ON ALGORITHMIC ASPECTS OF THE l-TORSION OF BRAUER GROUPS | |
Wang, Lin ; Xu, Mao-Zhi | |
2012 | |
关键词 | Brauer group K-2 group of a field invariant homomorphism Hilbert symbol discrete logarithm SIGNATURE CALCULUS FIELD SIEVE |
英文摘要 | We study the algorithmic aspects of the l-torsion of the Brauer group Br(K) of a field K which contains the l-th roots of unity mu(l), only provided with basic operations on the elements of K. We use a primitive root of unity and nonzero elements in K to represent elements of Br(K)[l]. An algorithm is given to compute the invariant homomorphism on Br(Q(l)(mu(l)))[l] for an odd prime l. We also give a remark on potential application of Brauer groups to solve the discrete logarithm problem of multiplicative groups of finite fields.; Mathematics; SCI(E); 0; ARTICLE; 3; 297-312; 35 |
语种 | 英语 |
出处 | SCI |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/157558] |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Wang, Lin,Xu, Mao-Zhi. ON ALGORITHMIC ASPECTS OF THE l-TORSION OF BRAUER GROUPS. 2012-01-01. |
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