Cryptography is a fundamental cornerstone of security on the modern internet, facilitating the confidentiality, integrity, and authenticity of data. Most cryptography in use today bases their security on the assumed hardness of certain computational problems like the discrete logarithm problem or the prime factorization of large integers. Both of these are problems that are easy to solve for a quantum computer, which motivates the need to transition to post-quantum encryption (PQC). Several PQC candidate encryption methods have been suggested, with NIST standardizing algorithms for key exchange and digital signatures. There are also methods, such as hybrid encryption, where a PQC algorithm is combined with a classical (non-PQC) algorithm to create a hybrid scheme. Utilizing hybrid encryption is an essential technique to accelerate the transition to post-quantum cryptography. Preliminary studies have shown that neural estimators can identify weak encryption algorithms and quantify information leaked through side channels. Our goal is to expand this analysis to identifying potential weaknesses introduced when combining encryption algorithms in hybrid encryption. This is a study to use newly developed neural estimators of Mutual information, such as for example MINE, InfoNCE, or CLUB, to quantify the amount of information leaked through side channels. Furthermore, the project aims to use these estimators to evaluate countermeasures to side channel attacks.