A zero-knowledge proof of training (zkPoT) enables a party to prove that they have correctly trained a committed model based on a committed dataset without revealing any additional information about the model or the dataset. An ideal zkPoT should offer provable security and privacy guarantees, succinct proof size and verifier runtime, and practical prover efficiency. In this work, we present Kaizen, a zkPoT targeted for deep neural networks (DNNs) that achieves all these goals at once. Our construction enables a prover to iteratively train their model via (mini-batch) gradient descent, where the number of iterations need not be fixed in advance; at the end of each iteration, the prover generates a commitment to the trained model parameters attached with a succinct zkPoT, attesting to the correctness of the executed iterations. The proof size and verifier time are independent of the number of iterations.

Most blockchain-based cryptocurrencies suffer from a heavily limited transaction throughput, which is a barrier to their growing adoption. Payment channel networks (PCNs) are one of the promising solutions to this problem. PCNs reduce the on-chain load of transactions and increase the throughput by processing many payments off-chain. In fact, any two users connected via a path of payment channels (i.e., joint addresses between the two channel end-points) can perform payments, and the underlying blockchain is used only when there is a dispute between users. Unfortunately, payments in PCNs can only be conducted securely along a path, which prevents the design of many interesting applications. Moreover, the most widely used implementation, the Lightning Network in Bitcoin, suffers from a collateral lock time linear in the path length, it is affected by security issues, and it relies on specific scripting features called Hash Timelock Contracts that hinders the applicability of the underlying protocol in other blockchains.