The Communication Overhead Challenge of Secure MPC vs. FHE

Introduction

When it comes to secure multi-party computation (MPC) and fully homomorphic encryption (FHE), the cryptographic community often finds itself torn between two seemingly opposing approaches. On one hand, MPC offers the promise of efficient computations on sensitive data without revealing the underlying information. On the other hand, FHE enables evaluations of arbitrary circuits on encrypted data, providing unparalleled flexibility. However, as we delve deeper into the nuances of these techniques, a crucial aspect emerges: communication overhead.

Secure MPC: A Tale of Efficiency and Overhead

Secure MPC protocols, such as those based on the Shamir's Secret Sharing (SSS) [1] and the SPDZ protocol [2], have gained significant attention in recent years. These protocols allow multiple parties to jointly compute a function on their private inputs without revealing the individual inputs. In theory, MPC offers a significant advantage in terms of computational efficiency, as it eliminates the need for expensive computations on encrypted data.

// Example of Shamir's Secret Sharing (SSS) in Python:
import numpy as np
from secrets import randbelow

def shamir_secret_sharing(p, shares, threshold):
    k = len(shares)
    s = int(np.random.randint(1, p))
    shares = [(s * pow(i, -1, p)) % p for i in range(1, k+1)]
    return shares

p = 23
threshold = 2
shares = shamir_secret_sharing(p, [i for i in range(1, threshold+1)], threshold)
print(shares)

FHE: The Cost of Flexibility

Fully homomorphic encryption, on the other hand, allows for the evaluation of arbitrary circuits on encrypted data. This flexibility comes at a significant cost, as FHE schemes require complex and computationally expensive algorithms to perform even simple operations. For example, the popular FHE scheme, Homomorphic Encryption for Arithmetic Circuits (HEA)[3], relies on the hardness of the Ring-LWE problem [4].

// Example of HEA in C++:
#include <iostream>
#include <cstdlib>
#include <random>

int main() {
    // Initialize public and private keys
    PublicKey pk;
    PrivateKey sk;

    // Encrypt a message
    Ciphertext ct = Encrypt(pk, "Hello, World!");

    // Perform a computation on the ciphertext
    Ciphertext result = Eval(ct, pk, "XOR");

    // Decrypt the result
    std::string decrypted = Decrypt(sk, result);

    std::cout << decrypted << std::endl;
    return 0;
}

The Communication Overhead Conundrum

While MPC and FHE offer distinct advantages, they both introduce significant communication overhead. In the case of MPC, the necessary secret-sharing protocols and multi-round exchanges between participating parties can be costly in terms of network bandwidth and latency. This overhead can be particularly problematic when deploying MPC protocols globally, as it may lead to increased latency and reduced scalability.

Security Implications and Best Practices

When evaluating the communication overhead of MPC and FHE, it is essential to consider the security implications of each approach. MPC protocols, for instance, rely on the secrecy of the shared information and the integrity of the communication channels. FHE schemes, on the other hand, require the secrecy of the private keys and the integrity of the encryption process.

Best practices for managing communication overhead include:

• Optimizing MPC protocols for reduced communication overhead
• Implementing efficient communication protocols, such as those based on secure multi-party computations
• Using FHE schemes with reduced overhead, such as those based on the Learning With Errors (LWE) problem [5]

Conclusion

In conclusion, the communication overhead challenge of secure MPC vs. FHE highlights the importance of carefully considering the trade-offs between computational efficiency, security, and communication costs. As the cryptographic community continues to develop and refine these techniques, it is crucial to prioritize practical applications and real-world implications. By doing so, we can ensure that the benefits of MPC and FHE are accessible to a broader range of users and applications.