Proof of Learning Using Zero-Knowledge Proof

Abstract

Machine learning is an important technology that can be applied to various services, such as medical diagnosis and sales data analysis. However, the machine learning often involves personal information in the data used for training, and data encryption is essential to prove the learning process without losing data privacy. Garg et al. proposed a method using zero-knowledge proofs to verify whether data owned by the prover has been correctly utilized for the training on a machine learning model. They applied their method to federated learning, in which multiple users learn a model from their data. On the other hand, their method requires each prover to share data using Multi-Party Computation (MPC), which results in significant computational overhead for each user. Furthermore, their method does not provide a solution for the case where a malicious prover proves the data that he/she has not actually used for the training. We propose a method to prove the correctness of the procedure that one's own data was used for training without using MPC by sharing models instead of sharing the data. In our scheme, each prover's model can only be accessed by two users: the verifier and the next prover, thus reducing the computational effort required for model sharing. The data and the model used for training can be applied to zero-knowledge proofs, and the verifier can verify only the model to prove that it has been trained without disclosing the data. We prove how we can identify the malicious prover when he/she sends different models to the verification phase.