1. A virtual machine system comprising: a processor having a first mode and a second mode, the processor executing a first operating system in the first mode, and the processor executing a second operating system executed in the second mode; write control circuitry that permits writing of data into a predetermined secure storage area in an external main memory, the writing of data into the secure storage area only being permitted when the processor is in the first mode; and a cache memory having a plurality of ways for storing data read by the processor from the main memory, wherein the cache memory includes: data storage circuitry that, when the processor has read data from the main memory, stores the data into any of the plurality of ways that is ready to newly store data, in a manner that allows for identification of whether the data has been read from the secure storage area; and write-back circuitry that (i) identifies whether data has been read from the secure storage area and (ii) writes back data stored by the data storage circuitry to the main memory with use of a predetermined algorithm according to a result of the identification, such that the number of times data stored in each of the ways is intermittently written back to the secure storage area is reduced and the number of times the processor is switched from the second mode to the first mode to perform writing of data to the secure storage area is reduced, and when the processor executing the second operating system accesses the main memory, the write-back circuitry writes back, to the secure storage area, data that is identified as having been read from the secure storage area and that is stored in at least one of the ways by (i) causing the processor to switch from the second mode to the first mode and (ii) writing, to the secure storage area, the data that is identified as having been read from the secure storage area and that is stored in at least one of the ways so that the at least one of the ways is ready to newly store data.