Algorithm–Physical Co-Security Insights

• Algorithm–Physical Co-Security is the integration of computation with physical layer dynamics to enforce secrecy and robustness against diverse attacks.
• It leverages methods like coding, beamforming, reinforcement learning, and optimization to convert physical characteristics into security advantages.
• Key applications span wireless, optical, power systems, and multi-robot networks, illustrating the practical impact of aligning physical processes with algorithmic defenses.

Searching arXiv for recent and foundational papers relevant to algorithm–physical co-security. First, searching for the phrase "algorithm physical co-security" and nearby terminology. In the literature represented by these works, algorithm–physical co-security can be understood as the co-design of algorithmic mechanisms—such as coding, beamforming, control, watermarking, game-theoretic coordination, reinforcement learning, and tri-level optimization—with physical mechanisms—such as channel asymmetry, interference, reserve capacity, actuator excitation, reachability, and mutual observation—so that secrecy, attack detection, or safety depend on both computation and embodied dynamics. Across wireless communication, optical networks, electric power systems, control, and multi-robot systems, the common theme is that security is not treated as a purely software property: it is enforced through the interaction between algorithms and the physical substrate itself (Liu et al., 2013, Karangelos et al., 27 Feb 2025, Goyal et al., 2022, Yang et al., 2024).

1. Conceptual foundations

A foundational strand of the field explicitly links cryptography and physical-layer security. "Practical Secrecy: Bridging the Gap between Cryptography and Physical Layer Security" argues that artificial noise can protect secret data without any form of secret key exchange and any restriction on the communication channels; by treating artificial noise as an unshared one-time pad secret key, the proposed scheme also achieves Shannon's perfect secrecy, and it further claims that achieving perfect secrecy is much easier than ensuring non-zero secrecy capacity, especially when the eavesdropper has more antennas than the transmitter (Liu et al., 2013). This establishes a central co-security idea: physical randomness and channel structure can play the role traditionally assigned to cryptographic key material.

A second foundational line combines channel coding with computational cryptography. "Physical-Layer Security: Combining Error Control Coding and Cryptography" shows, in Wyner’s wiretap setting, that the security of an LFSR-based keystream generator can be strengthened by exploiting properties of the physical layer, so that the computational complexity of discovering the secret key increases by orders of magnitude, or is altogether infeasible, for two fast correlation attacks (0901.0275). Here the physical channel does not replace the cipher; it changes the attack surface of the cipher.

A third foundation is the use of an explicitly physical secrecy metric. "Physical-Layer Security over Correlated Erasure Channels" defines security in terms of the attacker’s degrees of freedom $D$, and under the specified encoder proves

$\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$

It also shows that security improvements are achievable by means of judicious physical-layer design even when the eavesdropper has a better channel than the legitimate receiver, while highly correlated erasures are the exceptional regime in which this assertion may fail (Harrison et al., 2011). This suggests that algorithm–physical co-security is not limited to secrecy capacity; it also includes structured physical uncertainty that is translated into attack complexity or equivocation.

2. Physical-layer communication mechanisms

In communication systems, algorithm–physical co-security is often realized through precoding, interference shaping, and hardware-mediated channel reconfiguration. In the MIMO two-user wiretap network studied in "Improving Wireless Physical Layer Security via Exploiting Co-Channel Interference," a public source-destination pair is used as a cooperative secrecy resource, and the paper derives the maximum achievable secrecy degrees of freedom region together with precoding matrices that achieve the boundary (Li et al., 2016). The physical resource is co-channel interference; the algorithmic layer chooses subspaces so that interference harms the eavesdropper more than the legitimate receiver.

Relay systems provide the same pattern in a different architecture. "Relay Beamforming Strategies for Physical-Layer Security" studies amplify-and-forward beamforming under total and individual relay power constraints, then considers robust decode-and-forward beamforming under imperfect CSI, using optimization frameworks based on semidefinite programming and related reformulations (Zhang et al., 2010). The security objective is still secrecy rate, but the governing variables are beamforming weights constrained by the geometry and uncertainty of the relay channel.

Reconfigurable surfaces extend this model by making propagation itself programmable. "Physical Layer Security Enhancement Exploiting Intelligent Reflecting Surface" formulates secrecy-rate maximization through joint active and passive beamforming, derives the optimal transmit beamforming vector at the BS under fixed IRS phase shifts, and proposes a low-complexity algorithm based on fractional programming and manifold optimization for near-optimal IRS phase shifts (Feng et al., 2019). "RIS-assisted Physical Layer Security" pushes this further by using a strategically deployed RIS to create spatial separation between direct and RIS-assisted links, using orthogonal combiners at the legitimate receiver, and deriving an achievable secrecy rate under semantic security of the form

$$R_s = \big[I(\boldsymbol{X};\boldsymbol{Y}) - \max_j I(\boldsymbol{X};\boldsymbol{Z}_j)\big]^+,$$

followed by a secrecy-rate optimization over the resulting two-stream structure (Li et al., 30 Jan 2025). In both cases, the physical channel is an optimization variable rather than a fixed environment.

