Deployed widely and embedding sensitive data, IoT devices depend on the reliability of cryptographic libraries to protect user information. However when implemented on real systems, cryptographic algorithms are vulnerable to side channel attacks based on their execution behavior, which can be revealed by measurements of physical quantities such as timing or power consumption. Some countermeasures can be implemented in order to prevent those attacks. However those countermeasures are generally designed at high level description, and when implemented, some residual leakage may persist. In this article we propose a methodology to assess the robustness of the MbedTLS library against timing and cache-timing attacks. This comprehensive study of side-channel security allows us to identify the most frequent weaknesses in software cryptographic code and how those might be fixed. This methodology checks the whole source code, from the top level routines to low level primitives, that are used for the final application. We recover hundreds of lines of code that leak sensitive information.