In this paper, we propose a vertical side-channel leakage detection on the decryption function of the third round implementation of CPA-secure public-key encryption scheme underlying CRYSTALS-Kyber, a lattice-based key encapsulation mechanism, which is a candidate to the NIST Post-Quantum Cryptography standardization project. Using a leakage assessment metric, we show that the side-channel information can be efficiently used to pinpoint operations leaking the secret variable and how masking countermeasures can be applied. We detect leakages in the polynomial multiplication between the secret key and the ciphertext. We propose and evaluate two different masking countermeasures, based on additive and multiplicative masking. To the best of our knowledge, the multiplicative masking has not been proposed before as a countermeasure to CRYSTALS-Kyber vulnerabilities. We demonstrate their efficiency and discuss their impact in terms of performance. Our work is beneficial to assess and enhance the security of Post-Quantum Cryptography against advanced vertical side-channel analysis.