Natural numbers c, o, and a, and p-bit bit strings w1 and w2 are inputted. w1 and w2 are stored in an internal status storage unit and a generator storage unit respectively. The value g of p bits stored in the internal status storage unit is defined as a generator. The value of high order bits of the p bits stored in the internal status storage unit is defined as s. Then, g.sup.s represented by p bits is calculated, stored in the internal status storage unit, and high order o bits of the stored p bits are output. The series of processes are repeated a times, and a pseudo-random numbers are generated. Thus, pseudo-random numbers whose security has been mathematically guaranteed can be quickly generated.