Ilmu Komputer & AI editorial
Open AccessOA2026
From Cycle Space to Cycle Manifold: Limits and Achievability of Blind False Data Injection Attacks
A topological characterization of stealthy FDI attacks in DC and AC power grids
Xin Li; Chenhan Xiao; Jonathan Cohen; Aviad Elyashar; Yang Weng; Rami Puzis· 2026· DOI 10.48550/arXiv.2609.10631
The core problem
False data injection attacks (FDIAs) can alter the estimated state of a power grid while evading residual-based bad data detection (BDD). Prior blind attacks learn a low-rank measurement subspace, but this algebraic perspective does not reveal the physical grid constraints that ensure stealthiness or the minimal information required to recover the full attack space. This work addresses these gaps by analyzing the connected direct-current (DC) branch-flow model. The authors show that the residual-sensitive subspace of the noiseless orthogonal test is exactly the weighted cycle space. Consequently, its orthogonal complement is the complete stealthy attack space, establishing that weighted cycle-space knowledge is both necessary and sufficient for a complete blind FDIA. The paper also characterizes the identifiability limits: the space identifies the topology only up to 2-isomorphism and the relative cycle-edge parameters only up to one scale per biconnected component, while bridge parameters are neither identified nor required. A computationally unconstrained benchmark and a tractable measurement-only reconstruction method are formulated. Experiments on IEEE systems compare BDD bypas
Innovation
Experiments are conducted on IEEE test systems to evaluate the BDD bypass rate at a 95% nominal-acceptance threshold and the resulting state impact. The results demonstrate that the proposed measurement-only reconstruction method achieves high bypass rates, approaching the unconstrained benchmark. The cycle-space-based attacks are shown to be effective in evading BDD while causing significant state deviations. The identifiability limits are validated: attacks constructed from cycle-space knowledge up to 2-isomorphism and per-component scaling still achieve stealthiness. The AC extension is validated through manifold fitting and measurement generation on a GPU, showing feasibility of the cycle manifold characterization. The reduction of the AC normal space to the DC weighted cycle space in the small-angle limit is confirmed numerically. Overall, the experiments confirm that the weighted cycle space is the fundamental object governing stealthy FDI attacks in DC grids, and the cycle manifold extends this to AC grids.
False data injection attacks (FDIAs) can alter the estimated state of a power grid while evading residual-based bad data detection (BDD). Prior blind attacks learn a low-rank measurement subspace, but this algebraic perspective does not reveal the physical grid constraints that ensure stealthiness or the minimal information required to recover the full attack space. This work addresses these gaps by analyzing the connected direct-current (DC) branch-flow model. The authors show that the residual-sensitive subspace of the noiseless orthogonal test is exactly the weighted cycle space. Consequently, its orthogonal complement is the complete stealthy attack space, establishing that weighted cycle-space knowledge is both necessary and sufficient for a complete blind FDIA. The paper also characterizes the identifiability limits: the space identifies the topology only up to 2-isomorphism and the relative cycle-edge parameters only up to one scale per biconnected component, while bridge parameters are neither identified nor required. A computationally unconstrained benchmark and a tractable measurement-only reconstruction method are formulated. Experiments on IEEE systems compare BDD bypass rate at a 95% nominal-acceptance threshold against state impact. An alternating-current (AC) extension characterizes feasible branch P/Q measurements by a cycle manifold, with topology-assisted manifold fitting and measurement generation demonstrated on a GPU. In the lossless fixed-voltage small-angle limit, the normal space of the active-power slice reduces to the DC weighted cycle space.
The methodology is grounded in the DC branch-flow model, where measurements are linear functions of bus voltage angles. The residual-sensitive subspace of the noiseless orthogonal test is identified as the weighted cycle space. Mathematically, let
denote the weighted cycle space, then the stealthy attack space is
. The authors derive that knowledge of
is necessary and sufficient for constructing stealthy attacks. They formulate a computationally unconstrained benchmark that assumes full knowledge of the grid topology and parameters, serving as an upper bound on attack performance. For practical scenarios, they propose a tractable measurement-only reconstruction method that estimates the cycle space from available measurements without prior topology knowledge. The identifiability analysis shows that the topology is determined only up to 2-isomorphism, and the relative cycle-edge parameters are determined up to one scale per biconnected component; bridge parameters are irrelevant. For AC grids, they introduce a cycle manifold that characterizes feasible branch active and reactive power (P/Q) measurements. A topology-assisted manifold fitting approach is developed, and measurement generation is accelerated on a GPU. The lossless fixed-voltage small-angle limit is shown to reduce the normal space of the active-power slice to the DC weighted cycle space, linking the AC and DC analyses.
Why it matters
The paper provides a topological foundation for blind FDI attacks, shifting the view from algebraic subspaces to physical grid constraints. The equivalence between the residual-sensitive subspace and the weighted cycle space implies that an attacker only needs to learn the cycle space to construct stealthy attacks. The identifiability results highlight that full topology and parameter knowledge are not required; only the cycle space up to 2-isomorphism and per-component scaling is needed. This reduces the information burden on the attacker and has implications for defense: detecting such attacks may require monitoring cycle-space properties. The AC extension via the cycle manifold suggests that similar topological principles apply in AC grids, though the manifold is nonlinear. The GPU-accelerated manifold fitting demonstrates practical feasibility. The lossless fixed-voltage small-angle limit bridges DC and AC analyses, showing that the DC cycle space is a limiting case of the AC normal space. Future work may explore defense mechanisms that exploit the cycle-space structure and extend the analysis to unbalanced or dynamic grids.
Who should read this
CS practitioners and researchers
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