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@article{2316137,
author = {Bernard, Olivier and Kučera, Radan},
article_number = {March 2024},
doi = {http://dx.doi.org/10.1090/mcom/3863},
keywords = {Cyclotomic fields; Stickelberger ideal; short basis; relative class number},
language = {eng},
issn = {0025-5718},
journal = {Mathematics of Computation},
title = {A short basis of the Stickelberger ideal of a cyclotomic field},
url = {https://doi.org/10.1090/mcom/3863},
volume = {93},
year = {2024}
}
TY - JOUR
ID - 2316137
AU - Bernard, Olivier - Kučera, Radan
PY - 2024
TI - A short basis of the Stickelberger ideal of a cyclotomic field
JF - Mathematics of Computation
VL - 93
IS - March 2024
SP - 887-909
EP - 887-909
PB - American Mathematical Society
SN - 00255718
KW - Cyclotomic fields
KW - Stickelberger ideal
KW - short basis
KW - relative class number
UR - https://doi.org/10.1090/mcom/3863
N2 - We exhibit an explicit short basis of the Stickelberger ideal of cyclotomic fields of any conductor, i.e., a basis containing only short elements. An element of the group ring Z[G], where G is the Galois group of the field, is said to be short if all of its coefficients in basis G are 0 or 1. As a direct practical consequence, we deduce from this short basis an explicit upper bound on the relative class number that is valid for any conductor. This basis also has several concrete applications, in particular for the cryptanalysis of the Shortest Vector Problem on Ideal Lattices.
ER -
BERNARD, Olivier a Radan KUČERA. A short basis of the Stickelberger ideal of a cyclotomic field. \textit{Mathematics of Computation}. American Mathematical Society, 2024, roč.~93, March 2024, s.~887-909. ISSN~0025-5718. Dostupné z: https://dx.doi.org/10.1090/mcom/3863.
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