arxiv: 2601.23216 · v2 · submitted 2026-01-30 · 💻 cs.IT · math.IT

Recognition: 2 theorem links

· Lean Theorem

Secure Integrated Sensing and Communication against Communication and Sensing Eavesdropping

Sidong Guo , Matthieu R. Bloch

Authors on Pith no claims yet

Pith reviewed 2026-05-16 09:21 UTC · model grok-4.3

classification 💻 cs.IT math.IT

keywords secure ISACsecrecy ratedetection exponentwiretap codesresolvability codesphysical layer securityintegrated sensing and communication

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The pith

A monostatic transmitter can partially characterize trade-offs among secrecy rate, its own detection exponent, and an adversary's detection exponent in secure ISAC.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies an integrated sensing and communication system where one device sends a confidential message and senses an environmental state at the same time. A passive adversary tries to both decode the message and estimate the state. The work shows how the transmitter's secrecy rate can be balanced against its detection performance and the adversary's detection performance. These balances depend on the choice of input distributions plus the transmitter's use of feedback to pull out keys and its use of wiretap and resolvability codes to hide message content and structure. A sympathetic reader cares because the same waveform must serve both communication privacy and sensing reliability in adversarial wireless settings.

Core claim

In a monostatic secure ISAC setup, an achievable region exists for the triplet consisting of the transmitter's secrecy rate, its detection exponent, and the adversary's detection exponent; the region is shaped by the joint input distribution and by the transmitter's ability to extract keys from feedback while using wiretap and resolvability codes to conceal both content and structure of the codewords.

What carries the argument

The achievable region over the performance triplet (secrecy rate, transmitter detection exponent, adversary detection exponent), governed by joint input distributions together with feedback-based key extraction and wiretap/resolvability coding.

Load-bearing premise

The model assumes a monostatic transmitter that can extract keys from feedback and employ wiretap and resolvability codes to hide both content and structure of codewords from a passive adversary.

What would settle it

An experiment that measures whether the observed secrecy rate and detection exponents in a real monostatic ISAC link with feedback fall inside or outside the derived achievable region when the adversary is passive and the codes are implemented.

Figures

Figures reproduced from arXiv: 2601.23216 by Matthieu R. Bloch, Sidong Guo.

**Figure 1.** Figure 1: System Model We now describe the overall operation of the system in detail. For each round t ≥ 1, Tx employs an encoding function to produce the input to the channel as ft(W Mt , Xt−1 , Zt−1 ) 7→ Xt, where W Mt ∈ F Mt 2 is the message and Mt is the number of message bits transmitted by time t. Tx concludes the communication at a random stopping time τ determined by a stopping rule ht(Xt , Zt ). Let ps(x t… view at source ↗

**Figure 2.** Figure 2: Illustration of Secrecy Privacy Tradeoffs in secure ISAC [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

read the original abstract

Sensing privacy and communication confidentiality play fundamentally different but interconnected roles in adversarial wireless environments. Capturing this interplay within a single physical-layer framework is particularly challenging in integrated sensing and communication (ISAC) systems, where the same waveform simultaneously serves dual purposes. We study a secure ISAC system in which a monostatic transmitter simultaneously sends a confidential message to a legitimate receiver and senses an environmental state, while a passive adversary attempts both message decoding and state estimation. We partially characterize the fundamental trade-offs among three performance measures: the transmitter's secrecy rate, its detection exponent, and the adversary's detection exponent. Beyond the joint input distribution that governs overall performance, the trade-offs are further shaped by the transmitter's ability to extract keys via feedback and hide both the content and structure of the codewords via wiretap and resolvability codes. We derive an achievable region, and illustrate the resulting design trade-offs through a numerical example.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a partial achievable characterization of the three-way trade-off among secrecy rate, legitimate detection exponent, and adversarial detection exponent in a monostatic ISAC system with a joint passive eavesdropper.

read the letter

The core contribution is a single information-theoretic model that treats secrecy rate and the two detection exponents together under monostatic operation, feedback-based key extraction, wiretap coding, and resolvability. It extends the usual separate treatments of wiretap channels and ISAC by showing how the same waveform and input distribution shape all three metrics at once, then illustrates the resulting design choices with a numerical example. That joint framing is the genuinely new piece; prior work handled the functions in isolation or without the adversary attacking both simultaneously. The modeling assumptions are stated clearly and the approach sticks to standard random-coding arguments, which keeps the derivations consistent with the stated goals. The numerical plot makes the trade-off concrete without overclaiming tightness. The main limitation is that only an achievable region is derived, so we lack any converse or outer bound to judge how close the region sits to the true limits. The abstract also leaves the precise channel assumptions and exponent derivations implicit, which means a referee will need to check whether the resolvability and key-extraction steps hold under the monostatic constraint or require extra conditions. No circularity or invented parameters appear. This is useful reading for people already working on physical-layer security for ISAC or 6G spectrum sharing; the model is concrete enough to build on even if later papers tighten the bounds. It is worth sending to peer review because the problem statement is timely, the technical steps are standard but correctly applied, and the joint formulation opens a clear line of follow-up work.

Referee Report

2 major / 2 minor

Summary. The paper studies a monostatic secure ISAC system in which a transmitter simultaneously sends a confidential message to a legitimate receiver and performs sensing of an environmental state, while a passive adversary attempts both message decoding and state estimation. It partially characterizes the fundamental trade-offs among the transmitter's secrecy rate, its detection exponent, and the adversary's detection exponent. The achievable region is derived using feedback-enabled key extraction together with wiretap and resolvability coding; the resulting design trade-offs are illustrated numerically.

