An apparatus has processing circuitry for processing instructions from multiple threads. A storage structure is shared between the threads and has a number of entries. Indexing circuitry generates a target index value identifying an entry of the storage structure to be accessed in response to a request from the processing circuitry specifying a requested index value corresponding to information to be accessed from the storage structure. The indexing circuitry generates the target index value as a function of the requested index value and a key value selected depending on which of the threads trigger the request. The key value for at least one of the threads is updated from time to time.