Daily Summary for 2026-10-19

Introduction to the show: ident: Security Radio. Generated commentary on the latest security and cryptography papers.

Nadia: It's the nineteenth of October, twenty twenty-six, and this is the day's research.

Elias: 25 new papers came out today.

Nadia: I'm Nadia.

Elias: And I'm Elias, here with Priya.

Nadia: We'll take the day in one pass, then pull out the papers we're staying with.

Elias: Start us off with Can Autonomous Vehicles Keep Their Cool? A Survey of Thermal Side-Channel and Perception Attacks.

The summary: Nadia: Welcome. Today is the nineteenth of October, twenty twenty six.

Elias: The survey frames thirteen works into areas like thermal perception integrity and telemetry leakage.

Priya: It distinguishes between attack families and adversary classes while mapping defenses to residual risk.

Nadia: This survey keeps thermal management operational while framing these issues.

Elias: A key concern is how physical adversaries can spoof infrared sensors in autonomous vehicles for night driving.

Priya: Interfaces built for night perception were never designed as confidentiality boundaries, leaving other paths intact.

Nadia: This contrasts with unprivileged software co-tenants fingerprinting workloads using thermal data and telemetry.

Elias: They use dynamic voltage and frequency scaling telemetry and thermal event interrupt telemetry for package safety.

Priya: Further down the list is work on model theft where streaming image classifiers expose trained models to theft via volatile memory rotation.

Nadia: This shows that a chunkable multi-exit model can still be captured if it streams into volatile memory.

Elias: The adversary gains usable CIFAR-100 seizures at high rates over time in that scenario.

Priya: Another concern involves agent harnesses leaking information through covert rewriting attacks.

Nadia: Provenance marks can be rewritten by large language models, allowing a plagiarist to pass a leaked harness.

Elias: This suggests selection protects marks only when each decision sees enough games.

Priya: Mobile app fingerprinting is countered with MAppPrint which proposes a behavior-level traffic fingerprinting framework.

Nadia: It improves app fingerprinting precision by incorporating unit traffic behaviors and correlation graphs.

Elias: This relates to inference as seen in MAppPrint's work on robust and real-time mobile app fingerprinting.

Priya: Finally, security types can be enforced in secure multi-party computation protocols using SMT-Boosted Security Types.

Nadia: This develops a new Hoare logic to automatically enforce correctness and confidentiality properties in protocols.

Elias: The Hybrid DeepXAI Fusion Network tackles the tension between big data models and understanding their decisions for trust.

Priya: It merges temporal features from CNNs with contextual modeling from Transformer encoders using graph neural networks.

Nadia: This architecture uses an attention-based fusion mechanism to combine representations and adds an explanation loss.

Elias: The setup is designed for deployment in a federated cloud architecture using homomorphic encryption and blockchain auditing.

Nadia: The network achieved ninety-eight point four two percent accuracy.

Elias: That performance beats CNN-LSTM, Transformer-only, and XGBoost baselines.

Priya: Under adversarial attacks, accuracy stayed above ninety-one point five percent.

Nadia: Scalability tests show eighty thousand messages per second with low latency.

Elias: This suggests promise for secure decision-support systems in the cloud.

Priya: ExecWeave tackles tracing agentic software execution across evidence planes.

Nadia: It builds a local-first system creating a typed execution graph.

Elias: It materializes provider semantics and observed runtime events there.

Priya: This separates logical operations from raw telemetry for better understanding.

Nadia: It addresses ambiguity when application traces describe logic only.

Elias: OS telemetry records machine activity, which is a different view indeed.

Priya: OS effects are assigned after linking processes via command-to-process association.

Nadia: This is more rigorous than observing session-correlated file system events.

Elias: A concern exists with the reaction attack on CKKS deployments.

Priya: That attack recovers a ternary secret key using optimal O H reaction queries.

Nadia: Observable validity reactions show a practical key-recovery channel in CKKS.

Elias: This exposes a surface vulnerability contrasting RAG privacy accounting work.

Priya: The survey moves beyond simple epsilon reporting for differential privacy in RAG systems.

Nadia: It proposes a framework interpreting guarantees across three dimensions there.

Elias: This helps users understand trade-offs between privacy and utility in multi-query systems.

Priya: Hardware security looks at hardware-software leakage contracts at the instruction set architecture level.

Nadia: This abstraction allows programmers to generate code resistant to side-channel attacks.

