Public-Key Cryptography Based on Tropical Circular Matrices
Some public-key cryptosystems based on the tropical semiring have been proposed in recent years because of their increased efficiency, since the multiplication is actually an ordinary addition of numbers and there is no ordinary multiplication of numbers in the tropical semiring. However, most of th...
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| Format: | Article |
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MDPI AG
2022-07-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/15/7401 |
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| author | Huawei Huang Chunhua Li Lunzhi Deng |
| author_facet | Huawei Huang Chunhua Li Lunzhi Deng |
| author_sort | Huawei Huang |
| collection | DOAJ |
| description | Some public-key cryptosystems based on the tropical semiring have been proposed in recent years because of their increased efficiency, since the multiplication is actually an ordinary addition of numbers and there is no ordinary multiplication of numbers in the tropical semiring. However, most of these tropical cryptosystems have security defects because they adopt a public matrix to construct commutative semirings. This paper proposes new public-key cryptosystems based on tropical circular matrices. The security of the cryptosystems relies on the NP-hard problem of solving tropical nonlinear systems of integers. Since the used commutative semiring of circular matrices cannot be expressed by a known matrix, the cryptosystems can resist KU attacks. There is no tropical matrix addition operation in the cryptosystem, and it can resist RM attacks. The new cryptosystems can be considered as a potential post-quantum cryptosystem. |
| first_indexed | 2024-03-09T05:37:24Z |
| format | Article |
| id | doaj.art-13ec70b819444bd6b2f229a2eb1d6a51 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T05:37:24Z |
| publishDate | 2022-07-01 |
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| series | Applied Sciences |
| spelling | doaj.art-13ec70b819444bd6b2f229a2eb1d6a512023-12-03T12:26:58ZengMDPI AGApplied Sciences2076-34172022-07-011215740110.3390/app12157401Public-Key Cryptography Based on Tropical Circular MatricesHuawei Huang0Chunhua Li1Lunzhi Deng2School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, ChinaSchool of Science, East China Jiaotong University, Nanchang 330013, ChinaSchool of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, ChinaSome public-key cryptosystems based on the tropical semiring have been proposed in recent years because of their increased efficiency, since the multiplication is actually an ordinary addition of numbers and there is no ordinary multiplication of numbers in the tropical semiring. However, most of these tropical cryptosystems have security defects because they adopt a public matrix to construct commutative semirings. This paper proposes new public-key cryptosystems based on tropical circular matrices. The security of the cryptosystems relies on the NP-hard problem of solving tropical nonlinear systems of integers. Since the used commutative semiring of circular matrices cannot be expressed by a known matrix, the cryptosystems can resist KU attacks. There is no tropical matrix addition operation in the cryptosystem, and it can resist RM attacks. The new cryptosystems can be considered as a potential post-quantum cryptosystem.https://www.mdpi.com/2076-3417/12/15/7401cryptographic algorithmkey exchange protocolpublic-key encryption schemetropical algebratropical circular matrices |
| spellingShingle | Huawei Huang Chunhua Li Lunzhi Deng Public-Key Cryptography Based on Tropical Circular Matrices Applied Sciences cryptographic algorithm key exchange protocol public-key encryption scheme tropical algebra tropical circular matrices |
| title | Public-Key Cryptography Based on Tropical Circular Matrices |
| title_full | Public-Key Cryptography Based on Tropical Circular Matrices |
| title_fullStr | Public-Key Cryptography Based on Tropical Circular Matrices |
| title_full_unstemmed | Public-Key Cryptography Based on Tropical Circular Matrices |
| title_short | Public-Key Cryptography Based on Tropical Circular Matrices |
| title_sort | public key cryptography based on tropical circular matrices |
| topic | cryptographic algorithm key exchange protocol public-key encryption scheme tropical algebra tropical circular matrices |
| url | https://www.mdpi.com/2076-3417/12/15/7401 |
| work_keys_str_mv | AT huaweihuang publickeycryptographybasedontropicalcircularmatrices AT chunhuali publickeycryptographybasedontropicalcircularmatrices AT lunzhideng publickeycryptographybasedontropicalcircularmatrices |