The article presents a review on the potential of the distributed ledger technology (DLT), particularly federated blockchain, that can be used to create a secure, transparent and patient-managed ecosystem of medical data. The hybrid architecture reviewed uses the blockchain to store immutable metadata and hashes, and manage large amounts of data (for example, diagnostic images) on external cloud storage, which ensures the integrity of data without network overloading. The key aspect of the research is to analyze long-term threats posed by quantum computing that makes current cryptographic standards vulnerable. It is stressed that adoption of post-quantum cryptography (PQC) is required to ensure future security of medical data. An analysis was carried out to compare the leading global (CRYSTALS-Dilithium, Falcon) and Russian (Hypericum, Shipovnik) post-quantum cryptography algorithms.