Elias: It does so without needing explicit knowledge of the underlying microarchitecture.

Nadia: The Pulsar verifier shows feasible commercial implementation for GNSS receivers using an SDR platform.

Elias: That demonstrates practical application for securing positioning services.

Priya: PAGE404 reveals side-channel vulnerabilities in NVIDIA's Grace Hopper architecture across MIG partitions.

Nadia: It exposes a security gap in hardware-managed heterogeneous memory systems.

Elias: The graph structures in gossip protocols affect honest node messages for blockchain consensus integrity.

Priya: Sparse or poorly connected networks can cause Byzantine fault-tolerant systems to fail quorum.

Nadia: We assessed Bitcoin's Erdős-Rényi graphs and Polkadot's grid topology against realistic attacks.

Elias: The parameters in these random models are often inadequate for guaranteeing message delivery for quorum formation.

Priya: Solana’s dynamic trees proved bandwidth-efficient but became fragile under adaptive attacks.

Nadia: Polkadot's grid achieved strong robustness but incurred a high bandwidth overhead.

Elias: GossipSub in Ethereum was both efficient and resilient though sensitive to chosen parameters.

Priya: ER graphs showed a tradeoff between robustness and efficiency when fanout exceeded fifteen nodes.

Nadia: Can Autonomous Vehicles Keep Their Cool? A Survey of Thermal Side-Channel and Perception Attacks shows thermal risks in compute.

Elias: This paper describes streaming image classifiers into volatile memory to limit adversary capture during physical seizure.

Priya: What Survives Self-Evolution investigates how provenance marks survive copying and rewriting attacks by analyzing proposer habits.

Nadia: My Credentials, Please: Detecting Filesystem Capability Laundering in MCP Servers at Scale introduces detection for AI agent misuse of tool permissions.

Elias: From Detection to Decision evaluates probabilistic models for blocking prompt injections in large language models.

Priya: Poisoning the Neighborhood presents an attack exploiting graph structure of retrieval systems to poison knowledge bases.

Nadia: Hybrid DeepXAI Fusion Network proposes a framework combining feature types with explainable AI for secure cloud decision-making.

Elias: Blind Watermarking of Software Repositories via Module Placement introduces embedding identifiers by strategic module placement.

Priya: NOMAI presents a scalable multi-party computation system protecting model, data, and integrity privacy in federated learning.

Nadia: On the Complexity of Symmetric Boolean Functions in Multiparty Private Simultaneous Messages provides bounds on communication complexity.

Elias: Can Autonomous Vehicles Keep Their Cool? A Survey of Thermal Side-Channel and Perception Attacks shows thermal risks in compute.

Priya: When Rotation Bounds Nothing: Streaming Image Classifiers to Field Nodes Under Physical Capture describes streaming image classifiers into volatile memory.

Nadia: What Survives Self-Evolution investigates how provenance marks survive copying and rewriting attacks by analyzing proposer habits.

Elias: My Credentials, Please: Detecting Filesystem Capability Laundering in MCP Servers at Scale introduces detection for AI agent misuse of tool permissions.

Priya: Poisoning the Neighborhood presents an attack exploiting graph structure of retrieval systems to poison knowledge bases.

Nadia: Hybrid DeepXAI Fusion Network proposes a framework combining feature types with explainable AI for secure cloud decision-making.

Elias: Blind Watermarking of Software Repositories via Module Placement introduces embedding identifiers by strategic module placement.

Priya: NOMAI presents a scalable multi-party computation system protecting model, data, and integrity privacy in federated learning.

Nadia: On the Complexity of Symmetric Boolean Functions in Multiparty Private Simultaneous Messages provides bounds on communication complexity.

Elias: Can Autonomous Vehicles Keep Their Cool? A Survey of Thermal Side-Channel and Perception Attacks shows thermal risks in compute.

Priya: When Rotation Bounds Nothing: Streaming Image Classifiers to Field Nodes Under Physical Capture describes streaming image classifiers into volatile memory.

Nadia: What Survives Self-Evolution investigates how provenance marks survive copying and rewriting attacks by analyzing proposer habits.

Elias: My Credentials, Please: Detecting Filesystem Capability Laundering in MCP Servers at Scale introduces detection for AI agent misuse of tool permissions.

Priya: Poisoning the Neighborhood presents an attack exploiting graph structure of retrieval systems to poison knowledge bases.

Nadia: Hybrid DeepXAI Fusion Network proposes a framework combining feature types with explainable AI for secure cloud decision-making.

