An exchange of information between a communication entity e.g. a mobile telephone and the operator server upon which it is dependent, in order to carry out authentication operations by exchanging keys and using cryptography algorithms. According to the invention, an algorithm is used, comprising: algorithmic treatments using, as input data, all or part of a random number and operating keys derived from two keys, and a combined treatment using data derived from algorithmic treatments in order to provide results to enable the linkage.