PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density

Abstract

By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit attacker has to solve at least two hard number-theoretic problems, namely integer factorization and simultaneous Diophantine approximation problems. In PKCHD, the encryption function is nonlinear about the message vector. Under the re-linearization attack model, PKCHD obtains a high density and is secure against the low-density subset sum attacks, and the success probability for an attacker to recover the message vector with a single call to a lattice oracle is negligible. The infeasibilities of other attacks on the proposed PKCHD are also investigated. Meanwhile, it can use the hardest knapsack vector as the public key if its density evaluates the hardness of a knapsack instance. Furthermore, PKCHD only performs quadratic bit operations which confirms the efficiency of encrypting a message and deciphering a given cipher-text.

Post-Quantum Cryptosystems for Internet-of-Things: A Survey on Lattice-Based Algorithms

“…Figure 5 depicts the communication bandwidths of LBC algorithms implemented with public key encryption (PKE) or with Key encapsulation mechanisms (KEM) schemes [128,135,136]. It can be seen from the results that Saber and ThreeBears variants both consume less bandwidth at diverse NIST security levels and can be considered as the suitable candidates for lightweight implementation of LBC in the IoT networks.…”

“…The principle of replacing matrices with polynomials in integer rings over ideals enables both to be minimized. Therefore, in very effective structures, the substitution of lattices with perfect lattices occurs [136,137]. It is recommended that, for IoT devices (based on communication technologies, such as IEEE 802.11ah, 802.15.4, low-power Wi-Fi, BLE, Lo-Rawan, Sigfox, NB-IoT, etc.…”