The　integration　of　5 G　edge　computing　in　the　Internet　of　Medical　Things　(IoMT)　holds　the　promise　for　decentralized　medical　services.　However,　this　advancement　raises　substantial　security　concerns,　particularly　concerning　data　integrity　and　access　control.　The　preservation　of　patient　privacy　and　data　security　is　imperative,　given　the　sensitive　nature　of　medical　data.　Despite　existing　research　efforts,　current　solutions　exhibit　notable　drawbacks.　In　particular,　integrity　and　access　control　issues　are　often　addressed　in　isolation,　resulting　in　elevated　input/output　(I/O)　and　communication　costs.　Additionally,　many　solutions　lack　the　efficiency　necessary　for　deployment　on　small　IoMT　devices.　This　paper　introduces　a　groundbreaking　cryptographic　solution,　named　online/offline　remote　signcryption　($\text{O}^{2}\text{RSC}$),　effectively　addressing　these　limitations.　$\text{O}^{2}\text{RSC}$　facilitates　the　simultaneous　provision　of　integrity　and　access　control　services,　minimizing　computational　operations　in　online　mode.　Our　inspection　is　executed　without　the　need　for　complete　data　downloads,　significantly　reducing　communication　costs.　Our　analysis　shows　that　$\text{O}^{2}\text{RSC}$　is　secure　and　cost-effective　than　current　state-of-the-art　schemes.　Our　online/offline　technique　significantly　reduces　system　overhead.　For　200 KB　of　data,　$\text{O}^{2}\text{RSC}$　is　over　100　times　faster　in　encryption　and　decryption,　and　it　reduces　ciphertext　size　by　over　100　times.　For　200 MB　of　data,　$\text{O}^{2}\text{RSC}$　tags　over　100　times　faster.　IEEE