Social Cyber Vulnerability Index (SCVI)

• SCVI is a quantitative metric that integrates social and cyber dimensions to assess multi-level human-centric risks.
• It employs rigorous methods including convex combinations, contingency analysis, and network diffusion models to derive robust vulnerability scores.
• Empirical validation shows SCVI’s effectiveness in informing targeted digital literacy campaigns, adaptive security controls, and policy interventions.

The Social Cyber Vulnerability Index (SCVI) is a multifaceted, quantitative metric designed to assess and integrate social and cyber dimensions of vulnerability in the context of human-centered cyber risk, social engineering, attack propagation, and system-level susceptibility to social-cyber threats. Developed across distinct lines of research, SCVI encapsulates both individual and systemic risks, deriving its structure from behavioral sciences, psychometrics, attack modeling, contingency analysis, and network science (Mitra et al., 24 Mar 2025, Rogers et al., 2023, Pan et al., 2020, Papatsaroucha et al., 2021).

1. Conceptual Foundations

SCVI emerged as a response to the inadequacy of purely technical or social indices to meaningfully quantify socio-technical risk posed by adversaries exploiting both human and infrastructural weaknesses. It explicitly bridges individual-level factors (awareness, behavior, psychological traits), attack-level characteristics (frequency, consequence, sophistication), and system-level inferability (data structure, susceptibility to inference, coupled network cascades) (Mitra et al., 24 Mar 2025, Rogers et al., 2023). Unlike traditional risk-scoring frameworks (CVSS, SVI), SCVI is operationalized for social cyber phenomena, including social engineering, disinformation diffusion, and mixed human–cyber-physical attacks (Pan et al., 2020).

2. Mathematical Formulation and Index Structure

2.1 Individual-Level SCVI

The individual-centric SCVI is defined as a convex combination of the Individual Vulnerability Index (IVI) and Attack Severity Index (ASI):

$$\mathrm{SCVI}_{i,k} = \alpha \,\mathrm{IVI}_{i,k} + \beta\, \mathrm{ASI}_{i,k}; \quad \alpha + \beta = 1,\;\alpha,\beta \in [0,1]$$

• $\mathrm{IVI}_{i,k}$: Aggregates subfactors of awareness (+ knowledge), risky & secure behaviors, credulity & impulsivity, past encounters & responses. Each component is encoded in [0,5] based on survey instruments (e.g., Likert scale) and/or behavioral proxies.
• $\mathrm{ASI}_{i,k}$: Captures attack-centric attributes—frequency (attempted/actual), consequence (financial, psychological, safety), and sophistication (credibility, SE technique), again normalized to [0,5].
• Weights $w_A, w_B, w_P, w_E$ (for IVI) and $w_F, w_C, w_S$ (for ASI) are derived from expert judgment or Dirichlet sampling, enabling robustness checks via Monte Carlo analysis (Mitra et al., 24 Mar 2025).

2.2 System-Level SCVI (Contingency Inference)

For datasets and operational workflows where vulnerability arises via inferability from structured records, SCVI is computed by decomposing contingency-table data with orthogonalized log-linear analysis (Rogers et al., 2023):

1. Model cell counts via $\log m_i = \sum_{r} \theta_r f_r(i)$, or in matrix form $\log m = X \alpha$.
2. Orthogonalize the design matrix $X$ to obtain $\bar X$, partitioned by attribute subset.
3. For each subset $c$, compute component Pearson chi-square $\mathrm{IVI}_{i,k}$0 and define:
   • Vulnerability index $\mathrm{IVI}_{i,k}$1
   • Salience $\mathrm{IVI}_{i,k}$2 (fraction of log-variance explained)
4. Aggregate over subsets $\mathrm{IVI}_{i,k}$3 with weights $\mathrm{IVI}_{i,k}$4: $\mathrm{IVI}_{i,k}$5 Weight schemes may be uniform, size-penalized, or risk-driven. High SCVI reflects high structural non-uniformity (identity attributes are inferable), presenting significant social engineering risk.

2.3 Networked and Interdependent SCVI

In cyber-physical or networked domains (e.g., social-cyber-physical smart grids), SCVI formalizes system-wide vulnerability using models of misinformation diffusion and subsequent infrastructural impact (Pan et al., 2020):

• Model the social ($\mathrm{IVI}_{i,k}$6) and power ($\mathrm{IVI}_{i,k}$7) networks, and map user–load correspondences.
• Propagate attacks via Independent Cascade (IC) model; compute influence spread $\mathrm{IVI}_{i,k}$8 for seeds $\mathrm{IVI}_{i,k}$9.
• Simulate cascade/failure using DC power-flow, iteratively removing overloaded lines and tracking failed loads.
• Define $\mathrm{ASI}_{i,k}$0 as the expected maximum impact from the most damaging attack adhering to a seed budget: $\mathrm{ASI}_{i,k}$1 with weights for information diffusion, physical damage, and resilience penalties.

