A cryptography method involving a keyholder having a number m≧1 of private keys Q1, Q2, . . . , Qm and respective public keys G1, G2, . . . , Gm, each pair of keys (Qi, Gi) (where i=1, . . . , m) satisfying either the relationship G1=Qiv mod n or the relationship Gi×Qiv=1 mod n, where n is a public integer equal to the product of f (where f>1) private prime factors p1, . . . , pf, 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.