In the present paper, we extend previous results of an id scheme based on
compact knapsack problem defined by one equation. We present a sound three-move
id scheme based on compact knapsack problem defined by an integer matrix. We
study this problem by providing attacks based on lattices. Furthermore, we
provide the corresponding digital signature obtained by Fiat-Shamir transform
and we prove that is secure under ROM. These primitives are post quantum
resistant.