A method for enabling a personal computer to be authenticated by a server is provided. The method comprises the step, which includes for the user in launching the execution of a log-on procedure software, introducing personal identifiers providing access to a signature private key for long-term use relative to the duration of the session. The log-on procedure software produces: identification data of the session Id, a public ephemeral module, a public exponent and at least a pair of ephemeral pubic numbers and ephemeral private numbers related by a generic equation of the type: G.sub.i.ident.Q.sub.i.sup.v (mod n) or G.sub.iQ.sub.i.sup.v.ident.1 (mod n), an ephemeral certificate linking, by means of said signature private key, Id and public ephemeral module. The public ephemeral module is of reduced size relative to the signature private key.