The growing complexity of software with respect to technological advances encourages model-based analysis of software systems for validation and verification. Process mining is one recently investigated technique for such analysis which enables the discovery of process models from event logs collected during software execution. However, the usage of logs in process mining can be harmful to the privacy of data owners. While for a software user the existence of sensitive information in logs can be a concern, for a software company, the intellectual property of their product and confidential company information within logs can pose a threat to company's privacy. In this paper, we propose a privacy-preserving protocol for the discovery of process models for software analysis that assures the privacy of users and companies. For this purpose, our proposal uses encrypted logs and processes them using cryptographic protocols in a two-party setting. Furthermore, our proposal applies data packing on the cryptographic protocols to optimize computations by reducing the number of repetitive operations. The experiments show that using data packing the performance of our protocol is promising for privacy-preserving software analysis. To the best of our knowledge, our protocol is the first of its kind for the software analysis which relies on processing of encrypted logs using process mining techniques.</p