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.

翻译：本文扩展了先前基于单一方程定义紧致背包问题的身份识别方案结果。我们提出了一种基于整数矩阵定义紧致背包问题的可靠三轮识别方案，并通过格基攻击方法对该问题进行了研究。此外，我们给出了通过Fiat-Shamir变换对应的数字签名方案，并证明了其在随机预言机模型下的安全性。这些密码原语具有抗量子特性。