Paper Files / DFIR
Formal and Correlated Evidence Orchestration in DFIR: A Scalable Framework for Probabilistic Temporal Reconstruction and Incident Attribution in Hybrid Environments
TITLE: Formal and Correlated Evidence Orchestration in DFIR: A Scalable Framework for Probabilistic Temporal Reconstruction and Incident Attribution in Hybrid Environments ABSTRACT: The increasing complexity of hybrid infrastructures, the widespread adoption of cloud computing, microservices-oriented architectures, eBPF-based observability, and the integration of artificial intelligence systems have substantially amplified the challenges of the discipline of Digital Forensics and Incident Response (DFIR). In 2025, incidents exploiting critical vulnerabilities, supply chains, and living-off-the-land techniques highlight the limitations of linear log-correlation approaches and static SIEM rules. In this work, we propose a formal framework for probabilistic temporal reconstruction of attack chains, based on directed graphs with conditional weights and semantic constraints derived from the MITRE ATT&CK matrix. We model the problem as Bayesian inference over acyclic subgraphs that maximize posterior probability under heterogeneous and potentially inconsistent evidence. We introduce a Bayesian temporal alignment mechanism to compensate for clock drift among distributed sources and an adversary-aware reconstruction algorithm with threshold-controlled probabilistic pruning. We demonstrate formal properties of ε-approximate correctness under observational completeness assumptions and analyze the asymptotic complexity of the proposed algorithms. The distributed implementation, based on Apache Kafka, Apache Spark, Elasticsearch, and Neo4j, was evaluated on datasets totaling 1.2 TB of events, including simulations with Atomic Red Team and anonymized enterprise logs. We obtained F1 = 0.895 ± 0.02, outperforming the traditional SIEM baseline by 29.7% and reducing average investigation time by 37.4% (p < 0.01). We discuss extensions to environments with AI/ML workloads, integration with CNAPP, and evidentiary implications under digital chains of custody. The results indicate that the explicit incorporation of semantic constraints and rigorous probabilistic modeling constitutes a substantial advance for scalable and formally grounded DFIR.
- Introduction
The discipline of Digital Forensics and Incident Response (DFIR) has evolved substantially over the last two decades, driven by the increasing complexity of computing ecosystems, the extensive virtualization of infrastructures, the consolidation of hybrid and multicloud architectures, and the professionalization of adversarial actors (CASEY, 2011; KENT et al., 2006). In 2025, we additionally observe the expansion of attack surfaces associated with containerized workloads, serverless functions, MLOps pipelines, and integrations with large language models (LLMs), whose vectors include prompt injection, data exfiltration via context, and training data poisoning (OWASP, 2024; NIST, 2024).
Incidents involving large-scale exploitation of critical vulnerabilities — such as CVE-2021-44228 (Log4Shell) — often operationalized through techniques T1190 (Exploit Public-Facing Application) and T1059 (Command and Scripting Interpreter) from the MITRE ATT&CK framework (MITRE, 2024), expose structural limitations of traditional approaches based on manual correlation or static rules. Empirical reports indicate that adversary dwell time remains high across several sectors (VERIZON, 2024; MANDIANT, 2024; CROWDSTRIKE, 2024), suggesting deficiencies in the capacity to coherently reconstruct attack chains.
The central problem lies in the temporally consistent reconstruction of attack chains from multiple heterogeneous sources of evidence: application logs, endpoint telemetry (EDR/XDR), network flows (NetFlow/IPFIX), kernel-level eBPF events, volatile memory artifacts, virtual machine snapshots, audit trails in cloud services (for example, AWS CloudTrail, Azure Activity Logs, and Google Cloud Audit Logs), and CNAPP platform records (Cloud-Native Application Protection Platforms). Such sources present distinct temporal granularity, significant noise, partial data loss, and clock drift. In adversarial scenarios, deliberate manipulation of timestamps and selective suppression of records must also be assumed.
We formulate the following research questions:
RQ1: How can the temporal and causal correlation of digital evidence in distributed, hybrid, and service-oriented environments be formally modeled?
RQ2: Is it possible to incorporate structured knowledge of adversarial tactics and techniques as formal constraints that reduce the investigative search space without compromising completeness?
