An identification card, comprising several laminated layers, one of which is of material capable of being magnetized, has 350 spots on it, each of which is capable of having one portion of the spot magnetized north and the other portion magnetized south. The 350 spots are divided into groups of randomly selected spots. One group, for example, represents the serial number of the card and has the portions of its spots magnetized accordingly. Apparatus for reading, and for remagnetizing the card to change the information recorded thereon, is also provided. This apparatus includes a horseshoe core (for each spot) that bridges the two magnetized portions of the spot. A "Hall effect" device detects the direction of the flux in said horseshoe core to respond to the direction of the magnetism of the portions of the spot. The polarity of the portions comprising the spot may be reversed by energizing a coil on the horseshoe core.