Communication-Efficient Private Federated Reinforcement Learning with Post-Quantum Authentication for Vehicular Networks

Hojat Allah Salehi; Devrim Aras; Md Jueal Mia; M. Hadi Amini; Imtiaz Karim; Mashrur Chowdhury; Bhavani Thuraisingham

cs.LGOct 29, 2026

Communication-Efficient Private Federated Reinforcement Learning with Post-Quantum Authentication for Vehicular Networks

Authors: Hojat Allah Salehi, Devrim Aras, Md Jueal Mia, M. Hadi Amini, Imtiaz Karim, Mashrur Chowdhury, Bhavani Thuraisingham

Organizations: Knight Foundation School of Computing and Information Sciences, Florida International University, Miami, FL 33199, USA · Security, Optimization, and Learning for Interdependent Networks Lab (solid lab), Miami, FL 33199, USA · Department of Computer Science, The University of Texas at Dallas, Richardson, TX 75080, USA · Glenn Department of Civil Engineering, Clemson University, Clemson, SC 29634, USA

Abstract

Federated reinforcement learning supports cooperative vehicular routing without centralizing trajectory data, but model updates may reveal private information and incur communication overhead over intermittent vehicle-to-infrastructure links, particularly when post-quantum authentication is required. We study correlated private quantization, using complementary shared randomness between paired vehicles to reduce aggregation mean squared error while preserving the marginal parameter-level local differential privacy and one-bit communication cost of independent quantization. A tunable extension mixes shared and independent randomness to bound privacy leakage given paired outputs and shared-randomness side information. For this extension, Rényi differential privacy accounting establishes vector-level local differential privacy for one model upload even when pairings are revealed. Under matched vector-level privacy and identical local and global parameters, the extension yields 16.5% lower analytical aggregation mean squared error than independent quantization. We evaluate cooperative routing by coupling traffic simulation with packet-level simulation of post-quantum-authenticated vehicle-to-infrastructure communication. Compared to full-precision updates, one-bit uploads reduce authenticated uplink size by 92.4% and increase mean verified updates aggregated per round from 19.6 to 26.5. Under mobility-constrained communication at a parameter-level privacy budget of 1, correlated private quantization reduces mean travel time by 14.3% relative to independent quantization at the same budget and communication cost. At a parameter-level privacy budget of 0.3, a vehicle-origin inference attack trained on independent simulations reaches 30% accuracy with correlated private quantization and 22% with independent quantization after 100 rounds, versus 91% without privacy and 10% for random guessing.

Figures & tables

Figure 1: Architecture of the proposed privacy-preserving and post-quantum-authenticated vehicular FRL framework. SUMO trajectories drive ns-3 V2I communication, with signed full-precision global-model downlinks and privacy-protected, signed model-update uplinks.

Mechanism	Calibration	MSE formula	MSE $\downarrow$	Bits/ weight
LDP-FL	$s_{0}=0.001185$	$A(s_{0})^{2}/K$	22.79	1
CPQ- $\lambda$	$s=0.001010$	$(1-\lambda^{2})A(s)^{2}/K$	19.03	1
Gaussian	$\sigma=33.76$	$\sigma^{2}/K$	22.79	32
Laplace	$\beta=33.75$	$2\beta^{2}/K$	45.55	32

Table 1: Analytical FedAvg MSE under matched vector-level privacy.

Figure 2: Evolution of mean evaluation travel time across privacy budgets during federated training.

