Lightweight cryptography is becoming essential as emerging technologies in digital identity systems and Internet of Things verification continue to demand strong cryptographic assurance on devices with limited processing power, memory, and energy resources. As these technologies move into routine use, they demand cryptographic primitives that maintain strong security and deliver predictable performance through clear theoretical models of time complexity. Although NIST's lightweight cryptography project provides empirical evaluations of the ten finalist algorithms, a unified theoretical understanding of their time-complexity behavior remains absent. This work introduces a symbolic model that decomposes each scheme into initialization, data-processing, and finalization phases, enabling formal time-complexity derivation for all ten finalists. The results clarify how design parameters shape computational scaling on constrained mobile and embedded environments. The framework provides a foundation needed to distinguish algorithmic efficiency and guides the choice of primitives capable of supporting security systems in constrained environments.

翻译：随着数字身份系统和物联网验证等新兴技术对处理能力、内存和能源资源受限设备上的强密码学保障需求日益增长，轻量级密码学正变得至关重要。随着这些技术进入常规应用，它们需要能够通过清晰的时间复杂度理论模型来维持强安全性并提供可预测性能的密码原语。尽管NIST轻量级密码学项目已对十个决赛算法进行了实证评估，但目前仍缺乏对其时间复杂度行为的统一理论理解。本研究提出了一个符号模型，将每个方案分解为初始化、数据处理和完成三个阶段，从而为全部十个决赛算法实现了形式化的时间复杂度推导。研究结果阐明了设计参数如何影响其在受限移动和嵌入式环境中的计算扩展性。该框架为区分算法效率提供了必要基础，并指导选择能够支持受限环境下安全系统的密码原语。