Elias: Blind Watermarking of Software Repositories via Module Placement introduces embedding identifiers by strategic module placement.

Priya: NOMAI presents a scalable multi-party computation system protecting model, data, and integrity privacy in federated learning.

Nadia: On the Complexity of Symmetric Boolean Functions in Multiparty Private Simultaneous Messages provides bounds on communication complexity.

Elias: Can Autonomous Vehicles Keep Their Cool? A Survey of Thermal Side-Channel and Perception Attacks shows thermal risks in compute.

Lucky paper: 2610.21034: Nadia: So, we're looking at Can Autonomous Vehicles Keep Their Cool? A Survey of Thermal Side-Channel and Perception Attacks.

Elias: It systematically frames thirteen representative works into thermal perception integrity, telemetry leakage, and model information extraction.

Priya: It compares these by privilege, timescale, co-tenancy, deployability, and AV relevance.

Nadia: The survey addresses the vulnerability of autonomous vehicles that couple safety-critical perception to thermally constrained compute.

Elias: Physical adversaries can spoof thermal infrared sensors used for night driving in autonomous vehicles.

Priya: That's a key concern because interfaces built for night perception were never designed as confidentiality boundaries, leaving other paths intact.

Nadia: This contrasts with unprivileged software co-tenants fingerprinting perception workloads from thermal, dynamic voltage and frequency scaling, and thermal event interrupt telemetry required for package safety.

Elias: Both exploit interfaces that autonomous vehicle stacks cannot disable without compromising Safety of the Intended Functionality, or SOTIF.

Priya: The survey maps sensor, OS-telemetry, DVFS, packaging, and model controls to residual risk when thermal management must remain functional.

Nadia: Key Observation four states that no single defense layer closes both access paths without residual risk.

Elias: The survey compares thermal infrared spoofing, unprivileged silicon telemetry leakage, and energy-based model extraction along privilege, timescale, co-tenancy, deployability, and AV relevance axes.

Priya: It organizes works into physical thermal IR attacks, unprivileged silicon telemetry leakage, and energy-based model extraction.

Nadia: The survey measures software-path telemetry accessibility under an unprivileged policy on commodity hardware.

Elias: This mechanism baseline doesn't validate the physical IR branch or production AV stacks; it supplies a mechanism baseline for the software co-tenant class.

Priya: The results show that fused temperature, frequency, and GPU features dominate workload fingerprinting macro-F1 on the commodity proxy.

Nadia: That means fused temperature and frequency features are key to understanding what's happening on commodity hardware.

Elias: The survey identifies five key observations synthesizing the literature and software-path proxy.

Priya: Those include that heat was instrumented for reliability or night perception, not confidentiality.

Nadia: And that naive thermal-only fusion under RGB collapse can allow an infrared spoof to dominate fused decisions.

Elias: Another finding is that restricting a single energy interface leaves residual frequency and accelerator telemetry informative.

Priya: So the survey identifies open problems needing concrete research directions on on-target co-tenant evaluation and chiplet thermal coupling.

Nadia: It also points toward standards-ready TARA artifacts for capability-based telemetry under SOTIF budgets.

Elias: The broader impact is a residual-risk frame linking sensor, OS, silicon, and standards concerns that prior surveys leave fragmented.

Lucky paper: 2610.22301: Nadia: We're looking at the paper, My Credentials, Please: Detecting Filesystem Capability Laundering in MCP Servers at Scale.

Elias: This paper studies how AI agents invoke external tools via the Model Context Protocol or MCP standard.

Priya: It focuses on filesystem capability laundering where attacker-steered arguments cause a tool to access sensitive host files outside its declared contract and deployment scope.

Nadia: How does it characterize this mechanism?

Elias: Filesystem capability laundering is characterized by three conditions: the implemented effect exceeds the scope justified by the tool contract and deployment, attacker-influenced arguments select the filesystem target, and the call is admitted while surrounding controls fail to constrain that effect.

Priya: The authors analyze this across three layers: server-category screening at L1, per-tool contract analysis at L2, and bypassable path-validation checks at L3.

Nadia: What's the threat model they focus on?

Elias: The threat model focuses on local stdio MCP servers launched as separate processes where the server runs with the user’s ambient filesystem permissions and the client’s tool-approval prompt enforces no per-tool path restrictions on that underlying process.

Priya: An attack succeeds when the MCP response contains contents of a file outside the tool’s legitimate scope.