Mechanism	$\epsilon_{p}=0.3$	$\epsilon_{p}=0.5$	$\epsilon_{p}=1$	$\epsilon_{p}=2$	$\epsilon_{p}=5$
A. Mean evaluation travel time (s) $\downarrow$
CPQ	165.3 $\pm$ 21.4	137.9 $\pm$ 59.7	144.7 $\pm$ 26.5	118.6 $\pm$ 23.1	125.7 $\pm$ 24.5
CPQ- $\lambda$ ( $\lambda=0.75$ )	191.0 $\pm$ 36.4	178.8 $\pm$ 42.7	152.8 $\pm$ 17.5	141.1 $\pm$ 41.7	127.8 $\pm$ 11.9
LDP-FL	206.6 $\pm$ 33.2	199.5 $\pm$ 21.8	187.7 $\pm$ 25.3	126.7 $\pm$ 45.5	138.3 $\pm$ 38.3
Gaussian	412.8 $\pm$ 30.5	323.8 $\pm$ 56.4	226.2 $\pm$ 41.8	186.1 $\pm$ 30.9	164.6 $\pm$ 43.1
Laplace	257.1 $\pm$ 19.7	215.1 $\pm$ 19.6	196.9 $\pm$ 37.8	148.4 $\pm$ 15.9	121.5 $\pm$ 20.0

Table 2: Privacy–utility performance of federated routing across privacy budgets.

$\lambda$	$\epsilon_{S}$	$\epsilon_{C}$	MSE ( $10^{-5}$ )	Travel time (s)	Arrival (%)
LDP-FL	1.00	1.00	$3.717\pm 0.003$	$184\pm 27$	$79\pm 6$
$0.25$	1.06	1.38	$3.497\pm 0.002$	$149\pm 28$	$87\pm 6$
$0.50$	1.25	1.86	$2.825\pm 0.005$	$145\pm 28$	$87\pm 5$
$0.75$	1.75	2.63	$1.708\pm 0.007$	$142\pm 16$	$90\pm 5$
$0.90$	2.54	3.59	$0.828\pm 0.011$	$153\pm 19$	$84\pm 5$
$1$	$\infty$	$\infty$	$0.145\pm 0.015$	$138\pm 21$	$89\pm 6$

Table 3: CPQ-

\lambda

ablation at

\epsilon_{p}=1

Figure 3: Authenticated V2I communication under mobility-dependent connectivity using ML-DSA-44. Panels show wireless traffic, distance-dependent uplink attempt success, and successful-uplink latency.

Scheme	Update	UL size (KB)	Attempt success (%)	UL delivery (%)
ML-DSA-44	FP	113.60	32.2	74.7
	CPQ	8.65	97.0	99.8
Falcon-512	FP	111.90	33.3	78.1
	CPQ	6.89	99.4	99.8
SLH-DSA-SHA2-128f	FP	128.40	29.9	74.8
	CPQ	23.34	48.2	93.1

Table 4: Signature-scheme sensitivity of V2I uplinks. FP denotes full-precision model updates.

Method	Travel (s) $\downarrow$	Arrival (%) $\uparrow$	DL reach (%) $\uparrow$	UL delivery (%) $\uparrow$	Updates per round $\uparrow$	$\Delta T$ (s)
No privacy	$152.6\pm 20.2$	$80.4\pm 8.1$	$51.8\pm 2.0$	$75.7\pm 1.3$	$19.6\pm 0.9$	$+40.8\pm 56.4$
CPQ	$167.0\pm 33.5$	$79.8\pm 8.8$	$53.3\pm 1.1$	$99.4\pm 0.2$	$26.5\pm 0.6$	$+22.4\pm 35.8$
CPQ- $\lambda$ ( $\lambda=0.75$ )	$177.2\pm 41.5$	$75.8\pm 9.2$	$52.4\pm 0.3$	$99.5\pm 0.3$	$26.1\pm 0.2$	$+24.4\pm 54.9$
LDP-FL	$194.9\pm 53.0$	$72.8\pm 11.0$	$53.4\pm 1.2$	$99.4\pm 0.3$	$26.5\pm 0.5$	$+7.2\pm 64.7$
Gaussian	$290.3\pm 28.3$	$51.8\pm 6.9$	$55.6\pm 1.8$	$74.0\pm 1.1$	$20.6\pm 0.9$	$+64.1\pm 48.7$
Laplace	$218.4\pm 33.3$	$66.4\pm 9.0$	$53.8\pm 2.2$	$75.9\pm 2.3$	$20.4\pm 1.4$	$+21.5\pm 50.1$

