The subset sum problem and arithmetic coding

Abstract

The security offered by symmetric cryptosystems based on the arithmetic coding algorithm is examined. It is shown that this can be reduced naturally to the subset sum problem. The subset sum problem is NP-complete, however, the cases which arise in practical cryptosystems based on this problem tend to be solvable in polynomial time because the sums formed are either superincreasing or of low density. Our attack is therefore similar to attacks on public-key cryptosystems based on the subset sum problem (knapsack systems).