Construction of Multi-sequences With High Nonlinear Complexity via Narrow Ray Class Fields

2026-09-09

AI Summary

本文通过窄射类域提供了一个统一框架，用于构造具有高非线性复杂度的多序列，解决了密码学中伪随机序列评估的关键问题。

Abstract

Nonlinear complexity is a fundamental criterion in the evaluation of pseudorandom sequences. The construction of multi-sequences with high nonlinear complexity is both theoretically and practically important in cryptography. Motivated by prior constructions of multi-sequences with high nonlinear complexity in [IEEE Trans. Inf. Theory, 60(10), 2014] and [IEEE Trans. Inf. Theory, 63(12), 2017], we provide a unified framework via narrow ray class fields, the cyclic descent due to Guruswami and Xing in [J. Combin. Theory Ser. A 129 (2015) ]. Then we can generate new multi-sequences with high nonlinear complexity over function fields with arbitrary genera.

Problem

• nonlinear complexity
• multi-sequences
• cryptography

Innovation

• narrow ray class fields
• high nonlinear complexity
• multi-sequences
• function fields