On ideal class group computation of imaginary multiquadratic fields

IF 0.2 Q4 MATHEMATICS, APPLIED

Prikladnaya Diskretnaya Matematika Pub Date : 2023-01-01 DOI:10.17223/20710410/58/3

S. Novoselov

引用次数: 0

Abstract

In the paper, we extend Biasse - van Vredendaal (OBS, 2019, vol. 2) implementation and experiments of the class group computation from real to imaginary multiquadratic fields. The implementation is optimized by introducing an explicit prime ideal lift operation and by using LLL reduction instead of HNF computation. We provide examples of class group computation of the imaginary multiquadratic fields of degree 64 and 128, that has been previously unreachable.

查看原文本刊更多论文

虚多重二次域的理想类群计算

在本文中，我们将Biasse - van Vredendaal (OBS, 2019, vol. 2)的类群计算的实现和实验从实多二次域扩展到虚多二次域。通过引入显式素数理想升力操作和使用LLL减少而不是HNF计算，实现了优化。我们给出了64次和128次的虚多重二次域的类群计算的例子，这是以前无法达到的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Prikladnaya Diskretnaya Matematika MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

50.00%

发文量

期刊介绍： The scientific journal Prikladnaya Diskretnaya Matematika has been issued since 2008. It was registered by Federal Control Service in the Sphere of Communications and Mass Media (Registration Witness PI № FS 77-33762 in October 16th, in 2008). Prikladnaya Diskretnaya Matematika has been selected for coverage in Clarivate Analytics products and services. It is indexed and abstracted in SCOPUS and WoS Core Collection (Emerging Sources Citation Index). The journal is a quarterly. All the papers to be published in it are obligatorily verified by one or two specialists. The publication in the journal is free of charge and may be in Russian or in English. The topics of the journal are the following: 1.theoretical foundations of applied discrete mathematics – algebraic structures, discrete functions, combinatorial analysis, number theory, mathematical logic, information theory, systems of equations over finite fields and rings; 2.mathematical methods in cryptography – synthesis of cryptosystems, methods for cryptanalysis, pseudorandom generators, appreciation of cryptosystem security, cryptographic protocols, mathematical methods in quantum cryptography; 3.mathematical methods in steganography – synthesis of steganosystems, methods for steganoanalysis, appreciation of steganosystem security; 4.mathematical foundations of computer security – mathematical models for computer system security, mathematical methods for the analysis of the computer system security, mathematical methods for the synthesis of protected computer systems;[...]