Random Integer Lattice Generation via the Hermite Normal Form
Lattices used in cryptography are integer lattices. Defining and generating a “random integer lattice” are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the rand...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1509 |
| _version_ | 1797510348625936384 |
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| author | Gengran Hu Lin You Liang Li Liqin Hu Hui Wang |
| author_facet | Gengran Hu Lin You Liang Li Liqin Hu Hui Wang |
| author_sort | Gengran Hu |
| collection | DOAJ |
| description | Lattices used in cryptography are integer lattices. Defining and generating a “random integer lattice” are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the random integer lattice given by G. Hu et al. and present an improved generation algorithm for it via the Hermite normal form. It can be proven that with probability ≥0.99, this algorithm outputs an <i>n</i>-dim random integer lattice within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> operations. |
| first_indexed | 2024-03-10T05:31:13Z |
| format | Article |
| id | doaj.art-197f0c17bb274ab68213184da3831b2e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:31:13Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-197f0c17bb274ab68213184da3831b2e2023-11-22T23:16:01ZengMDPI AGEntropy1099-43002021-11-012311150910.3390/e23111509Random Integer Lattice Generation via the Hermite Normal FormGengran Hu0Lin You1Liang Li2Liqin Hu3Hui Wang4School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, ChinaSchool of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, ChinaSchool of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, ChinaSchool of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, ChinaSchool of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, ChinaLattices used in cryptography are integer lattices. Defining and generating a “random integer lattice” are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the random integer lattice given by G. Hu et al. and present an improved generation algorithm for it via the Hermite normal form. It can be proven that with probability ≥0.99, this algorithm outputs an <i>n</i>-dim random integer lattice within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> operations.https://www.mdpi.com/1099-4300/23/11/1509random integer latticeHermite normal formgeneration algorithm |
| spellingShingle | Gengran Hu Lin You Liang Li Liqin Hu Hui Wang Random Integer Lattice Generation via the Hermite Normal Form Entropy random integer lattice Hermite normal form generation algorithm |
| title | Random Integer Lattice Generation via the Hermite Normal Form |
| title_full | Random Integer Lattice Generation via the Hermite Normal Form |
| title_fullStr | Random Integer Lattice Generation via the Hermite Normal Form |
| title_full_unstemmed | Random Integer Lattice Generation via the Hermite Normal Form |
| title_short | Random Integer Lattice Generation via the Hermite Normal Form |
| title_sort | random integer lattice generation via the hermite normal form |
| topic | random integer lattice Hermite normal form generation algorithm |
| url | https://www.mdpi.com/1099-4300/23/11/1509 |
| work_keys_str_mv | AT gengranhu randomintegerlatticegenerationviathehermitenormalform AT linyou randomintegerlatticegenerationviathehermitenormalform AT liangli randomintegerlatticegenerationviathehermitenormalform AT liqinhu randomintegerlatticegenerationviathehermitenormalform AT huiwang randomintegerlatticegenerationviathehermitenormalform |