Results 1 to 10 of about 198 (140)
The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings [PDF]
Entropy, 2021 Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring ...
Jheyne N. Ortiz +4 more
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Class groups of real cyclotomic fields [PDF]
Monatshefte Fur Mathematik, 2021 We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
Lawrence Washington
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On the Plus Parts of the Class Numbers of Cyclotomic Fields
Chinese Annals of Mathematics Series BWe exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields. At the end, we provide some numerical examples supporting our results.
Azizul Hoque, Kalyan Chakraborty
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Schubert Class and Cyclotomic NilHecke Algebras [PDF]
Algebra Colloquium, 2021 Let [Formula: see text] and [Formula: see text] be positive integers such that [Formula: see text], and let [Formula: see text] be the Grassmannian which consists of the set of [Formula: see text]-dimensional subspaces of [Formula: see text]. There is a [Formula: see text]-graded algebra isomorphism between the cohomology [Formula: see text] of ...
Zhou, Kai, Hu, Jun
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Cyclotomic Function Fields with Ideal Class Number One
Journal of Algebra, 2001 A congruence function field is a function field whose field of constants is the finite field of \(q\) elements \(\mathbb{F}_q\). A congruence function field \(K/\mathbb{F}_q\) is an imaginary quadratic extension of \(\mathbb{F}_q(x)\) if \(K/\mathbb{F}_q(x)\) is a quadratic separable extension of non-zero genus such that the infinite prime are ramified.
exaly +4 more sources
On Some New Almost Difference Sets Constructed from Cyclotomic Classes of Order 12
Recoletos Multidisciplinary Research Journal, 2023 Almost Difference Sets have extensive applications in coding theory and cryptography. In this study, we introduce new constructions of Almost Difference Sets derived from cyclotomic classes of order 12 in the finite field GF(q), where q is a prime ...
Benedict Estrella
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The Class Number of the Cyclotomic Field [PDF]
Proceedings of the National Academy of Sciences, 1949 Let g denote an odd prime, and h = h(g) the class number of the cyclotomic field R(), where is a primitive gth root of unity. It is known that we can write
Ankeny, Nesmith C., Chowla, Sarvadaman
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Mathematics, 2021 Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences.
Jiang Ma +4 more
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Research on Linear Complexity of Quaternary Sequences with Period 2pq [PDF]
Jisuanji gongcheng, 2016 Linear complexity is an important index for measuring the randomness properties of the sequences.Based on the theory of generalized cyclotomic,a new class of quaternary balanced generalized cyclotomic sequences with period 2pq over finite field F4 is ...
WEI Wanyin,DU Xiaoni,WANG Guohui
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Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq
Journal of Mathematics, 2021 Ding constructed a new cyclotomic class V0 ,V1. Based on it, a construction of generalized cyclotomic binary sequences with period pq is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed.
Yan Wang +3 more
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