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应用的技术，因为这些数学难题计算复杂度高，能为加密方法提供抵御潜在攻击的安全性。子集和问题（SSP）可定义为：从给定整数集合中寻找一个子集，使得该子集元素之和等于指定整数。经典的SSP存在多种变体，其中之一即为多重子集问题（MSSP）。MSSP的目标是从给定集合中选取物品，并将其分配到多个容器中，确保每个容器的容量不被超出，同时最大化所选物品的总重量。本文以不同视角探讨了一个相关但不同类型的问题：给定一个由多个集合组成的集合A={A1, A2..., An}，寻找一个整数s，使得每个给定集合的某个子集的元素之和均等于s（若此整数存在）。当将该问题视为SSP的变体时，它属于NP完全问题。然而，存在一种针对已知私钥的相对高效的算法，该算法基于剔除潜在总和中的非相关值。本文提出了基于MSSP的加密方案，并展示了该方案在通信中的新型应用与实现。