Time-Complexity Characterization of NIST Lightweight Cryptography Finalists

TL;DR

The paper tackles the lack of a unified theoretical understanding of time complexity among NIST LWC finalists. It introduces a symbolic three-phase model that partitions operation into initialization, data processing, and finalization, with $T_{\text{total}} = T_{\text{init}} + T_{\text{process}} + T_{\text{finalize}}$ and additional component equations. The authors derive symbolic expressions for all ten finalists, highlighting how design choices—permutation-based, block-based, stream, or hybrid—shape computational scaling on constrained devices and providing a platform-independent basis for comparison. This framework supports principled primitive selection for secure, efficient operation in resource-limited environments and sets the stage for real-world validation in digital identity contexts like mobile driver's licenses.

Abstract

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.

Figures (1)

• Figure 1: Time complexity model showing the Initialization ($T_{\text{init}}$), Data Processing ($T_{\text{process}}$), and Finalization ($T_{\text{finalize}}$) phases with their equations.