A circuit arrangement and method couple a hardware-based pseudorandom number generator (PRNG) to an execution unit in such a manner that pseudorandom numbers generated by the PRNG may be selectively output to the execution unit for use as an operand during the execution of instructions by the execution unit. A PRNG may be coupled to an input of an operand multiplexer that outputs to an operand input of an execution unit so that operands provided by instructions supplied to the execution unit are selectively overridden with pseudorandom numbers generated by the PRNG. Furthermore, overridden operands provided by instructions supplied to the execution unit may be used as seed values for the PRNG. In many instances, an instruction executed by an execution unit may be able to perform an arithmetic operation using both an operand specified by the instruction and a pseudorandom number generated by the PRNG during the execution of the instruction, so that the generation of the pseudorandom number and the performance of the arithmetic operation occur during a single pass of an execution unit.