Nadia: So they designed a solution called MCP-FSD to counter this?

Elias: Yes, they designed MCP-FSD, which catalogs servers across registries and discovers tools inside per-repository sandboxes.

Priya: They screen candidates with MCP-aware static filters and then dynamically validate each one against an inferred least-privilege boundary in two passes.

Nadia: What does the static screening phase actually use to identify tool registrations?

Elias: The static screening phase uses a large language model to identify tool registrations, handlers, and path parameters.

Priya: It classifies each finding into five rule categories spanning CWE-twenty-two for path traversal and CWE-fifty-nine for link resolution.

Nadia: That includes PT-one missing validation and PT-four symlink TOCTOU as examples of what they're looking for.

Elias: Four MCP-aware filters select candidates based on whether they can plausibly return out-of-scope file contents, like a git add example.

Priya: The Boundary Inference Algorithm derives the scope from the tool’s legitimate operation rather than from the suspected bug.

Nadia: It uses four signals: launch configuration L, path-bearing schema fields S, tool description D, and repository source signals R to build a policy hypothesis.

Elias: They extract roots from the launch tuple and walk the JSON Schema for path parameters to construct a policy hypothesis that is partitioned into read-write and read-only halves.

Priya: Then there's the Dynamic Three-Case Validation pass which confirms exploitability with three cases.

Nadia: What are those three cases?

Elias: PoC one runs the malicious payload without the sandbox and succeeds only when the response contains planted credential contents. PoC two runs the benign in-scope payload with the sandbox and requires no denial event. PoC three replays PoC one’s malicious payload with the sandbox and requires absent credential contents plus an explicit denial or a non-disclosing response.

Priya: These cases establish that detected disclosures represent genuine vulnerabilities remediated by least-privilege containment.

Nadia: The evaluation phase shows results across the cataloged servers.

Elias: They cataloged twenty-one thousand ninety-seven listings from nine registries and dynamic validation confirmed one hundred fifty vulnerable instances under tested sandbox policies.

Priya: Among the flagged servers, seven hundred eighty-seven exhibit filesystem capability flags without a FileSystem category label during L1 screening.

Nadia: The evaluation also confirmed that L3 defense-bypass classifiers achieve ninety-five point three percent precision and ninety-nine point three percent recall over two hundred ninety-seven labeled findings.

Elias: Two CVEs in Anthropic’s Git MCP Server were reported, illustrating laundering across distinct boundaries at L2.

Priya: The paper concludes that ecosystem-scale registry screening and explicit, runtime-enforced per-tool filesystem contracts are necessary to bridge the gap between client-side tool approval and unconfined server filesystem execution.

Lucky paper: 2610.21031: Nadia: Let's talk about Blind Watermarking of Software Repositories via Module Placement, which is paper number three of five in this round.

Elias: This paper introduces PLACEMARK, a blind watermarking system that encodes a payload by placing modules within a repository instead of inserting or deleting code lines.

Priya: The core mechanism involves encoding a payload into the placement of modules where each eligible module is identified by its filename and top-level definition names.

Nadia: A secret key determines the ordered candidate destinations and its position in the reading order, which then determines the encoded symbol for that module's location.

Elias: The design has several formal requirements, including effectiveness, blindness, robustness, and behavior preservation.

Priya: Effectiveness means the message is recovered from an unmodified marked repository exactly when every selected payload position is writable.

Nadia: Blindness means extraction requires only the marked repository, the key, and agreed decoding parameters without any original copy or stored side information.

Elias: Robustness means it survives modification of the artifact, but behavior preservation is where things get tricky because moving a module out of a directory can change its meaning.

Priya: To handle that risk, they devote a selection rule to behaviour preservation, which is the constraint that makes it work.

Nadia: The carrier set and reading order are derived from the repository and key, and the decoder has to recompute those quantities without being told anything beforehand.

Elias: The identity of a carrier is defined by its content, its filename combined with the names it defines in the file structure.

Priya: A keyed pseudorandom function assigns each carrier an ordered list of packages it may legally occupy, and the index of a module’s package within that list encodes the symbol it carries.

Nadia: Capacity measurements on ten Python repositories show nominal capacities ranging from two hundred forty-nine to two thousand one hundred sixty-six bits in nine of them.

Elias: One repository provides no placement channel at all, which shows capacity is determined by architecture, not just repository size.

