There is provided an authentication method for a system (10) comprising several devices (30). The method involves: a) providing each device (30) with an identity value (pi: i=1, . . . , n) and a polynomial (P) for generating a polynomial key; (b) including a verifier device (p1) and a prover device (P2)amongst said devices (30); (c) arranging for the prover device (p2) to notify its existence to the verifier device (P1); (d) arranging for the verifier device (pi) to challenge the prover device (p2) to encrypt a nonce using the prover (P2)device's polynomial (P) key and communicate the encrypted nonce as a response to the verifier device (p1); (e) arranging for the verifier device (p1) to receive the encrypted nonce as a further challenge from the prover device (pZ) and: (i ) encrypt the challenge using the polynomial keys generated from a set of stored device identities; or (ii) decrypt the challenge received using the set of polynomial keys; until said verifier device (p1) identifies an authentication match.