After a key pair with a public key and a corresponding private key has been determined on the basis of an initial value, the initial value is made available to a user. The private key can then be erased. When the user wishes to carry out a cryptographic operation based on the "Public-Key-Technology", the user enters the initial value into a computer and, upon utilization of the initial value, a regenerated private key is formed, which corresponds to the private key that had been previously formed but was then erased.