On The Secrecy Gain Of Extremal Even l-modular Lattices
The secrecy gain is a lattice invariant that appears in the context of wiretap lattice coding. It has been studied for unimodular lattices, for 2 −, 3 −, and 5 −modular lattices. This paper studies the secrecy gain for extremal even l-modular lattices, for l ∈ {2, 3, 5, 6, 7, 11, 14, 15, 23}. We com...
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| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/86844 http://hdl.handle.net/10220/44358 |
| _version_ | 1811697097490038784 |
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| author | Oggier, Frédérique Belfiore, Jean-Claude |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Oggier, Frédérique Belfiore, Jean-Claude |
| author_sort | Oggier, Frédérique |
| collection | NTU |
| description | The secrecy gain is a lattice invariant that appears in the context of wiretap lattice coding. It has been studied for unimodular lattices, for 2 −, 3 −, and 5 −modular lattices. This paper studies the secrecy gain for extremal even l-modular lattices, for l ∈ {2, 3, 5, 6, 7, 11, 14, 15, 23}. We compute the highest secrecy gains as a function of the lattice dimension and the lattice level l. We show in particular that l = 2, 3, 6, 7, 11 are best for the respective ranges of dimensions {80, 76, 72}, {68, 64, 60, 56, 52, 48}, {44, 40, 36}, {34, 32, 30, 28, 26, 24, 22}, {18, 16, 14, 12, 10, 8}. This suggests that within a range of dimensions where different levels exist, the highest value of l tends to give the best secrecy gain. A lower bound computation on the maximal secrecy gain further shows that extremal lattices provide secrecy gains which are very close to this lower bound, thus confirming the good behavior of this class of lattices with respect to the secrecy gain. |
| first_indexed | 2024-10-01T07:49:50Z |
| format | Journal Article |
| id | ntu-10356/86844 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:49:50Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/868442023-02-28T19:34:17Z On The Secrecy Gain Of Extremal Even l-modular Lattices Oggier, Frédérique Belfiore, Jean-Claude School of Physical and Mathematical Sciences Lattices Secrecy Gain The secrecy gain is a lattice invariant that appears in the context of wiretap lattice coding. It has been studied for unimodular lattices, for 2 −, 3 −, and 5 −modular lattices. This paper studies the secrecy gain for extremal even l-modular lattices, for l ∈ {2, 3, 5, 6, 7, 11, 14, 15, 23}. We compute the highest secrecy gains as a function of the lattice dimension and the lattice level l. We show in particular that l = 2, 3, 6, 7, 11 are best for the respective ranges of dimensions {80, 76, 72}, {68, 64, 60, 56, 52, 48}, {44, 40, 36}, {34, 32, 30, 28, 26, 24, 22}, {18, 16, 14, 12, 10, 8}. This suggests that within a range of dimensions where different levels exist, the highest value of l tends to give the best secrecy gain. A lower bound computation on the maximal secrecy gain further shows that extremal lattices provide secrecy gains which are very close to this lower bound, thus confirming the good behavior of this class of lattices with respect to the secrecy gain. Accepted version 2018-01-31T02:32:32Z 2019-12-06T16:30:04Z 2018-01-31T02:32:32Z 2019-12-06T16:30:04Z 2018 2018 Journal Article Oggier, F., & Belfiore, J.-C. (2018). On The Secrecy Gain Of Extremal Even l-modular Lattices. Experimental Mathematics, in press. 1058-6458 https://hdl.handle.net/10356/86844 http://hdl.handle.net/10220/44358 10.1080/10586458.2017.1423249 203069 en Experimental Mathematics © 2018 Taylor & Francis. This is the author created version of a work that has been peer reviewed and accepted for publication by Experimental Mathematics, Taylor & Francis. 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/10.1080/10586458.2017.1423249]. 30 p. application/pdf |
| spellingShingle | Lattices Secrecy Gain Oggier, Frédérique Belfiore, Jean-Claude On The Secrecy Gain Of Extremal Even l-modular Lattices |
| title | On The Secrecy Gain Of Extremal Even l-modular Lattices |
| title_full | On The Secrecy Gain Of Extremal Even l-modular Lattices |
| title_fullStr | On The Secrecy Gain Of Extremal Even l-modular Lattices |
| title_full_unstemmed | On The Secrecy Gain Of Extremal Even l-modular Lattices |
| title_short | On The Secrecy Gain Of Extremal Even l-modular Lattices |
| title_sort | on the secrecy gain of extremal even l modular lattices |
| topic | Lattices Secrecy Gain |
| url | https://hdl.handle.net/10356/86844 http://hdl.handle.net/10220/44358 |
| work_keys_str_mv | AT oggierfrederique onthesecrecygainofextremalevenlmodularlattices AT belfiorejeanclaude onthesecrecygainofextremalevenlmodularlattices |