可截取签名允许签名人根据需要,在不与原始签名人交互的情况下删除已签名中的敏感数据块,并为截取后的数据计算一个公开并且可验证的签名.目前大多数可截取签名方案都是基于传统数论的困难假设构造的,鉴于量子计算机可能构成的威胁,构造能够抵抗量子计算攻击的可截取签名方案尤为重要.因此基于格的Ring-SIS(ring short integer solution)问题,提出一种理想格上基于身份的可截取签名方案,证明了该方案在选择身份和消息攻击下存在不可伪造性和隐私性.理论分析和效率分析表明,相较于同类方案,该方案在功能性上同时具备身份认证、隐私性和抗量子攻击等多种功能,用户公钥尺寸更短、安全性更高、算法耗时更低.
周宏毅在论文关于Herman环与临界点中给出了三次有理函数且其临界点严格位于Herman环的边界分支的例子。该构造中主要用到临界点都位于单位圆周且保持单位圆周不动的有理函数的存在性。本文给出了一般的有理函数临界点均在单位圆周且保持单位圆周不动的存在性证明。同时讨论了一般显示构造的方法。In A Note on Herman, Hongyi Zhou gave an example of a cubic rational function whose critical points strictly lie on the boundary of the Herman ring. The construction mainly relies on the existence of rational functions whose critical points are located on the unit circle and keep the unit circle invariant. In this paper, we provide a general proof for the existence of rational functions whose critical points are all on the unit circle and keep the unit circle invariant. Additionally, we discuss the general methods for explicit constructions.
本文研究了具有两个Herman环的有理函数的拓扑性质。之前的研究中,Wang和Zhang从有理函数的拓扑性质入手,提出了构造具有一个Herman环有理函数的方法,结合周弘毅在2023年的研究,可以得到判断有理函数的拓扑等价类中是否有一个Herman环的充要条件。基于他们的研究,本文进一步给出了具有次数大于或等于2的有理函数拓扑等价于具有两个Herman环的有理函数的必要条件。This paper studies the topological properties of rational functions with two Herman rings. In previous research, Wang and Zhang proposed a method for constructing rational functions with one Herman ring based on the topological properties of rational functions. Combined with Zhou Hongyi’s research in 2023, a necessary and sufficient condition for determining whether there is a Herman ring in the topological equivalence class of rational functions can be obtained. Based on their research, this paper further presents the necessary condition for a rational function with a degree greater than or equal to 2 to be topologically equivalent to a rational function with two Herman rings.
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