Zeben Yang1, Yi Tian2, Jun Yan3, and Zhenqiang Wu4, 5, *
Zhenqiang Wu
1School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, China
2School of Economics and Management, Shangluo University, Shangluo, 726000, China
3School of Mathematics and Computer Applications, Shangluo University, Shangluo, 726000, China
4Shaanxi Key Laboratory of Network and System Security, Xidian University, Xi'an, 710071, China
5School of Artificial Intelligence and Computer Science, Shaanxi Normal University, Xi'an, 710119, China
*Corresponding author
With the rapid development of emerging network infrastructures, including the Internet of Things (IoT), non-terrestrial networks, and edge computing, lightweight cryptography has been widely adopted in resource-constrained network devices. As the exclusive-or (XOR) operation is commonly used for linear mixing and masking, the distinguishability of its outputs over noisy channels warrants dedicated investigation. Standard models of classical cryptanalysis generally adopt an idealized noise-free assumption, under which an adversary can obtain complete and accurate ciphertexts. In practical transmission, however, channel noise and environmental interference may cause random bit flips in ciphertexts, producing uncertain ciphertext observations and severely degrading or even invalidating conventional distinguishing attacks. To address this issue, this paper constructs a noise-perturbation model based on a transition probability matrix, investigates key-bit distinguishing from repeated XOR observations over a binary asymmetric channel, and proposes a Manhattan-distance-based mean-prototype key-bit distinguishing framework. When the channel noise parameters are known, deterministic prototypes are constructed from the theoretical means of the two conditional distributions, and each key bit is classified according to the Manhattan distances between the observation vector and the two prototypes. A closed-form Gaussian approximation to the single-key-bit distinguishing success rate is derived, followed by an analysis of the special case of symmetric perturbations. When the channel noise parameters are unknown, a data-driven approach to prototype construction using method-of-moments estimation is further developed. An approximate expression for the probability of correctly distinguishing a single key bit is then derived to account for the effect of training sample size. Monte Carlo experiments compare the theoretical approximations with empirical results under different channel parameters and sample sizes, demonstrating that p+q = 1 constitutes the non-identifiability boundary of the observation channel. The proposed method provides a low-complexity and interpretable statistical tool for XOR key-bit distinguishing in noisy network environments, as well as methodological and theoretical support for key-recovery attacks in practical network scenarios.
Applied cryptography, binary asymmetric channel, uncertain ciphertext, key-bit distinguishing attack, Manhattan distance
Zeben Yang, Yi Tian, Jun Yan, and Zhenqiang Wu (2026). Key-Distinguishing Attack on XOR Operations Under Uncertain Ciphertext. Journal of Networking and Network Applications, Volume 6, Issue 3, pp. 132–143. https://doi.org/10.33969/J-NaNA.2026.060303.
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