The same logic appears in less conventional hardware. "Physical Layer Security in Multimode Fiber Optical Networks" uses measured transmission matrices, inverse precoding, mode-dependent losses, dynamic mode channel changes, and artificial noise so that Bob obtains a near-identity channel while Eve faces an ill-conditioned inversion problem with strongly amplified noise (Rothe et al., 2019). "Pinching-Antenna Systems for Physical Layer Security" studies a dielectric waveguide with pre-installed pinching antennas, formulates secrecy-rate maximization through discrete antenna activation, and uses amplitude control to enhance Bob while phase alignment is designed to degrade Eve; cooperation among pinching antennas is modeled as a coalitional game whose individual contributions are evaluated by Shapley value and marginal contribution (Wang et al., 14 Jul 2025). These works show that algorithm–physical co-security includes optical and waveguide hardware, not only RF beamforming.

3. Optimization, games, and learning as co-security machinery

A striking feature of the literature is that the algorithmic layer is rarely incidental. It is usually the mechanism that converts physical asymmetry into enforceable security. In decentralized wireless networks, "Physical Layer Security: Coalitional Games for Distributed Cooperation" models cooperation for secrecy capacity as a coalitional game with non-transferable utility and proposes a distributed merge-and-split coalition formation algorithm. Users autonomously self-organize into disjoint coalitions while accounting for the secrecy cost of information exchange, and the reported simulations show up to $25.32\%$ improvement in average secrecy capacity per user relative to the non-cooperative case (0906.4827). The physical layer provides link-level secrecy gains; the coalition algorithm determines whether those gains survive the cost of cooperation.

The same game-theoretic structure reappears in hardware selection. In the pinching-antenna setting, secrecy-rate maximization is recast as a coalitional game over activated antennas, and a Shapley-value-based activation rule is used to decide which physical radiators should be turned on or off (Wang et al., 14 Jul 2025). This indicates that co-security can be organized as a resource-allocation problem over physical components rather than only over data streams.

Learning-based formulations occupy the same conceptual space. "An Adaptive Multi-Agent Physical Layer Security Framework for Cognitive Cyber-Physical Systems" defines each agent’s utility as a weighted combination of security, QoS, and cost, builds a network utility metric, and uses a secure transmission policy selection mechanism formulated as an MDP and realized by Q-learning to choose among SC-AN, FD-AI, AN, and beamforming policies and their parameter settings (Demir et al., 2021). The security signal itself is physical-layer secrecy pressure, while the policy-selection engine is algorithmic. This suggests that algorithm–physical co-security naturally extends to adaptive and cognitive settings where physical conditions change over time.

In infrastructure settings, optimization becomes explicitly adversarial. "Electric power system security: the case for an integrated cyber-physical risk management framework" formulates a probabilistic defender–attacker–defender tri-level problem that co-optimizes preventive physical measures, namely reserve capacity, and cyber-security measures, namely firewall-rule updates, under uncertainty about whether advanced attackers can bypass the latter (Karangelos et al., 27 Feb 2025). The result that physical- and cyber-security measures are non-exchangeable complements is especially important: it rejects the substitution view in which stronger software defenses can simply replace physical robustness.

4. Cyber-physical infrastructures and control systems

In power-system security, algorithm–physical co-security appears as a systems problem rather than a link-level secrecy problem. The integrated framework of (Karangelos et al., 27 Feb 2025) treats security as the ability of the transmission grid to maintain acceptable electricity supply in the presence of malicious cyber-physical attackers who can intrude into digital substations, remotely disconnect generators and transmission branches, and thereby force redispatch and load shedding. Its upper-level planner chooses base dispatch $p_g$, reserve capacity $r_g$, and firewall updates $z_n$; attackers choose infiltrations and disconnections; operators react through redispatch and load shedding. The conclusion that physical- and cyber-security measures are non-exchangeable complements is not merely terminological: reserves mitigate attacks that bypass cyber controls, while firewall updates shrink the feasible attack set for basic attackers (Karangelos et al., 27 Feb 2025).

A related but more diagnostic perspective appears in "Co-simulation for Cyber Security Analysis: Data Attacks against Energy Management System." That work extends an analytic framework that characterizes data attacks as optimization problems whose objectives are security metrics and whose constraints correspond to communication-network properties, then couples DIgSILENT PowerFactory, OMNeT++, and Matlab in a co-simulation platform (Pan et al., 2017). The resulting framework makes explicit how communication routing, state estimation, bad-data detection, and optimal power flow together determine physical consequences such as generator redispatch and line-flow changes. This suggests that co-security can also mean multi-simulator integration that preserves the coupling between cyber decision logic and physical process evolution.

