Wiretap lattice codes from number fields with no small norm elements
We consider the problem of designing reliable and con dential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for nite lattice constellations a nite sum of inverse of algebraic norms, in fact the analogous for nite sums of the known cr...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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2014
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| Online Access: | https://hdl.handle.net/10356/103869 http://hdl.handle.net/10220/19314 |
| _version_ | 1811690532102995968 |
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| author | Ong, Soon Sheng Oggier, Frédérique |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Ong, Soon Sheng Oggier, Frédérique |
| author_sort | Ong, Soon Sheng |
| collection | NTU |
| description | We consider the problem of designing reliable and con dential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for nite lattice constellations a nite sum of inverse of algebraic norms, in fact the analogous for nite sums of the known criterion for in nite
constellations, which motivates us to study totally real number elds with few elements of small norms, over which ideal lattices can be built to provide wiretap lattice codes. More precisely, we rst narrow down our search to abelian number
elds known to provide reliable lattice codes, among which we look for no small inert primes and large regulators. |
| first_indexed | 2024-10-01T06:05:29Z |
| format | Journal Article |
| id | ntu-10356/103869 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:05:29Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1038692023-02-28T19:41:00Z Wiretap lattice codes from number fields with no small norm elements Ong, Soon Sheng Oggier, Frédérique School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Recreational mathematics We consider the problem of designing reliable and con dential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for nite lattice constellations a nite sum of inverse of algebraic norms, in fact the analogous for nite sums of the known criterion for in nite constellations, which motivates us to study totally real number elds with few elements of small norms, over which ideal lattices can be built to provide wiretap lattice codes. More precisely, we rst narrow down our search to abelian number elds known to provide reliable lattice codes, among which we look for no small inert primes and large regulators. Accepted version 2014-05-12T02:00:21Z 2019-12-06T21:21:56Z 2014-05-12T02:00:21Z 2019-12-06T21:21:56Z 2014 2014 Journal Article Ong, S. S., & Oggier, F. Wiretap lattice codes from number fields with no small norm elements. Designs, Codes and Cryptography, in press. 0925-1022 https://hdl.handle.net/10356/103869 http://hdl.handle.net/10220/19314 10.1007/s10623-014-9935-7 175796 en Designs, codes and cryptography © 2014 Springer Science+Business Media New York. This is the author created version of a work that has been peer reviewed and accepted for publication by Designs, Codes and Cryptography, Springer Science+Business Media New York. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s10623-014-9935-7]. 17 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Recreational mathematics Ong, Soon Sheng Oggier, Frédérique Wiretap lattice codes from number fields with no small norm elements |
| title | Wiretap lattice codes from number fields with no small norm elements |
| title_full | Wiretap lattice codes from number fields with no small norm elements |
| title_fullStr | Wiretap lattice codes from number fields with no small norm elements |
| title_full_unstemmed | Wiretap lattice codes from number fields with no small norm elements |
| title_short | Wiretap lattice codes from number fields with no small norm elements |
| title_sort | wiretap lattice codes from number fields with no small norm elements |
| topic | DRNTU::Science::Mathematics::Recreational mathematics |
| url | https://hdl.handle.net/10356/103869 http://hdl.handle.net/10220/19314 |
| work_keys_str_mv | AT ongsoonsheng wiretaplatticecodesfromnumberfieldswithnosmallnormelements AT oggierfrederique wiretaplatticecodesfromnumberfieldswithnosmallnormelements |