common MPC use case where two parties compute the intersection of their datasets without revealing any items outside the intersection. E.g., comparing a list of known compromised passwords with user passwords without the server learning the user's password or the user learning the entire breached list.