At the control level, "Co-Design of Watermarking and Robust Control for Security in Cyber-Physical Systems" makes the coupling especially explicit. The plant is a discrete-time LTI system with additive process and measurement noise, the control input is augmented by a Gaussian watermark $\Delta u_k \sim \mathcal{N}(0,U)$, and replay attacks are detected by a $\chi^2$ detector based on innovations. For a general dynamic controller, the paper proves that under replay attack

$$\lim_{k\to\infty}\mathbb{E}[g_k] = mT + 2 \operatorname{trace}\!\left(C^T \mathcal{X}^{-1} C \mathcal{U}\right)T,$$

where $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$0 solves a Lyapunov equation driven by the watermark covariance (Goyal et al., 2022). The watermark is a security mechanism only because it is also a physical actuator excitation; the controller is acceptable only because LMIs keep the resulting $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$1 degradation within bounds.

5. Distributed embodied security in multi-agent systems

Multi-agent systems make the physical meaning of co-security particularly clear. In cognitive cyber-physical systems, the RL-based secure transmission policy selection mechanism of (Demir et al., 2021) combines agent-specific security, QoS, and cost requirements into a dynamic network utility, then adapts physical-layer security policy in real time. Security is not a fixed property of the radio stack; it is a controlled operational variable continuously traded against reliability and resource use.

In mobile robotics, "Enhancing Security in Multi-Robot Systems through Co-Observation Planning, Reachability Analysis, and Network Flow" defines a multi-robot trajectory plan as secure against plan-deviation attacks if any potential deviations to forbidden regions will cause the corresponding robot to miss its next co-observation (Yang et al., 2024). The physical adversary can arbitrarily change a compromised robot’s motion subject only to the same kinematic bound $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$2. Security is then enforced by a geometric reachability condition: between consecutive co-observations at $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$3 and $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$4, the reachable set is over-approximated by the ellipsoid

$\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$5

and planning requires this ellipsoid not to intersect any forbidden region (Yang et al., 2024). The algorithmic layer consists of ADMM-based trajectory optimization, ellipsoidal intersection constraints with gradients, and a network-flow coverage problem on a checkpoint graph; the physical layer consists of motion bounds, spatial forbidden regions, and actual mutual observation events.

The introduction of sub-teams in (Yang et al., 2024) is especially revealing. A sub-team replaces individual robot assignments along a route, allowing redundant robots to deviate for cross-trajectory co-observations without modifying the secured reference trajectories. This suggests a broader principle: redundancy becomes a security primitive when it is scheduled through physically meaningful observability constraints rather than treated only as backup capacity.

6. Guarantees, misconceptions, and limitations

The literature does not treat all guarantees as equivalent. Some works target secrecy rate or secrecy degrees of freedom (Li et al., 2016, Feng et al., 2019); some target Shannon perfect secrecy or strong secrecy (Liu et al., 2013); some explicitly derive semantic security for a RIS-assisted AWGN channel (Li et al., 30 Jan 2025); some quantify security by degrees of freedom $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$6 and equivocation $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$7 (Harrison et al., 2011); and some measure security as replay-attack detection rate under a $\mathbb{E}[D] = H(X|Z) = (1-\Pr(R_{ef}))n.$8 detector (Goyal et al., 2022). A common misconception is that algorithm–physical co-security names a single guarantee class. The record instead shows several distinct security notions tied to different physical mechanisms and attack models.

A second misconception is that physical mechanisms simply replace cyber or cryptographic ones. The grid risk-management framework explicitly states that there is no such thing as perfectly effective cyber-security and concludes that physical- and cyber-security measures are non-exchangeable complements (Karangelos et al., 27 Feb 2025). The coding-and-cryptography work on LFSR keystream generators likewise strengthens, rather than replaces, the cryptographic primitive by making attacks computationally harder through residual channel errors (0901.0275). This suggests that co-security is usually layered, not substitutional.

A third misconception is that more physical resources automatically improve security. The pinching-antenna study shows that secrecy depends on activation patterns and phase relations, not just on the number of active antennas, and its Shapley-value analysis is designed precisely because individual elements can help or hurt coalition performance (Wang et al., 14 Jul 2025). Similar caveats appear in RIS and relay beamforming, where performance depends on CSI quality, geometry, and power constraints rather than on hardware scale alone (Feng et al., 2019, Zhang et al., 2010).

Finally, the field repeatedly relies on strong modeling assumptions. Many communication papers assume perfect or effectively known CSI, including the eavesdropper’s channel (Feng et al., 2019, Li et al., 30 Jan 2025, Zhang et al., 2010). Infrastructure papers often use DC power flow and static or single-stage formulations (Karangelos et al., 27 Feb 2025, Pan et al., 2017). Multi-robot security assumes adversaries are constrained by the same motion bounds as nominal robots and that co-observation cannot be spoofed physically (Yang et al., 2024). These assumptions do not invalidate the results, but they delimit the current scope of the field. A plausible implication is that future work will continue shifting from idealized asymmetry toward robust, uncertain, and multi-stage forms of co-design, while retaining the central insight already common to these papers: security can be created, amplified, and operationalized by aligning algorithms with the structure of the physical world itself.