High speed calculation of cryptographic hash functions by CNN chips

The paper is concerned with the implementation of cryptographic hash functions on the regular array of simple cellular neural network (CNN) cells with periodic boundary conditions. Cryptographic hash functions enable message origin authentication and validation of message content integrity. A class of cryptographic hash functions-termed Cartesian authentication codes-provide provable (unconditional) security for message authentication between two mutually trustful parties sharing a secret key. We succeeded in implementing existing constructions of Cartesian authentication codes on today´s CNN Universal Machine (CNN-UM) chips. Here we prove that rather complex (binary) arithmetic can be performed on a simple CNN chip, by providing an algorithm to implement a specific Cartesian authentication code based on the computation of a polynomial expression over a finite field. The bitrate of the computation is in the 100 Mbit/sec range with existing chips