Investigation of problems related to lattice-based cryptography using algebraic nu...
Metrics that agree on the support of vectors and nearest neighbor decoding
Study of Gluon and Quark propagators in Lattice QCD at Finite Temperature
| Full text | |
| Author(s): |
de Araujo, Robson Ricardo
Total Authors: 1
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| Document type: | Journal article |
| Source: | DISCRETE MATHEMATICS; v. 347, n. 1, p. 6-pg., 2024-01-01. |
| Abstract | |
Recently, in coding theory and cryptography, it has been important the diversified use of lattices. One use of them is to cover a space. Each lattice has a covering radius, a number corresponding to the radius of a ball whose translations by all the points of the lattice cover efficiently the space generated by a basis of it. A way to obtain lattices algebraically is from subgroups of the multiplicative group of units of a number field via the logarithm embedding. This includes the logarithm lattice. In this work, it is presented an upper bound on the covering radius of the logarithm lattice obtained from the units of general cyclotomic number fields via the logarithm embedding, which generalizes an upper bound present in a previous work for cyclotomic number fields of prime-power indices.& COPY; 2023 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 13/25977-7 - Security and reliability of Information: theory and practice |
| Grantee: | Marcelo Firer |
| Support Opportunities: | Research Projects - Thematic Grants |