The subset sum problem, which is often called as the knapsack
  problem, is known as an NP-hard problem, and there are
  several cryptosystems based on the problem.
  The low-density attack algorithm by Lagarias and Odlyzko and
  its variants solve the subset sum problem efficiently, when the
  ``density'' of the given problem is smaller than some threshold.
  In the definition of the density, knapsacks are usually assumed
  to be chosen uniformly at random from the same interval.
  However, in general subset sum problem case, this assumption
  may not always hold. Further, changing values of knapsacks with
  maximum value fixed can affect the success probability of problem
  solving algorithms. In this paper, we assume that knapsacks are
  chosen from different intervals, and make analysis of the effect
  on the success probability of above algorithms  both
  theoretically and experimentally.