The security assessment of post-quantum cryptography, from the perspective of physical attacks, has been extensively studied in the literature, particularly with regard to the ML-KEM and ML-DSA standards, which are based on Euclidean lattices. Furthermore, in March 2025, the HQC scheme, based on error-correcting codes, was standardized as an alternative key encapsulation mechanism to ML-KEM. Recently, Soft-Analytical Side-Channel Attacks (SASCA) have been used on a wide variety of algorithms to combine information related to intermediate variables in order to trace back to the secret, providing a form of “correction” to the uncertainty associated with profiled attacks. SASCA is based on probabilistic models called “factor graphs,” to which a “belief propagation” algorithm is applied. In the case of attacks on post-quantum cryptosystems, it is theoretically possible to use the underlying mathematical structure to process the output of a SASCA attack in the form of cryptanalysis. This has been demonstrated, for example, on ML-KEM. The objective of this thesis is to develop a methodology and the necessary tools for cryptanalysis and residual complexity calculation for cryptography based on error-correcting codes. These tools will need to take into account information (“hints”) obtained from a physical attack. A second part of the thesis will be to study the impact that this type of tool can have on the design of countermeasures.