A Multiple-Iterated Trapdoor for Dense Compact Knapsacks

A modification to the multiple-iterated Merkle-Hellman trapdoor is described that permits a knapsack density exceeding the critical density 0.94 of the Lagarias-Odlyzko low-density attack. A high density level also permits fast signature generation. Compaction and common knapsack weights are used to reduce the public-key size. The security of the new trapdoor depends on a simultaneous diophantine approximation problem plus a residue recombination problem.

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