A method is presented for enabling authentication of a prover in a Radio Frequency Identification system comprising the prover and a verifier, the method comprising the steps of: the prover sending a prover identifier and a parent identifier to the verifier, the verifier sending a verifier identifier to the prover, the prover calculating a first common secret by means of a prover polynomial, where an unknown in the prover polynomial is substituted by a result calculated using a function of at least the verifier identifier, and the verifier calculating the first common secret by means of a first verifier polynomial, wherein a first unknown in the first verifier polynomial is substituted by the prover identifier and a second unknown in the first verifier polynomial is substituted by the parent identifier, the prover creating a first message by modulating a first core secret with regard to at least the first common secret, aid prover sending the first message to the verifier, and the verifier creating a first candidate for the first core secret by demodulating the first message with the first common secret, whereby the candidate for the first core secret is for use in the authentication. This allows the verifier and prover to independently create a common secret, used for modulating the core secret. Furthermore, no pre-registration of the prover with the verifier is required and calculation using polynomials requires little processing power. A corresponding system, prover and verifier are also presented.