Multiple Subset Problem as an encryption scheme for communication
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909079453040640 |
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| author | Zadok, Yair Voloch, Nadav Voloch-Bloch, Noa Hajaj, Maor Meir |
| author_facet | Zadok, Yair Voloch, Nadav Voloch-Bloch, Noa Hajaj, Maor Meir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09221 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple Subset Problem as an encryption scheme for communication Zadok, Yair Voloch, Nadav Voloch-Bloch, Noa Hajaj, Maor Meir Cryptography and Security 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. |
| title | Multiple Subset Problem as an encryption scheme for communication |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2401.09221 |