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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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