Reviving Knapsack-Based Public-Key Encryption: A New Approach 🔑

Public-key cryptography is a ubiquitous building-block of modern telecommunication technology. Among the most historically important, the knapsack-based encryption schemes, from the early years of public-key cryptography, performed particularly well in computational resources (time and memory), and mathematical and algorithmic simplicity. Although effective cryptanalyses readily curtailed their widespread adoption to several different attempts, the possibility of actual usage of knapsack-based asymmetric encryption schemes remains unsettled. This paper aims to present a novel construction that offers consistent security improvements on knapsack-based cryptography. We propose two improvements upon the original knapsack cryptosystem that address the most important types of attacks: the Diophantine approximations-based attacks and the lattice problems oracle attacks. The proposed defences demonstrably preclude the types of attacks mentioned above, thus contributing to revive knapsack schemes or settle the matter negatively. Finally, we present the Nep.Sec, a contest that is offering a prize for breaking our proposed cryptosystem. KEYWORDS: Knapsack Problem. Subset Sum Problem. Public-Key Cryptosystem. Merkle-Hellman Cryptosystem. Lattice Oracle. Diophantine Approximation. Shamir Cryptanalysis