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Using well-known mathematical problems for encryption is a widely usedtechnique because they are computationally hard and provide security againstpotential attacks on the encryption method. The subset sum problem (SSP) can bedefined as finding a subset of integers from a given set, whose sum is equal toa specified integer. The classic SSP has various variants, one of which is themultiple-subset problem (MSSP). In the MSSP, the goal is to select items from agiven set and distribute them among multiple bins, en-suring that the capacityof each bin is not exceeded while maximizing the total weight of the selecteditems. This approach addresses a related problem with a different perspective.Here a related different kind of problem is approached: given a set of setsA={A1, A2..., An}, find an integer s for which every subset of the given setsis summed up to, if such an integer exists. The problem is NP-complete whenconsidering it as a variant of SSP. However, there exists an algorithm that isrelatively efficient for known pri-vate keys. This algorithm is based ondispensing non-relevant values of the potential sums. In this paper we presentthe encryption scheme based on MSSP and present its novel usage andimplementation in communication.

Multiple Subset Problem as an encryption scheme for communication