A multiple-iterated trapdoor for dense compact knapsacks

Abstract

A modification to the multiple-iterated Merfcle-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.