An apparatus and method are provided for controlling use of bounded pointers. The apparatus includes storage to store bounded pointers, where each bounded pointer comprises a pointer value and associated attributes, with the associated attributes including range information indicative of an allowable range of addresses when using the pointer value. Processing circuitry is used to perform a signing operation on an input bounded pointer in order to generate an output bounded pointer in which a signature generated by the signing operation is contained within the output bounded pointer in place of specified bits of the input bounded pointer. In addition, the associated attributes include signing information which is set by the processing circuitry within the output bounded pointer to identify that the output bounded pointer has been signed. Such an approach provides increase resilience to control flow integrity attack when using bounded pointers.