Priya: The robustness to content-level removal transformations is high because across two hundred sixteen measured trials on three repositories, no payload bit was lost under renaming up to one hundred percent of local variable names or dead-code insertion.

Nadia: However, relocation degrades recovery gradually rather than abruptly on Django, Airflow, and Salt systems.

Elias: The sharpest boundary occurs when renaming carrier files or their top-level definitions because that input changes the mid(m) drive bit accuracy to chance level from a quarter of the files upward.

Priya: The two carriers have complementary attack surfaces rather than disjoint ones because reformatting leaves placement untouched, relocation leaves code text untouched, and a refactor that renames files while reorganizing them reaches both.

Nadia: This scheme applies to languages in which a module’s location is a free choice, like Python.

Elias: The census covers ten repositories and the experiments cover a subset that varies by experiment.

Priya: The adversary models are fixed strategies, including the carrier-aware one; they do not evaluate an adaptive adversary that learns from repeated extraction attempts.

Nadia: The scheme is recovered exactly when the selected payload positions were all writable.

Lucky paper: 2610.21059: Nadia: We're moving on to paper number four of five today, which is NOMAI: Scalable Federated Learning with Private Weights.

Elias: This framework aims to simultaneously achieve model privacy, data privacy, and data integrity within a single coordinating server environment.

Priya: It’s presented as the first scalable Multi-Party Computation based Federated Learning system that can provide all three security guarantees concurrently.

Nadia: NOMAI operates under an honest-majority assumption in the semi-honest model with an extension to the malicious with abort setting.

Elias: The paper introduces a new architecture that keeps a single coordinating server while distributing computation across small, disjoint committees of participating users who act as MPC helpers.

Priya: Each user's data is assigned to one specific committee and that data is secret-shared among the members of that committee.

Nadia: This structure allows committees to operate in parallel on their respective data shards enabling massive scalability beyond traditional n-party protocols.

Elias: Within each committee, NOMAI uses Packed Shamir Secret Sharing, which enables SIMD style parallelism and significantly reduces the computational cost associated with operations there.

Priya: This cryptographic primitive allows for SIMD style parallelism that cuts down the computation overhead within a committee.

Nadia: They incorporate several new cryptographic primitives tailored for machine learning workloads to drastically reduce per-user overhead.

Elias: Specifically, they have efficient linear layers using ML inspired transformations and novel packing strategies under PSS.

Priya: There are also efficient secure exponentiation protocols that minimize the required rounds for secure exponentiation by converting PSS sharing into additive shares.

Nadia: They also have a protocol for efficient degree reduction that integrates repacking directly, eliminating explicit unpacking and repacking steps.

Elias: And there's an efficient truncation protocol compatible with PSS leveraging Mersenne prime fields for highly efficient bit operations.

Priya: NOMAI is engineered to satisfy data privacy where no other user learns raw private data from the coordinating server beyond the final aggregate gradient G.

Nadia: Weight privacy is also achieved so model parameters held by the central server remain hidden from all participating users.

Elias: Data integrity is guaranteed by enforcing a validation predicate Valid(times) which defines necessary constraints like norm bounds on individual user gradients.

Priya: Crucially, they execute the computationally expensive gradient computation under the cheaper semi-honest model and reserve malicious security checks only for final validation and aggregation steps.

Nadia: The system demonstrates exceptional practical deployability at unprecedented scales with speed improvements of three orders of magnitude over prior work.

Elias: NOMAI reduces per-user computation to less than three hundred fifty ms in semi-honest mode for MNIST training iterations and less than seven hundred ms in malicious mode.

Priya: That represents three orders of magnitude improvement over prior work, which is significant because of the per machine cost independence from the total number of users N.

Nadia: It successfully supports user populations exceeding one hundred six users in this system.

Elias: Comparative gains are ten cubed to ten to the five times over baselines including a two times ten cubed to one point seven times ten to the five times improvement against POSEIDON.

Priya: A key finding is that the dominant cost in NOMAI is the semi-honest secure training computation, whose per committee member workload is largely independent of the total user population N.

Nadia: Increasing N primarily impacts the number of committees that need coordination and checking for malicious security leading to a relatively weak dependence on N for fixed costs.

Elias: For CNN architectures, NOMAI shows significant communication advantages due to packing requiring only one degree reduction per packed output regardless of spatial dimension.

Priya: This yields bandwidth reductions up to twenty-nine thousand two hundred fifty-eight times for MNIST-CNN and SVHN-CNN compared to HMMPC's O n communication.