Table 5: Routing performance and participation under mobility-constrained V2I communication.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Mechanism	One-bit configuration and equivalence conditions
Duchi et al. (2018)	Scalar case $d=1$ , with the input mapped to the common clipping interval $[c-r,c+r]$ .
1BitMean ( Ding et al., 2017 )	Counter range $[0,m]$ , with $m=2r$ and input mapping $u=x+r$ .
PBM ( Chen et al., 2022 )	One Bernoulli trial ( $m=1$ ), $C=r$ , and $\theta=\frac{1}{2}\tanh(\epsilon_{p}/2)$ . The original constraint $\theta\leq 1/4$ requires $\epsilon_{p}\leq\ln 3$ .
RQM ( Youn et al., 2023 )	Two output levels ( $m=2$ ), $C=r$ , and $\Delta=2r/(e^{\epsilon_{p}}-1)$ , using exact local-privacy calibration.
MVU ( Chaudhuri et al., 2022 )	One output bit, pure- $\epsilon_{p}$ -LDP, hard unbiasedness, and exact optimization on a grid containing the clipping endpoints. The unique optimum yields the LDP-FL reconstruction levels.
$\beta$ -StoSign ( Xiang and Su, 2023 )	Centered input $x=w-c$ , clipping bound $r$ , and $\beta=2r/(e^{\epsilon_{p}}-1)$ . Reconstruction uses $c\pm(r+\beta)$ , followed by arithmetic-mean aggregation.

Appendix

Table A.1: One-bit mechanisms equivalent to LDP-FL under specified configurations.

Figure F.1: Topology of the synthetic road network implemented in the SUMO environment. The network comprises 10 junctions (J0–J6 and J10–J12) and 30 directed edges (15 bidirectional corridors) covering a total distance of 5.37 km.

Parameter	Symbol	Value
State dimension	$3M+4$	94
Action space size	$\|\mathcal{A}_{\max}\|$	3
Network architecture	—	94–150–100–3
Optimizer	—	Adam
Learning rate	$\eta$	$10^{-3}$
Discount factor	$\gamma$	0.99

Appendix

Table G.1: FLDQN configuration for the privacy–utility experiment.

Parameter	Symbol	Value
Chunk payload size	$L_{\rm chunk}$	1200 B
Chunk header size		44 B
Initial window	$W_{0}$	32 chunks
Maximum window	$W_{\max}$	128 chunks
Retransmission timeout	$\tau_{\rm rto}$	120 ms
Per-chunk retry cap	$R_{\max}$	8

Appendix

Table G.2: SR-ARQ transport parameters used in ns-3.

Component	Tool	Version
Traffic simulator	SUMO	1.26
Network simulator	ns-3	3.46
DQN training	TensorFlow (Keras)	2.x
Privacy processing	NumPy	1.x
FL coordination	Flower ( flwr )	1.x
PQC signatures and ML-KEM	liboqs / liboqs-python	0.15.0 / 0.14.1

Appendix

Table G.3: Software components and reported versions.

Algorithm	Basis	PK (B)	Sig. (B)	Keygen (ms)	Sign (ms)	Verify (ms)
ML-DSA-44	MLWE/MSIS	1312	2420	$0.037\pm 0.009$	$0.105\pm 0.063$	$0.045\pm 0.009$
Falcon-512	NTRU/SIS	897	655.1	$5.771\pm 1.285$	$0.210\pm 0.027$	$0.059\pm 0.012$
SLH-DSA-SHA2-128f	Hash	32	17088	$0.989\pm 0.086$	$23.078\pm 1.377$	$1.412\pm 0.110$
SLH-DSA-SHA2-128s	Hash	32	7856	$61.707\pm 2.624$	$469.949\pm 4.877$	$0.491\pm 0.030$
RSA-2048-PSS-SHA256	IFP	256	256	$38.741\pm 24.430$	$0.799\pm 0.025$	$0.048\pm 0.003$
ECDSA-P256-SHA256	ECDLP	65	71.0	$0.022\pm 0.004$	$0.053\pm 0.006$	$0.084\pm 0.008$

Appendix

Table H.1: Controlled signature microbenchmark on the evaluation workstation. Timing values are mean

\pm

standard deviation in milliseconds over

N=200

measured trials using 4096-byte messages.

