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, en-suring that the capacity of each bin is not exceeded while maximizing the total weight of the selected items. This approach addresses a related problem with a different perspective. Here a related different kind of problem is approached: given a set of sets A={A1, A2..., An}, 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 pri-vate keys. This algorithm is based on dispensing non-relevant values of the potential sums. In this paper we present the encryption scheme based on MSSP and present its novel usage and implementation in communication.

翻译：利用已知数学难题进行加密是一种广泛使用的技术，因为这些难题在计算上具有困难性，能够为加密方法提供抵御潜在攻击的安全性。子集和问题可定义为从给定集合中寻找一个子集，使得该子集中整数的和等于指定整数。经典子集和问题存在多种变体，其中一种是多子集问题。在多子集问题中，目标是从给定集合中选择物品并将其分配到多个箱子中，确保每个箱子的容量不被超出，同时最大化所选物品的总重量。该方法以不同的视角处理一个相关的问题。本文探讨了一种不同形式的相关问题：给定集合簇A={A1, A2..., An}，寻找一个整数s使得每个给定集合的子集之和均等于该整数（若这样的整数存在）。当将该问题视为子集和问题的变体时，它是NP完全的。然而，存在一种对于已知私钥相对高效的算法，该算法基于剔除潜在求和中无关的值。本文提出了一种基于多子集问题的加密方案，并展示了其在通信中的新型应用与实现。