1. A cryptography apparatus, comprising: multiple multiplication units, which are arranged in two or more multiplication levels, and which are configured to operate in accordance with Galois-Field (GF) arithmetic over respective Galois fields; and logic circuitry, which is configured to receive input data, comprising plain-text or cipher-text data whose word-size exceeds a maximal input word-size among the multiplication units, to hold a cryptographic key, which comprises an authentication key comprising multiple sub-keys whose number does not exceed a number of the multiplication units, and to perform on the input data a cryptographic operation that comprises an authentication operation applied to the plain-text or to the cipher-text data, by applying the sub-keys to the multiplication units, wherein the logic circuitry is configured to authenticate the cipher-text data by comparing between a first signature calculated from first data that is derived from the cipher-text data during decryption, and a second signature calculated from second data that is derived from the plain-text during encryption, wherein when the first and second signatures are equal to one another, then the cipher text is considered authentic with high probability.