Trapdoor Knapsacks Without Superincreasing Structure

Abstract Shamir (1982) has recently presented a polynomial-time algorithm for breaking Merkle-Hellman public-key schemes. The flaw in such a scheme is not in the use of knapsacks per se, but in the embedding of superincreasing structure as a trapdoor technique. In this paper, several trapdoor techniques are outlined that are not dependent on hiding superincreasing sequences.