Evaluation of the Adleman Attack on Multiply Iterated Knapsack Cryptosystems

Early in 1982, A. Shamir [12] announced a polynomial time attack on the basic Merkle-Hellman knapsack cryptosystem. Since that time, attacks on various other knapsack cryptosystems have been proposed [1,2,4,6,7,11]. One of the most influential of the works in this area has been L. Adleman’s paper [1], which was the first to suggest the use of the Lenstra, Lenstra and Lovasz (L3) lattice basis reduction algorithm [9] in attacks on knapsack cryptosystems. The L3 algorithm is now the most important tool used in such attacks.