A data processing system comprising: ownership circuitry to enforce ownership rights of memory regions within a physical memory address space, a given memory region having a given owning process specified from among a plurality of processes and independently of privilege level, said given owning process having exclusive rights to control access to said given memory region, wherein said given owning process designates said given memory region as one of: private to said given owning process; and shared between said given owning process and at least one further source of memory access requests.