Results 21 to 30 of about 7,243 (134)
Abstract algebra, projective geometry and time encoding of quantum information
, 2005 Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of the integers ...
Planat, Michel R. P., Saniga, Metod
core +4 more sources
Radical and cyclotomic extensions of the rational numbers [PDF]
Proceedings of the American Mathematical Society, 2007 The principal result in this article is the proof that the Galois closure \(E/\mathbb{Q}\) of a radical extension of the rational numbers \(\mathbb{Q}\) (i.e. an extension \(R = \mathbb{Q}[\alpha]\), where \(\alpha^n \in \mathbb{Q}\) for some positive integer \(n\)) contains a (maximal) cyclotomic extension \(K\) of \(\mathbb{Q}\) whose index in \(E ...
Gluck, David, Isaacs, I. M.
openaire +1 more source
Fast AVX-512 Implementation of the Optimal Ate Pairing on BLS12-381
Transactions on Cryptographic Hardware and Embedded SystemsNon-degenerate bilinear maps on elliptic curves, commonly referred to as pairings, have many applications including short signature schemes, zero-knowledge proofs and remote attestation protocols.
Hao Cheng +3 more
doaj +1 more source
A Result of Bass on Cyclotomic Extension Fields [PDF]
Proceedings of the American Mathematical Society, 1970 In [1] Bass stated the result given below as Proposition 1 and derived some consequences. His proof of the proposition itself, however, contains a gap; Lemmas 2 and 3 are false as stated. The purpose of this note is to fill the gap by proving the slightly stronger Proposition 2. We retain the notation of [1]. In particular k,,=k(Dm) where A;m = e2rilm.
openaire +1 more source
Iwasawa main conjecture for the Carlitz cyclotomic extension and applications [PDF]
Mathematische Annalen, 2019 Section 3 entirely ...
Bruno Anglès +3 more
openaire +3 more sources
Engineering Reports, Volume 8, Issue 4, April 2026.Smart meter (SM): Collect the data of users' electricity consumption periodically, and preprocess the noise reduction by using the Robust Local Weighted Regression algorithm, then encrypt the private data in it by Boneh‐Goh‐Nissim homomorphic encryption, and submit the encrypted private data to the fog node.
Jiangtao Guo +5 more
wiley +1 more source
Ideal class groups of cyclotomic number fields II [PDF]
, 1995 We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields.
Lemmermeyer, Franz
core
On the Z_p-ranks of tamely ramified Iwasawa modules
, 2013 For a prime number p, we denote by K the cyclotomic Z_p-extension of a number field k. For a finite set S of prime numbers, we consider the S-ramified Iwasawa module which is the Galois group of the maximal abelian pro-p-extension of K unramified outside
MANABU OZAKI +4 more
core +1 more source
When is a 2-Power Cyclotomic Extension cyclic?
, 2023 This paper characterizes the cyclicity property of $2$-power cyclotomic extensions through various means: the structure of the Galois groups, the nature of their subextensions, tower decompositions, and, most importantly, specific conditions on the base field.
Marques, Sophie, Mrema, Elizabeth
openaire +2 more sources
A P‐adic class formula for Anderson t‐modules
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In 2012, Taelman proved a class formula for L$L$‐series associated to Drinfeld Fq[θ]$\mathbb {F}_q[\theta]$‐modules and considered it as a function field analogue of the Birch and Swinnerton‐Dyer conjecture. Since then, Taelman's class formula has been generalized to the setting of Anderson t$t$‐modules.
Alexis Lucas
wiley +1 more source