A knapsack-type public key cryptosystem is introduced that is the system is based on a novel application of arithmetic in finite fields. By appropriately choosing the parameters, one can control the density of the resulting knapsack, which is the ratio between the number of elements in the knapsack and their size in bits. In particular, the density can be made high enough to foil so-called low-density attacks against the system. At the moment, no attacks capable of breaking the system in a reasonable amount of time are known.
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