The condition number associated with ideal lattices from odd prime degree cyclic number fields
The condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the “Ring Learning With Errors (RLWE)” and the “Pol...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-02-01
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| Series: | Journal of Mathematical Cryptology |
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| Online Access: | https://doi.org/10.1515/jmc-2024-0022 |
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| _version_ | 1823860496881680384 |
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| author | de Araujo Robson Ricardo |
| author_facet | de Araujo Robson Ricardo |
| author_sort | de Araujo Robson Ricardo |
| collection | DOAJ |
| description | The condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the “Ring Learning With Errors (RLWE)” and the “Polynomial Learning With Errors (PLWE)”. In this work, we compute the condition number of a generator matrix of the ideal lattice from the whole ring of integers of any odd prime degree cyclic number field using canonical embedding. |
| format | Article |
| id | doaj-art-60ef7636cffd4e74ae9ec8d49d615650 |
| institution | Kabale University |
| issn | 1862-2984 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Mathematical Cryptology |
| spelling | doaj-art-60ef7636cffd4e74ae9ec8d49d6156502025-02-10T13:24:30ZengDe GruyterJournal of Mathematical Cryptology1862-29842025-02-0119113510.1515/jmc-2024-0022The condition number associated with ideal lattices from odd prime degree cyclic number fieldsde Araujo Robson Ricardo0Federal Institute of São Paulo, Av. Pastor José Dutra de Moraes, 239 - Distrito Industrial Antônio Zácaro - Catanduva - SP, 15808-305, BrazilThe condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the “Ring Learning With Errors (RLWE)” and the “Polynomial Learning With Errors (PLWE)”. In this work, we compute the condition number of a generator matrix of the ideal lattice from the whole ring of integers of any odd prime degree cyclic number field using canonical embedding.https://doi.org/10.1515/jmc-2024-0022condition numberrlweplweabelian number fieldsideal lattices11t7115a1211r2011c99 |
| spellingShingle | de Araujo Robson Ricardo The condition number associated with ideal lattices from odd prime degree cyclic number fields Journal of Mathematical Cryptology condition number rlwe plwe abelian number fields ideal lattices 11t71 15a12 11r20 11c99 |
| title | The condition number associated with ideal lattices from odd prime degree cyclic number fields |
| title_full | The condition number associated with ideal lattices from odd prime degree cyclic number fields |
| title_fullStr | The condition number associated with ideal lattices from odd prime degree cyclic number fields |
| title_full_unstemmed | The condition number associated with ideal lattices from odd prime degree cyclic number fields |
| title_short | The condition number associated with ideal lattices from odd prime degree cyclic number fields |
| title_sort | condition number associated with ideal lattices from odd prime degree cyclic number fields |
| topic | condition number rlwe plwe abelian number fields ideal lattices 11t71 15a12 11r20 11c99 |
| url | https://doi.org/10.1515/jmc-2024-0022 |
| work_keys_str_mv | AT dearaujorobsonricardo theconditionnumberassociatedwithideallatticesfromoddprimedegreecyclicnumberfields AT dearaujorobsonricardo conditionnumberassociatedwithideallatticesfromoddprimedegreecyclicnumberfields |