An information security device receives an input of prime q, and generates prime N that is larger than prime q. In the information security device, a partial information setting unit generates number u such that 2.times.u.times.q+1.noteq.0 mod L.sub.i (i=1, 2, . . . , n). A random number generating unit generates random number R'. A judgement target generating unit generates R=u+L.sub.1.times.L.sub.2.times. . . . .times.L.sub.n.times.R' and N=2.times.R.times.q+1, using number u and random number R'. A primality judging unit judges the primality of number N, using numbers N and R generated by the judgement target generating unit.