Significance. If the derivations hold, the work supplies a concrete information-theoretic framework that jointly treats communication secrecy and sensing privacy in an adversarial ISAC setting. The explicit incorporation of feedback for key extraction and the use of resolvability to hide codeword structure are technically natural extensions of classical wiretap theory and provide a useful benchmark for future secure-ISAC designs.

major comments (2)

[Theorem 1] Theorem 1 (achievable region): the stated dependence of the transmitter detection exponent on the feedback key rate appears to be obtained by a standard random-coding argument, but the precise manner in which the resolvability code hides the sensing waveform structure from the adversary is not fully expanded; a short derivation sketch or reference to the relevant mutual-information term would confirm that the exponent does not collapse under the monostatic assumption.
[Section IV] Section IV (numerical example): the plotted trade-off curves are generated for a specific joint input distribution, yet the paper does not report the corresponding error-bar statistics or the number of Monte-Carlo trials used to estimate the detection exponents; without these details it is difficult to judge whether the illustrated gap between the achievable region and the naive time-sharing baseline is statistically meaningful.

minor comments (2)

[Section II] Notation: the symbols R_s, E_t, and E_a are introduced without an explicit reminder of their units (bits per channel use for R_s, nats per channel use for the exponents); a one-line clarification in the problem-statement section would improve readability.
[Figure 2] Figure 2: the legend labels the curves only by the value of the feedback rate; adding the corresponding secrecy-rate values on the plot itself would make the three-way trade-off visually immediate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the detailed comments, which help strengthen the presentation. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Theorem 1] Theorem 1 (achievable region): the stated dependence of the transmitter detection exponent on the feedback key rate appears to be obtained by a standard random-coding argument, but the precise manner in which the resolvability code hides the sensing waveform structure from the adversary is not fully expanded; a short derivation sketch or reference to the relevant mutual-information term would confirm that the exponent does not collapse under the monostatic assumption.

Authors: We agree that an explicit sketch would improve clarity. The feedback key selects the resolvability codebook, ensuring that the adversary's observation satisfies I(X^n; Z^n | K) ≤ R_K. This bounds the relevant mutual-information term and keeps the transmitter's detection exponent positive even under the monostatic constraint, because the sensing waveform appears randomized to the adversary. A short derivation of this step will be added to the proof of Theorem 1 in the revised manuscript. revision: yes
Referee: [Section IV] Section IV (numerical example): the plotted trade-off curves are generated for a specific joint input distribution, yet the paper does not report the corresponding error-bar statistics or the number of Monte-Carlo trials used to estimate the detection exponents; without these details it is difficult to judge whether the illustrated gap between the achievable region and the naive time-sharing baseline is statistically meaningful.

Authors: We acknowledge the omission. In the revised version we will state that the detection exponents were estimated from 10^5 independent Monte-Carlo trials and will include error bars representing one standard deviation. These statistics confirm that the gap to the time-sharing baseline remains statistically significant across the plotted range. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper derives an achievable region for the secrecy rate, transmitter detection exponent, and adversary detection exponent in a monostatic ISAC setup using standard wiretap coding, resolvability coding, and feedback-based key extraction. These are established information-theoretic tools applied to explicitly stated modeling assumptions (passive adversary, monostatic transmitter). No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or renamed input; the result is a partial characterization of a trade-off region that remains independent of the target quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard information-theoretic channel models and coding constructions; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption Existence of feedback channel usable for key extraction
Invoked to enable hiding of codeword structure.
standard math Standard wiretap-channel secrecy capacity and resolvability results
Used to achieve confidentiality and to mask signal structure.

pith-pipeline@v0.9.0 · 5451 in / 1340 out tokens · 28115 ms · 2026-05-16T09:21:58.453754+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We partially characterize the fundamental trade-offs among three performance measures: the transmitter's secrecy rate, its detection exponent, and the adversary's detection exponent... via wiretap and resolvability codes.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 2... R ≤ min(ρ R_key(s) + (1−ρ)[R1(s)−R2(s)+R_key(s)]+, R1(s)), E1 ≤ min D(...), E2 ≥ min C(...)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Secure Integrated Sensing and Communication: Information Theory Offers Insights
cs.IT 2026-04 unverdicted novelty 3.0

A survey organizing information-theoretic literature on secure ISAC by protected functionality and adversary models, covering formulations, metrics, and fundamental limits on tradeoffs among communication, sensing, an...

Reference graph

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TX t=1 E h L(1) s,s′;t|Ft−1 i + n−NX t=T+1 E h L(1) s,s′;t|Ft−1 i# ≥ 1 n

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applies on a packet-level adaptation. Fornsufficiently large, the probability of detection error can be bounded as Pd1 ≤max s∈S X s′̸=s Ps τX t=1 L(1) s,s′;t ≤n(D(W Y1|X,s||WY1|X,s′|PX,s)−ϵ) ! .(33) But the pairwise LLR can be expressed as 1 n τX t=1 L(1) s,s′;t = 1 n τX t=1 n L(1) s,s′;t −E[L (1) s,s′;t|Ft−1] o + 1 n τX t=1 n E[L(1) s,s′;t|Ft−1]−D(W Y1|X...

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