Quantum Encryption Resilience Score (QERS)

• Quantum Encryption Resilience Score (QERS) is a composite metric that aggregates performance, security, and energy measures to evaluate post-quantum cryptographic protocols.
• It is validated on resource-constrained devices like the ESP32-C6 and Raspberry Pi CM4, revealing nuanced trade-offs among protocols such as MQTT, HTTP, and HTTPS.
• QERS supports migration planning and protocol selection through its Basic, Tuned, and Fusion formulations, enabling tailored assessments for IoT and IIoT environments.

The Quantum Encryption Resilience Score (QERS) is a composite metric designed to quantify the resilience, performance, and security trade-offs of post-quantum cryptographic (PQC) protocols deployed on traditional computers, Internet of Things (IoT), and Industrial IoT (IIoT) platforms. QERS integrates a spectrum of system costs (latency, computational overhead, energy use) and security benefits (proven resistance, key size, cryptographic overhead), yielding a reproducible 0–100 score for comparative analysis, migration planning, and real-time assessment of PQC-enabled environments. The framework supports multiple operational scenarios through its Basic, Tuned, and Fusion formulations and is validated experimentally on platforms such as the ESP32-C6 client and ARM-based Raspberry Pi CM4 server using post-quantum schemes like Kyber and Dilithium (Rassekhnia, 19 Jan 2026, Rassekhnia, 19 Jan 2026).

1. Motivation, Scope, and Conceptual Overview

QERS addresses the multifactorial challenges introduced by deploying PQC on resource-limited devices. Traditional cryptographic benchmarking reports isolated measures such as computation time or energy consumption, which are insufficient for holistic system characterization. QERS fills this gap by aggregating performance penalties and security contributions into a single, interpretable metric reflective of real-world constraints and adversarial settings.

The primary goals are comparison and ranking of PQC algorithms under operational workloads, exposure of multidimensional trade-offs between efficiency and cryptographic strength, and facilitation of migration strategies in legacy and emerging systems, notably in IoT/IIoT (Rassekhnia, 19 Jan 2026, Rassekhnia, 19 Jan 2026).

2. Measurement Metrics and Experimental Testbed

QERS employs an empirically-driven approach based on measurements collected over extended intervals (e.g., 12–24 hours) on commodity and resource-constrained devices. The framework utilizes the following normalized metrics:

Metric	Type	Description
Latency (L)	Cost	End-to-end round-trip message delay (ms)
CPU (C)	Cost	Processor utilization (%) during cryptographic ops
RSSI (R)	Benefit	Wi-Fi signal strength indicator (dBm)
Energy (E)	Cost	Power consumption per operation (mJ or J)
Key Size (K)	Cost	Aggregate PQC key and signature size (bytes)
TLS Overhead(O)	Cost	Handshake time for PQC-based TLS (ms)
Packet Loss	Cost	Fraction of lost or corrupted packets
Jitter (J)	Cost	Variability in transmission/interarrival time (ms)
Proven Resistance (P_r)	Benefit	NIST category or equivalent quantum security constant
Crypt. Overhead (Co)	Cost	Memory/bandwidth allocated to PQC processing

Measurements are performed using, for example, ESP32-C6 clients and Raspberry Pi CM4 servers, with all relevant system parameters logged at 5 s intervals under varying network conditions (proximity to access point, RF stress).

3. Metric Normalization and Aggregation

To enable meaningful combination of heterogeneous metrics, QERS employs min–max normalization of each raw variable to the [0, 100] interval: $$X_{\text{norm}} = MS \cdot \frac{X - X_{\min}}{X_{\max} - X_{\min}}$$ where $MS = 100$ and $(X_{\min}, X_{\max})$ span the observed dataset range for each metric. Cost metrics (L, O, P_loss, C, E, K, J, Co) are penalized such that higher raw values yield higher normalized penalties. Benefit metrics (RSSI, proven resistance) are included as positive contributions, with appropriate sign inversion where required (Rassekhnia, 19 Jan 2026, Rassekhnia, 19 Jan 2026).

4. QERS Formulations: Basic, Tuned, and Fusion Modes

QERS supports three aggregation methodologies to serve diverse operational objectives and analytic depth:

Basic QERS: Focuses on core communication costs (latency, cryptographic overhead, packet loss).

$$\text{QERS}_\text{basic} = MS - (\alpha L_{\text{norm}} + \beta O_{\text{norm}} + \gamma P_{\text{loss,norm}})$$

with default weights typically $\alpha = 0.25, \beta = 0.15, \gamma = 0.15$.

Tuned QERS: Incorporates additional system constraints such as CPU load, energy draw, key size, and signal quality (RSSI).

$$\text{QERS}_\text{tuned} = MS - (\alpha L_{\text{norm}} + \beta O_{\text{norm}} + \gamma P_{\text{loss,norm}} + \delta C_{\text{norm}} + \zeta E_{\text{norm}} + \eta K_{\text{norm}}) + \epsilon R_{\text{norm}}$$

with the sum of cost weights equal to 1 and RSSI treated as a positive benefit ($\epsilon = 0.10$ in the reference experimental setup).

