Quadratic compact knapsack public‐key cryptosystem

Knapsack‐type cryptosystems were among the first public‐key cryptographic schemes to be invented. Their NP‐completeness nature and the high speed in encryption/decryption made them very attractive. However, these cryptosystems were shown to be vulnerable to the low‐density subset‐sum attacks or some key‐recovery attacks. In this paper, additive knapsack‐type public‐key cryptography is reconsidered. We propose a knapsack‐type public‐key cryptosystem by introducing an easy quadratic compact knapsack problem. The system uses the Chinese remainder theorem to disguise the easy knapsack sequence. The encryption function of the system is nonlinear about the message vector. Under the relinearization attack model, the system enjoys a high density. We show that the knapsack cryptosystem is secure against the low‐density subset‐sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions. It is shown that the proposed cryptosystem is also secure against some brute‐force attacks and some known key‐recovery attacks including the simultaneous Diophantine approximation attack and the orthogonal lattice attack.