Using the Multiple Subset Problem for encryption and communication

• Published in: 2024 IEEE International Conference on Microwaves, Communications, Antennas, Biomedical Engineering and Electronic Systems (COMCAS) pp. 1 - 4
• Main Authors: Zadok, Yair, Voloch, Nadav, Bloch, Noa Voloch, Hajaj, Maor Meir
• Format: Conference Proceeding
• Language: English
• Published: IEEE 09.07.2024
• Subjects: Biomedical engineering; communication; cryptography; Encryption; Microwave antennas; Microwave communication; Microwave theory and techniques; NP-complete problems; Safety; subset problem
• ISSN: 2150-8968
• DOI: 10.1109/COMCAS58210.2024.10666243

The use of well-known mathematical problems for encryption is a known technique since the computationally hard ones (NP-complete) ensure safety in possible attacks on the encryption method. The subset sum problem (SSP) can be simply described as: given a set of integers \boldsymbol{A} , and an integer \boldsymbol{s} , find a subset of items from \boldsymbol{A} summing up to \boldsymbol{s} . To this classic problem there are many variants; one is the multiple-subset problem (MSSP) in which there is a selection of items from a given set to several identical bins, having each bin capacity not exceeded, and the total weight of the items is maximized. Here a related different kind of problem is approached: given a set of sets \boldsymbol{A}=\{\boldsymbol{A}_{1},\boldsymbol{A}_{2},\ldots,\boldsymbol{A}_{\boldsymbol{n}}\} , find an integer \boldsymbol{s} , for which every subset of the given sets is summed up to, if such an integer exists. As a variant of SSP, the problem is NP-complete, and for known private keys, a relatively efficient algorithm is given, based on dispensing non-relevant values of the possible sums. In this paper we present the encryption scheme based on MSSP and present its novel usage and implementation in communication.