Disclosed is a method, system, and device to authenticate a product. A plurality of public parameters and a secret master key are selected. The public parameters include a hyperelliptic curve equation and a curve pairing function. A public product activation code and a private product activation code are generated based upon the public parameters and the secret master key. The public parameters and the public product activation code are stored with the product. Further, the private product activation code is associated with the product. The product is authenticated if the private product activation code entered to a client device satisfies a mathematical formula implemented with the public parameters and the public product activation code.