A converter uses a predetermined parameter a. A generating unit accepts generated inputs x.sub.1, . . . , x.sub.n, and generates generated outputs, y.sub.1, . . . , y.sub.n, using recurrence formulas, y.sub.1=F.sub.1(x.sub.1, a) and y.sub.i+1=F.sub.i+1(x.sub.i+1, y.sub.i) (1.ltoreq.i.ltoreq.n-1). A key accepting unit accepts key inputs, k.sub.1, . . . , k.sub.n, and gives them as generated inputs to said generating unit. A repetition controller gives the generated outputs as generated inputs to said generating unit, for an "m" (m.gtoreq.0) number of times, and sets one of the generated outputs to be given at the end as a random number string, r.sub.1, . . . , r.sub.n. The data accepting unit accepts data inputs, d.sub.1, . . . , d.sub.n. The converting unit converts data using, e.sub.i=d.sub.i r.sub.i, and, outputs data outputs, e.sub.1, . . . , e.sub.n. The converter can be used both for encrypting and decrypting data.