ightly larger than N and R=2n, and N=2n-1 +2n-2 ???2n-2 + . . . +a1 ???21 +a0 20, a second mode modular arithmetic A???B???R' mod N, where B is a number stored in said B register, and a third mode modular arithmetic A???R' mod N; and a timing/control circuit operable to output operation timing signals for controlling all circuits of said arithmetic apparatus, and, based on a prescribed procedure,