Large-scale cyber–physical systems (CPS) must remain stable while facing sophisticated post-quantum adversaries. This paper proposes a control architecture that steers the communication graph via supersingular-isogeny walks (SIW). Each isogeny re-keys the network with 192-bit post-quantum strength and, through a new isogeny Riccati equation (IRE), provably increases algebraic connectivity. An instance-optimal scheduler computes the next isogeny in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\tilde{O}(n^{1.5})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>O</mi> <mo stretchy="false">~</mo> </mover> <mrow> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow> <mn>1.5</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> time. Extensive simulations on the IEEE 118-bus grid and a 100-robot swarm show that the proposed SIW-based controller reduces attack-induced deviation by approximately <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$35\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>35</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> and cuts control energy by about <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$50\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>50</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> compared with lattice-based re-keying, while respecting real-time deadlines. Over 60 Monte Carlo trials on the P118 benchmark and multiple DoS+spoof scenarios on the R100 swarm confirm the statistical robustness of these gains. The main findings are that (i) deeper isogeny walks simultaneously enhance network connectivity and cryptographic hardness, (ii) the proposed scheduler achieves quasi-linear complexity in the number of agents, and (iii) the SIW controller substantially improves resilience–energy trade-offs relative to classical post-quantum CPS designs. Strengths and limitations of the approach are analysed through complexity, security, and scalability studies.

Isogeny-driven control for post-quantum cyber–physical systems

期刊论文
发表日期：

2026年1月2日

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Mohammed El Baraka,
Siham Ezzouak

摘要

Large-scale cyber–physical systems (CPS) must remain stable while facing sophisticated post-quantum adversaries. This paper proposes a control architecture that steers the communication graph via supersingular-isogeny walks (SIW). Each isogeny re-keys the network with 192-bit post-quantum strength and, through a new isogeny Riccati equation (IRE), provably increases algebraic connectivity. An instance-optimal scheduler computes the next isogeny in $\tilde{O}(n^{1.5})$ $\tilde{O} (n^{1.5})$ time. Extensive simulations on the IEEE 118-bus grid and a 100-robot swarm show that the proposed SIW-based controller reduces attack-induced deviation by approximately $35\%$ $35 %$ and cuts control energy by about $50\%$ $50 %$ compared with lattice-based re-keying, while respecting real-time deadlines. Over 60 Monte Carlo trials on the P118 benchmark and multiple DoS+spoof scenarios on the R100 swarm confirm the statistical robustness of these gains. The main findings are that (i) deeper isogeny walks simultaneously enhance network connectivity and cryptographic hardness, (ii) the proposed scheduler achieves quasi-linear complexity in the number of agents, and (iii) the SIW controller substantially improves resilience–energy trade-offs relative to classical post-quantum CPS designs. Strengths and limitations of the approach are analysed through complexity, security, and scalability studies.