On the critical density associated with the matrix type knapsack cryptosystem

The knapsack cryptosystem invented by Merkle and Hellman and most of its variants have already been broken. The method by Lagarias and Odlyzko, known as the low density attack, is a powerful tool for attacking knapsack cryptosystems. No successful attack, however, has been reported against the matrix type knapsack system. We derive the critical density associated with this system and show some results of computer experiments of attack.