Two-Party Decision Tree Training from Updatable Order-Revealing Encryption

Running machine learning algorithms on encrypted data is a way forward to marry functionality needs common in industry with the important concerns for privacy when working with potentially sensitive data. While there is already a variety of protocols in this setting based on fully homomorphic encryption or secure multiparty computation (MPC), we are the first to propose a protocol that makes use of a specialized Order-Revealing Encryption scheme. This scheme allows to do secure comparisons on ciphertexts and update these ciphertexts to be encryptions of the same plaintexts but under a new key. We call this notion Updatable Order-Revealing Encryption (uORE) and provide a secure construction using a key-homomorphic pseudorandom function. In a second step, we use this scheme to construct an efficient three-round protocol between two parties to compute a decision tree (or forest) on labeled data provided by both parties. The protocol is in the passively-secure setting and has some leakage on the data that arises from the comparison function on the ciphertexts. We motivate how our protocol can be compiled into an actively-secure protocol with less leakage using secure enclaves, in a graceful degradation manner, e.g. falling back to the uORE leakage, if the enclave becomes fully transparent. We also analyze the leakage of this approach, giving an upper bound on the leaked information. Analyzing the performance of our protocol shows that this approach allows us to be much more efficient (especially w.r.t. the number of rounds) than current MPC-based approaches, hence allowing for an interesting trade-off between security and performance.