Fusion QERS: Decomposes the assessment into separate performance penalties $P$ and security benefits $S$, then combines them in a parametrically balanced score: $$P = \sum_{i \in \{L, J, P_{\text{loss}}, E, C\}} w_i C_i^\text{norm}$$

$$S = \sum_{j \in \{K, R, P_r, Co\}} w_j B_j^\text{norm}$$

$$\text{QERS}_\text{fusion} = \alpha (MS - P) + \beta S, \quad \alpha+\beta=1$$

with default split $\alpha = \beta = 0.5$ (Rassekhnia, 19 Jan 2026, Rassekhnia, 19 Jan 2026).

5. Post-Quantum Cryptography Integration

QERS directly supports resource and security impact analysis across diverse PQC algorithms. In the referenced experiments, the following schemes are prominent:

• Kyber512 (KEM for key exchange): Public key (800 bytes) plus ciphertext (768 bytes), yielding $K_{\text{raw}} \approx 1568$ bytes.
• Dilithium2 (Signature): Signature size (approx. 2420 bytes for two LMS levels).

The raw sizes are normalized for aggregation, with the proven resistance level ($P_r$) treated as a maximal value (100) for all PQC runs. Key exchange and authentication overheads are empirically measured and factored into the cryptographic overhead and CPU normalization terms. Other PQC candidates (Falcon, SPHINCS+, NTRU) are similarly evaluated within the general QERS schema (Rassekhnia, 19 Jan 2026, Rassekhnia, 19 Jan 2026).

6. Experimental Findings and Trade-Off Analysis

Empirical results reveal nuanced trade-offs between evaluated protocols and algorithms. For MQTT, HTTP, and HTTPS over PQC:

Scenario	Protocol	QERS_basic	QERS_tuned	QERS_fusion
Close-range	MQTT	61.39	60.76	50.87
	HTTP	25.44	24.13	49.97
	HTTPS	11.06	11.67	54.65
Far-range	MQTT	60.44	59.77	50.87
	HTTP	24.22	22.92	50.09
	HTTPS	10.75	11.15	54.69

Key observations:

• MQTT yields the highest Basic/Tuned QERS due to low handshake cost and minimal latency, suitable for unconstrained or pre-authenticated environments, but does not offer built-in authentication.
• HTTPS incurs the most severe performance penalty under PQC (lowest Basic/Tuned scores) but attains the highest Fusion QERS, a direct result of rewarded cryptographic strength and integrated authentication.
• Fusion QERS exhibits reduced variability compared to Basic/Tuned scores, suggesting its suitability as a robust composite readiness indicator.
• Across algorithm comparisons (Dilithium, NTRU, Kyber, SPHINCS+, Falcon), Dilithium and NTRU score highest on QERS_fusion due to their moderate key size and stable execution, while Kyber and SPHINCS+ demonstrate reduced resilience under increased packet loss or lowered RSSI (Rassekhnia, 19 Jan 2026).

7. Applications: Protocol Selection and Migration Planning

QERS is directly operationalized for migration planning and protocol selection in PQC-enabled environments:

• For latency- and energy-sensitive deployments (battery-powered IoT sensors), protocols with high Basic/Tuned QERS (MQTT+PQC) are preferable if authentication can be handled externally.
• For moderate security, HTTP with PQC suffices when certificate management overhead must be avoided, at the cost of some resilience.
• For critical infrastructure requiring both confidentiality and authentication (e.g., IIoT control, remote updates), HTTPS with PQC, despite lower efficiency scores, is optimal as indicated by its Fusion QERS.
• QERS thresholds (e.g., Fusion QERS ≥ 50 for "Moderate readiness") provide actionable targets for field deployment readiness, guidance on required device upgrades, and benchmarking of alternative PQC parameterizations (such as Kyber512 versus Kyber768).
• Fusion score weights ($\alpha, \beta$) are tunable, allowing organizations to emphasize performance or security as dictated by their risk profile or operational needs (Rassekhnia, 19 Jan 2026, Rassekhnia, 19 Jan 2026).

8. Extension to General PQC and Comparative Assessment

While QERS was experimentally validated on classic PQC candidates and established communication protocols, the same paradigm is applicable to new families of quantum-resistant schemes and applications:

• For schemes like Exact Homomorphic Encryption (EHE), the QERS metric aligns naturally with bit-security estimates derived from hardness against known classical and quantum attack models. In such a context,

$$QERS(\text{EHE}) := \min\{\log_2(T_\text{XL}), \log_2(T_\text{ICRP}), \log_2(T_\text{deNC}), \log_2(T_\text{Grover})\}$$

where the parameters ($k, w, d, l, \{h_i\}$) are chosen to ensure post-quantum (≥128 bits) or hyper-quantum (≥1024 bits) resilience standards (Su et al., 2024).

This approach generalizes: for any post-quantum scheme $S$, QERS can be explicitly defined in terms of the lowest bit-security among all relevant attack surfaces, allowing for direct, reproducible comparison across otherwise incommensurable cryptographic frameworks.

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References:

(Rassekhnia, 19 Jan 2026): Quantum Encryption Resilience Score (QERS) for MQTT, HTTP, and HTTPS under Post-Quantum Cryptography in Computer, IoT, and IIoT Systems (Rassekhnia, 19 Jan 2026): QERS: Quantum Encryption Resilience Score for Post-Quantum Cryptography in Computer, IoT, and IIoT Systems (Su et al., 2024): Exact Homomorphic Encryption