Nadia: The work on NOMAI is a highly optimized, architecture specific MPC framework that leverages advanced cryptographic packing and ML aware transformations.

Elias: It delivers state of the art performance in scalable federated learning while rigorously enforcing simultaneous data privacy and integrity guarantees.

Lucky paper: 2610.21216: Nadia: We're moving into Paper number five of five today, which is On the Complexity of Symmetric Boolean Functions in Multiparty Private Simultaneous Messages.

Elias: This paper studies communication complexity for symmetric Boolean functions in Multiparty Private Simultaneous Messages, or PSM.

Priya: The authors establish lower bounds and upper bounds for various symmetric functions within this model of non-interactive secure computation.

Nadia: They introduce a new combinatorial technique to get better lower bounds than those from Ball et al., which only yielded trivial linear bounds before.

Elias: Specifically, their results show that the communication complexity for OR is omega(n).

Priya: For MAJ or EMAJ when n is even, the communication complexity is proven to be omega(n log n).

Nadia: And for MODq when q is less than or equal to one minus c times n, the complexity satisfies omega(n log q) for a fixed constant c greater than zero.

Elias: These lower bounds are derived using a general combinatorial framework that reduces proving lower bounds in the PSM model to studying f-cube systems.

Priya: The authors construct perfectly private PSM protocols with total communication of Oe(n three/two) for every symmetric Boolean function, improving on the known quadratic bound.

Nadia: Theorem thirty proves that for any symmetric Boolean function f: zero one n → zero one there is a perfectly correct and perfectly private PSM with total complexity of Oe(n three/two).

Elias: For MAJ, a combination of known results matches the lower bound up to polylogarithmic factors, yielding a communication complexity of O(n log3 n log log n).

Priya: The universal support-private construction gives Oe(n two) communication for every symmetric function.

Nadia: They also obtain a quasilinear bound of Oe(n) for perfectly correct and support-private PSM protocols for every symmetric Boolean function.

Elias: The paper introduces an f-cube system representation to isolate the correctness and privacy properties used by lower bounds.

Priya: This framework allows them to use agreement lemmas, such as Lemma thirteen for OR, which relies on Higman’s lemma and Ramsey’s theorem.

Nadia: They also employ Plotkin’s bound for error-correcting codes to derive alphabet lower bounds for MAJ and MODq functions.

Elias: The lifting lemma in Section six converts individual message lower bounds into a total communication lower bound.

Priya: For OR, the communication complexity is proven to be C(OR) = omega(n).

Nadia: For MAJ and EMAJ when n is even, the communication complexity is omega(n log n).

Elias: For MODq, the communication complexity satisfies C(MODq) = omega(n log q) when q is less than or equal to one minus c times n for some constant c greater than zero.

Priya: They also show that there is a perfectly correct and perfectly private PSM protocol for MODq with cost O(n log q) when q is prime, and for EMAJn of cost O(n log n).

Nadia: The general lower bound approach involves defining a Consistent Coloring Family and showing that the non-existence of such a family implies the non-existence of an (n, K)-protocol satisfying perfect correctness and support privacy.

Elias: They relate this cube argument to the Nechiporuk bound, which states that every perfectly correct and support-private protocol for f with local alphabet sizes Ki satisfies P i∈S log Ki greater than or equal to log NS(f) minus one.

Priya: This leads to Corollary twenty-nine showing Cindiv-sum(f) greater than or equal to Xm i=one log NVi(f) minus m.

Nadia: The upper bound construction for a general symmetric function f(x) = g(x) involves composing an outer protocol that evaluates g on the weight reconstructed from residues modulo small primes with inner protocols that privately compute the outer messages.

Elias: This results in a total communication complexity of O(n three/two).

Priya: For support-private protocols, they obtain a quasilinear bound of Oe(n) for any symmetric Boolean function f.

Nadia: The upper bound for MAJ is achieved by combining a known permutation branching program with a standard PSM construction, yielding O(n log3 n log log n).

Elias: The upper bound for EMAJ and MODq with prime q follows from variants of the OR protocol in Theorem eleven resulting in O(n log q).

Priya: For EMAJn, a specific protocol yields a cost of O(n log n).

Nadia: The conclusion is that they successfully establish tight bounds for various symmetric Boolean functions in the PSM model.

Elias: They show that while perfect privacy allows for quadratic communication complexity, support privacy allows for quasilinear communication complexity.