Multiple Subset Problem as an Encryption Scheme for Communication

Using well-known mathematical problems for encryption is a widely used technique, because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as finding a subset of integers from a given set, whose sum is equal to a specified integer. The classic SSP has various variants, one of which is the multiple-subset problem (MSSP). In the MSSP, the goal is to select items from a given set and distribute them among multiple bins, ensuring that the capacity of each bin is not exceeded while maximizing the total weight of the selected items. This approach addresses a related problem from a different perspective. Here, a related different kind of problem is approached: given a set of sets A = {A₁, A₂,…, A_n}, find an integer s, for which every subset of the given sets is summed up to, if such an integer exists. The problem is NP-complete when considering it as a variant of SSP. However, there exists an algorithm that is relatively efficient for known private keys. This algorithm is based on dispensing nonrelevant values of the potential sums. In this paper, we present the encryption scheme based on MSSP and its novel usage and implementation in communication.