Secure computation of hidden Markov models and secure floating-point arithmetic in the malicious model

Hidden Markov model (HMM) is a popular statistical tool with a large number of applications in pattern recognition. In some of these applications, such as speaker recognition, the computation involves personal data that can identify individuals and must be protected. We thus treat the problem of designing privacy-preserving techniques for HMM and companion Gaussian mixture model computation suitable for use in speaker recognition and other applications. We provide secure solutions for both two-party and multi-party computation models and both semi-honest and malicious settings. In the two-party setting, the server does not have access in the clear to either the user-based HMM or user input (i.e., current observations) and thus the computation is based on threshold homomorphic encryption, while the multi-party setting uses threshold linear secret sharing as the underlying data protection mechanism. All solutions use floating-point arithmetic, which allows us to achieve high accuracy and provable security guarantees, while maintaining reasonable performance. A substantial part of this work is dedicated to building secure protocols for floating-point operations in the two-party setting, which are of independent interest.