Short cycling in the Kravitz-Reed public key encryption system

The Kravitz-Reed public key encryption system, a variant of the MIT system based on Galois fields, is interesting because it offers the potential of high security with efficient implementation. In the letter we demonstrate that high security and efficient implementation are not, in reality, compatible goals with this algorithm. Efficient implementation is subject to a short cycling attack that exposes the secret key to computation. If the parameters of the algorithm are selected for high security, then the algorithm cannot be efficiently implemented.