Privacy preserving probabilistic inference with Hidden Markov Models

Alice possesses a sample of private data from which she wishes to obtain some probabilistic inference. Bob possesses Hidden Markov Models (HMMs) for this purpose, but he wants the model parameters to remain private. This paper develops a framework that enables Alice and Bob to collaboratively compute the so-called forward algorithm for HMMs while satisfying their privacy constraints. This is achieved using a public-key additively homomorphic cryptosystem. Our framework is asymmetric in the sense that a larger computational overhead is incurred by Bob who has higher computational resources at his disposal, compared with Alice who has limited computing resources. Practical issues such as the encryption of probabilities and the effect of finite precision on the accuracy of probabilistic inference are considered. The protocol is implemented in software and used for secure keyword recognition.