Figure I.1: Distance-dependent uplink transfer-attempt success under IEEE 802.11p communication for three post-quantum signature schemes: (a) full-precision updates and (b) one-bit CPQ updates. Each point represents the percentage of successful uplink transfer attempts within the corresponding vehicle-to-RSU distance interval at transfer initiation (

\epsilon_{p}=1

Figure J.1: Seed-paired routing-performance differences between CPQ and LDP-FL.

$K$	Travel-time gain (s) $\uparrow$	Arrival-rate gain (pp) $\uparrow$	Faster seeds
$10$	$42.0\pm 142.0$	$8.6\pm 31.1$	$3/5$
$25$	$61.8\pm 43.5$	$10.8\pm 10.0$	$5/5$
$50$	$43.1\pm 26.5$	$8.8\pm 12.4$	$5/5$

Appendix

Table J.1: Population sensitivity at

\epsilon_{p}=1

Figure J.2: Seed-paired travel-time differences for CPQ-

\lambda

Figure J.3: Seed-level variability of late-round travel time and arrival rate across privacy budgets.

Figure J.4: Secondary routing-delay measures across privacy mechanisms and privacy budgets.

Figure K.1: Authenticated CPQ group-establishment progress across post-quantum signature schemes. All 49 recipients verified SETUP_OK after 7 (Falcon-512), 9 (ML-DSA-44), or 19 (SLH-DSA-SHA2-128f) communication drives. The vertical line marks the 20-drive setup limit.

A. Known-origin attack
Rounds	No privacy	CPQ	LDP-FL
10	$33.7\pm 4.5$	$11.3\pm 0.6$	$9.3\pm 2.5$
50	$63.7\pm 4.5$	$11.7\pm 1.5$	$10.0\pm 1.0$
100	$68.7\pm 6.8$	$13.0\pm 2.6$	$12.0\pm 3.5$
B. Shadow-run attack
10	$46.0\pm 7.2$	$13.3\pm 4.2$	$11.3\pm 2.3$

Appendix

Table L.1: Vehicle-origin inference accuracy (mean

\pm

SD).

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As vehicular networks move toward 5G/6G edge intelligence, federated learning (FL) is widely promoted as a privacy-preserving way for vehicles and infrastructure to train shared models without exposing raw sensor data. Yet the updates clients transmit still leak enough information to identify who sent them, which threatens the anonymity that safety-critical V2X applications assume and adds to existing concerns over adversarial ML, model poisoning, and backdoor attacks. We study server-side client identity inference from transmitted weight deltas using inertial (IMU) measurements, evaluated on the UCI Human Activity Recognition (HAR) benchmark as an accessible proxy for the IMU streams produced onboard connected vehicles. Across five attack classifiers and five non-IID partitions, an honest-but-curious server recovers client identity with near-perfect accuracy (approximately 1.000) from undefended updates, confirming a concrete identifiability risk. We then quantify the privacy-utility trade-off of a lightweight clip-then-noise defense by sweeping Gaussian noise (sigma in {0.00, 0.05, 0.10, 0.20, 0.50, 1.00}) at fixed clipping (C=1.0), and report formal (epsilon, delta)-DP budgets through Renyi accounting. A practical region (sigma in [0.1, 0.2]) drives attack accuracy to near-random while costing under 5% relative FL accuracy. Ensemble FL supplies complementary structural privacy with a 1/K anonymity-set bound and no noise penalty. Results are supported by cryptographic (SHA-256) train/evaluation gradient disjointness, three seeds, and a count-normalized attacker-advantage metric. We position HAR explicitly as a proxy and discuss what validation on true vehicular telemetry would require.

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