Morten Dahl, a Ph.D. and Machine Learning Engineer at Datadog, discusses the implementation of a private deep learning model using a secure multi-party computing protocol. Inspired by a recent blog on hybrid deep learning and homomorphic encryption, he explores the use of secure multi-party computation instead of homomorphic encryption for deep learning. In this article, we build a simple secure multiparty computing protocol from scratch and perform basic Boolean calculations to train a simple neural network. The code for this article is available on GitHub (mortendahl/privateml/simple-boolean-functions). We assume there are three non-colluding parties, P0, P1, and P2, who want to train a neural network together without revealing their models. Some users also wish to provide training data while maintaining privacy, and others want to use well-trained models without exposing their inputs. To achieve this, we need to securely compute rational numbers with specific precision, including addition and multiplication. We also need to calculate the sigmoid function 1/(1+np.exp(-x)). Traditional methods can be computationally heavy in secure settings, so we use polynomial approximations, similar to those used in homomorphic cryptographic neural networks, but with some optimizations. Secure Multi-Party Computation (MPC) and Homomorphic Encryption (HE) are closely related fields in modern cryptography. Both aim to compute functions on private data without revealing anything except the final output. While HE requires expensive computations, MPC involves more interaction but cheaper operations. For now, MPC offers better performance, making it a more mature technology. Fixed-point arithmetic is used to represent rational numbers as integers within a finite field. For example, using a 6-bit precision, we scale each number by 10^6 and represent it as a fixed-point number. This allows us to handle additions and multiplications while maintaining precision. Secret sharing is used to share data among parties without revealing it. Each party holds a part of the shared value, and only when all parts are combined can the original value be reconstructed. This ensures that no single party can access the full data. Addition and subtraction are straightforward in this setup, as each party can locally add or subtract their respective shares. Multiplication, however, requires more complex operations involving re-sharing and communication between parties to maintain security. Handling multiplication introduces challenges, such as managing precision and avoiding overflow. Techniques like truncation and careful scaling help maintain accuracy while ensuring security. A custom data type, SecureRational, is introduced to encapsulate these operations, allowing for safe manipulation of values. This enables the use of NumPy for neural network computations while maintaining privacy. Deep learning experiments show that even simple Boolean functions can be learned using this approach. However, more complex functions require additional layers and careful handling of the sigmoid approximation to avoid numerical instability. Polynomial interpolation is explored as an alternative to Taylor series approximations, offering better accuracy over certain intervals. This leads to improved stability and performance in training neural networks. The conclusion highlights the feasibility of private machine learning using secure multi-party computation, emphasizing the importance of optimizing both the protocol and the machine learning process for efficiency and accuracy.

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