French to English Tech/Engineering Mathematics & Statistics cryptology

In a document about the different types of attacks that can be carried out against symmetric algorithms (cryptology), the definition of a 'safe' algorithm is one where the most effective attack would be a 'brute force' attack:

c'est-à-dire la recherche systématique de la clef dans l'espace complet.

Now, I have no problems in understanding what is meant by a brute force attack, and I understand that they mean 'taking into consideration all possibilities', but I can't find the exact translation of this mathematical term 'espace complet', and I don't really want to paraphrase it.