A cryptography method involving a keyholder having a number m.gtoreq.1 of private keys Q.sub.1, Q.sub.2, . . . , Q.sub.m and respective public keys G.sub.1, G.sub.2, . . . , G.sub.m, each pair of keys (Q.sub.i, G.sub.i) (where i=1, . . . , m) satisfying either the relationship G.sub.1=Q.sub.i.sup.v mod n or the relationship G.sub.i.times.Q.sub.i.sup.v=1 mod n, where n is a public integer equal to the product of f (where f>1) private prime factors p.sub.1, . . . , p.sub.f, at least two of which are separate, and the exponent v is a public integer equal to a power of 2. Disclosed is what mathematical structure may be imparted to the public keys for it to be impossible to calculate said private keys from said public parameters in a reasonable time unless said prime factors are known. Devices adapted to implement the method are also disclosed.