An authentication method of a prover device by a verifier device using cryptographic coupons is provided, where a coupon includes a pseudo-random number ri, where i is an index for labeling the coupon, and a reduced-coupon xi such that xi=ƒ(ri), where ƒ is a predetermined one-way function, the method including the following steps: the verifier device sends a challenge consisting of a random value c to the prover device; the prover device sends to the verifier device a response y calculated by using the pseudo-random number ri, the challenge c, and a secret key s belonging to the prover device; and the verifier device checks the validity of the response y based on the challenge c, the reduced-coupon xi corresponding to the pseudo-random number ri, and a public key V corresponding to the secret key s, the reduced-coupon xi being received by the verifier device from a source external to the prover device.