Can Quantum Break ZUC? Only with a Million Qubits and a Billion Years to Spare

Anik Basu Bhaumik, Suman Dutta, Siyi Wang, Anubhab Baksi, Kyungbae Jang, Amit Saha, Hwajeong Seo, Anupam Chattopadhyay

Abstract: The ZUC stream cipher is integral to modern mobile communication standards, including 4G and 5G, providing secure data transmission across global networks. Recently, Dutta et al. (Indocrypt, 2024) presented the first quantum resource estimation of ZUC under Grover's search, Although preliminary, this work marks the beginning of quantum security analysis for ZUC. In this paper, we present an improved quantum resource estimation for ZUC, offering tighter bounds for Grover-based exhaustive key search. Beyond traditional quantum resource estimations, we also provide a concrete timescale required to execute such attacks using the specified quantum resources. Our findings show that a full-round, low depth implementation of ZUC-128 can be realized with a maximum of $375$ ancilla qubits, a T-count of $106536$, and a T-depth of $15816$. Furthermore, the Grover-based key search can be performed most efficiently using $1201$ logical qubits, $170681$ T gates, and a T-depth of $78189$, resulting in a runtime of $1.78\times10^{11}$ years, an improvement of 93.43% over the estimated $2.71 \times 10^{12}$ years by the implementation given by Dutta et al., we also provide akin analysis for ZUC-256 with an 99.23% decrease in time. These estimations are done assuming state-of-the-art superconducting qubit error-correcting technology.

External IDs:dblp:journals/iacr/BhaumikDWBJSSC25