In a distributed network there is always a need for communicating parties to authenticate each other. The prevalent solution is to build chains of certificates, issued by authorities. These chains must be communicated within the network, and checked, which often is a drawback. Assuming that the structure of the network is such that authorities are organized in a hierarchic tree, we tried a method to get individul, identity-based authentication without any certificate at all. The public key, in the pair of keys used for authentication, is essentially the identity itself. We also could certify information without chains of certificates. The authorities would be assigned primes in a scheme known to everyone. The security of the method was meant to be based upon the fact, that it is computationally difficult to calculate the root in a finite field. However, the method failed. For the two classes of functions that we have studied, exponentiation in a finite field and points on elliptic curves, we could not find a way to prevent two dishonest users to calculate a key that should not be known to them. Despite the failure, we still chose to report the method in case it could be used in some other class of functions.