We investigate two possible techniques to authenticate the q-digest data structure, along with a worst-case study of the computational complexity both in time and space of the proposed solutions, and considerations on the feasibility of the presented approaches in real-world scenarios. We conclude the discussion by presenting some considerations on the information complexity of the queries in the two proposed approaches, and by presenting some interesting ideas that could be the subject of future studies on the topic.

翻译：我们研究了认证q-digest数据结构的两种可行技术，并对所提出方案在时间和空间上的计算复杂度进行了最坏情况分析，同时探讨了所提方法在实际场景中的可行性。最后，通过讨论两种方法中查询的信息复杂性，并介绍一些可能成为该课题未来研究方向的思路，以此作为论述的总结。