论文标题
复杂偏移的非架构动力学
Non-Archimedean dynamics of the complex shift
论文作者
论文摘要
p字母字母fp = z/pz（p是p是素数）的（异步）自动机转换，是padic整数环的连续转换（w.r.t. p ad adic度量）。此外，自动机映射会在ZP上生成非架构的动态系统。这种动力系统的测量保护和终身性（W.R.T. HAAR测量）在密码学（例如，在流动机中）起着重要作用。本文的目的是提出一种实现P-ADICS复杂转变的新颖方式。特别是，我们介绍了有关P-ADICS转换的Mahler扩展的条件，这足以使其变得复杂。此外，就Mahler扩展而言，我们具有这种映射的足够条件。
An (asynchronous) automaton transformation of one-sided infinite words over p-letter alphabet Fp = Z/pZ, where p is a prime, is a continuous transformation (w.r.t. the p-adic metric) of the ring of p-adic integers Zp. Moreover, an automaton mapping generates a non-Archimedean dynamical system on Zp. Measure-preservation and ergodicity (w.r.t. the Haar measure) of such dynamical systems play an important role in cryptography (e.g., in stream cyphers). The aim of this paper is to present a novel way of realizing a complex shift in p-adics. In particular, we introduce conditions on the Mahler expansion of a transformation on the p-adics which are sufficient for it to be complex shift. Moreover, we have a sufficient condition of ergodicity of such mappings in terms of Mahler expansion.
