Efficient data integrity protection

A message authentication code, MAC, is generated in an electronic circuit, wherein the MAC integrity protects a data value, PD. A random challenge word, RND, is received from a source that is external to the electronic circuit. A first function G(RND,K) is evaluated that generates a first encrypted value, K?, from RND and K, wherein K is a secret key value that is stored on the electronic circuit. A second function F(RND,K) is evaluated that generates a second encrypted value, K?, from RND and K. The MAC is then generated in accordance with MAC=K?+m1K?+m2K?2+ . . . +MlK?l, wherein m1, m2, . . . , ml are derived by representing the data value, PD, as an l-tuple of elements in a field, GF(2n), wherein n is an integer greater than zero. A hardware-efficient arrangement is also disclosed for generating this and other MACs.