3. Feature Dimensions and Data Modalities

SCVI’s constituent variables are directly mapped from survey-scale data, psychometric inventories, text mining outputs, and system logs. Key domains:

• Personal: Personality (Big Five, Dark Triad), cognitive processing style, trust propensity, decision-making metrics, demographics (Papatsaroucha et al., 2021, Mitra et al., 24 Mar 2025).
• Social: Exposure, susceptibility to Cialdini’s persuasion principles (via STPS), social norm perception, insider propensity.
• Cultural: Hofstede dimensions (PDI, IDV, UAI, MAS, LTO), subculture indices.
• Behavioral: Security intention scales (SeBIS), past SE training results, emotional state (PANAS), workload and time pressure.
• Text/output modalities: Survey response encoding, LIWC/NLP-derived features from user-generated reports, statistical mapping from operational event logs (Mitra et al., 24 Mar 2025).

Extensive normalization (min–max or z-score to [0,1] or [0,5]) is applied for cross-domain aggregation.

4. Computational Workflow and Sensitivity

Computation proceeds in a modular, survey-drill–analysis-pipeline, exemplified in the following steps (Papatsaroucha et al., 2021, Mitra et al., 24 Mar 2025):

1. Data Acquisition: Administer psychometrics, log cyber-drill outcomes, extract system/statistical features.
2. Normalization and Scoring: Map raw results to normalized sub-scores per vectorized domain.
3. Weight Selection: Calibrate or sample weights; conduct robustness analysis via Dirichlet and uniform distributions.
4. SCVI Aggregation: Compose category or subset scores using weighted sums.
5. Interpretation: Map SCVI to low/moderate/high risk bands; flag entities (individuals, records, nodes) exceeding thresholds for intervention.
6. Continuous Update: Re-assess post-training, after simulated attacks, or periodically as behavioral or structural conditions change.

Sensitivity is quantifiable via analytic gradients—partial derivatives of SCVI with respect to each weight reveal which inputs most strongly influence the aggregated index (Mitra et al., 24 Mar 2025).

5. Comparative Evaluation and Empirical Findings

Empirical validation demonstrates SCVI’s ability to capture nuanced socio-cyber risk not recognized by baseline indices:

• Comparative analysis with CVSS and SVI at the population subgroup level shows only weak/moderate correlation; SCVI reveals disparities tied to age, race/ethnicity, and region overlooked by legacy schemes (Mitra et al., 24 Mar 2025).
• Monte Carlo variability analysis confirms robustness to weight selection and feature uncertainty.
• In real-world datasets, SCVI identifies high-risk segments (18–24, Hispanic respondents, select US states with data sparsity), and is actionable for targeted digital-literacy interventions and policy resource allocation.

Applications encompass real-time alerting (e.g., dialog monitoring using $\mathrm{ASI}_{i,k}$2 projections (Rogers et al., 2023)), data de-personalization by limiting inferable attributes, detection of SES-dependent risk, and optimization of protective controls in cyber-physical systems.

6. Extensions: Social Engineering, Data Sanitization, and Networked Cascades

Technical advances in SCVI encode both detection and mitigation:

• Dialog Monitoring: Real-time recomputation of $\mathrm{ASI}_{i,k}$3 triggers operator alerts when identity queries become overtly inferable (Rogers et al., 2023).
• Data De-personalization: Quantitative reduction of high-salience interactions in released datasets, via adjustment of marginal/interacting cell counts to reduce $\mathrm{ASI}_{i,k}$4 and $\mathrm{ASI}_{i,k}$5.
• Smart Grid Defense: Optimization-based strategies (Greedy Social Attack, Social-Power Attack) select critical nodes for defense or misinformation limitation to minimize SCVI in coupled social-cyber infrastructure (Pan et al., 2020).
• Continuous Assessment: Drill-and-update pipelines (CHEAT/DOGANA) maintain organizational SCVI as part of cyber-hygiene remediation (Papatsaroucha et al., 2021).

7. Operational and Policy Implications

SCVI underpins actionable workflows for organizations, policymakers, and platform operators:

• Demographic-specific digital-literacy campaigns are substantiated by empirical SCVI mapping (Mitra et al., 24 Mar 2025).
• Platform-level interventions may embed real-time LIWC-inspired feedback to flag manipulative or high-sophistication scam content.
• System administrators may mandate periodic SCVI re-evaluation, triggering personalized training modules if individual/organizational SCVI rises.
• Technical controls (data sanitization, network hardening, or real-time dialog escalation) are naturally steered by SCVI output.

The SCVI thus constitutes a unified, tunable, and empirically robust metric for social-cyber risk quantification, integrating diverse assessment paradigms into a single operational framework (Mitra et al., 24 Mar 2025, Rogers et al., 2023, Pan et al., 2020, Papatsaroucha et al., 2021).