论文标题
在某些较高等级的德林菲尔德模块中，作为德林菲尔德模块的内态词环发生的订单
Orders occurring as endomorphism ring of a Drinfeld module in some isogeny classes of Drinfeld modules of higher ranks
论文作者
论文摘要
我们建议在本文中回答的问题是：给定有限领域的德林菲尔德模块的同类类别类别，相应的内态内态代数（这是一个同构不变的）的顺序，这些命令是作为drinfeld模块的内态词环发生的，该命中率是那个同类的类别中？值得一提的是，这个问题与作者Kuhn，[6]中的Pink和[3]中的Papikian的作者所调查的问题不同。前者宁愿给出有关该问题的答案，因为给定德林菲尔德模块ϕ，一个人如何有效地计算ϕ的内态环？我们的问题的重要性在于，更好地理解高级德林菲尔德模块（R> 2）的同一症状图可能非常有帮助，并且可能会重新开放有关基于低血压的密码学应用程序的辩论。我们为此问题回答了这个问题，即内态代数是一个领域，通过为给定的命令提供必要和充分的条件，使给定的命令成为德林菲尔德模块的内态戒指。我们将结果应用于等级r = 3 drinfeld模块，并明确计算出在有限字段上以等级3 Drinfeld模块的内态态戒指的订单。
The question we propose to answer throughout this paper is the following: Given an isogeny class of Drinfeld modules over a finite field, what are the orders of the corresponding endomorphism algebra (which is an isogeny invariant) that occur as endomorphism ring of a Drinfeld module in that isogeny class? It is worth mentioning that this question is different from the ones investigated by the authors Kuhn, Pink in [6] and Garai, Papikian in [3]. The former authors rather provided an answer to the question, given a Drinfeld module ϕ, how does one efficiently compute the endomorphism ring of ϕ? The importance of our question resides in the fact that it might be very helpful to better understand isogeny graphs of Drinfeld modules of higher rank (r > 2) and may be reopen the debate concerning the application to isogeny-based cryptography. We answer that question for the case whereby the endomorphism algebra is a field by providing a necessary and sufficient condition for a given order to be the endomorphism ring of a Drinfeld module. We apply our result to rank r = 3 Drinfeld modules and explicitly compute those orders occurring as endomorphism rings of rank 3 Drinfeld modules over a finite field.
