We present an algorithm that enables privacy-preserving speech recognition transactions between multiple parties. We assume two commonplace scenarios. One being the case where one of two parties has private speech data to be transcribed and the other party has private models for speech recognition. And the other being that of one party having a speech model to be trained using private data of multiple other parties. In both of the above cases data privacy is desired from both the data and the model owners. In this paper we will show how such collaborations can be performed while ensuring no private data leaks using secure multiparty computations. In neither case will any party obtain information on other parties data. The protocols described herein can be used to construct rudimentary speech recognition systems and can be easily extended for arbitrary audio and speech processing.