This work performs a side-channel analysis on the Hybrid Homomorphic Encryption cipher Elisabeth-b4. In particular, a Correlation Power Analysis allows to recover the 2048-bit key with 35,000 traces. Mounting template attacks or using Machine Learning decreases this number to 1,000. We then implement 2-share masking and shuffling, which completely eliminates the leakage measure – a Test Vector Leakage Assessment (TVLA) – and mitigates the Correlation Power Analysis and template attacks. Using a Divide and Conquer Deep Learning approach, we manage to bypass them but the number of required traces increases to 250,000.