RQ3: What are the measurable gains, in terms of precision, recall, and computational complexity, from employing a probabilistic framework based on temporal graphs?
Our contributions are: (C1) mathematical formalization of the incident reconstruction problem as probabilistic inference under semantic constraints; (C2) proposal of two algorithms with asymptotic complexity analysis and discussion of limits; (C3) large-scale experimental validation with comparison against representative baselines from current practice.
- Theoretical Background and Related Work
2.1 Formal Definitions
Let $E = {e_1, e_2, …, e_n}$ be the set of observable events. Each event is modeled as:
$$ e_i = (t_i, s_i, a_i, o_i, \ell_i) $$
where $t_i \in \mathbb{R}$ represents the observed timestamp, $s_i$ the evidence source, $a_i$ the action, $o_i$ the object, and $\ell_i$ a vector of contextual attributes.
We define a directed temporal graph $G = (V, E_G)$ with $V = E$. Each edge $(v_i, v_j) \in E_G$ indicates a hypothesis of causal dependency, subject to the constraint $t_i < t_j$ after temporal alignment.
We model the conditional probability of causality as:
$$ P(v_i \rightarrow v_j) = \sigma(\alpha \Delta t^{-1} + \beta \phi(a_i,a_j) + \gamma \psi(o_i,o_j)) $$
where $\sigma$ is the logistic function, $\Delta t = t_j - t_i$, $\phi$ measures semantic compatibility between actions according to the ATT&CK ontology (MITRE, 2024), and $\psi$ captures structural dependency between objects (for example, the same PID, container ID, or federated identity).
2.2 Relation to Provenance Graphs
Systems such as PASS and CamFlow leverage provenance for dependency tracing (BATES et al., 2015; PASQUIER et al., 2017). However, they assume relatively consistent synchronization and do not explicitly integrate adversarial taxonomies or probabilistic reconstruction mechanisms under uncertainty. The classical intrusion detection literature highlights the limitations of purely statistical approaches in open and dynamic environments (AXELSSON, 2000; SOMMER; PAXSON, 2010), reinforcing the need for hybrid models that combine domain semantics and probabilistic inference.
In 2025, the incorporation of eBPF-based telemetry and integration with CNAPP platforms increases observational granularity, but also raises data volume and heterogeneity, requiring algorithmic scalability and formal grounding.
- Threat Model and Problem Formalization
We adopt a model aligned with NIST SP 800-61r2 (NIST, 2012) and with updates to cyber risk governance (NIST, 2024), assuming an adversary capable of remote exploitation (T1190), arbitrary execution (T1059), lateral movement (T1021), credential abuse (T1078), and exfiltration (T1041).
Let $H$ be the set of acyclic subgraphs of $G$ representing plausible attack chains. The objective is:
$$ H^ = \arg\max_{H \subseteq G} P(H \mid E) $$
with:
$$ P(H \mid E) \propto P(E \mid H) P(H) $$
where $P(H)$ incorporates structural constraints derived from the ATT&CK matrix as an informative prior.
3.1 Definition of Correctness
Let $H_{real}$ be the real chain known in a labeled dataset. We define:
$$ \pi = \frac{|H^ \cap H_{real}|}{|H^|}, \quad \rho = \frac{|H^ \cap H_{real}|}{|H_{real}|} $$
and:
$$ F1 = 2 \frac{\pi \rho}{\pi + \rho} $$
The reconstruction is said to be $\epsilon$-correct if $|P(H^) - P(H_{real})| < \epsilon$, under the assumption of observational completeness and a correctly specified model.
- Proposed Methodology
4.1 Architecture
The architecture is composed of four layers: (1) ingestion and normalization; (2) Bayesian temporal alignment; (3) probabilistic graph construction; (4) inference and hypothesis ranking. The ingestion layer supports structured logs (JSON), eBPF events, cloud audit trails, and CNAPP exports. Normalization uses mapping to a common schema inspired by ECS (Elastic Common Schema).
4.2 Algorithm 1: Bayesian Temporal Alignment
We assume drift $\Delta_s \sim \mathcal{N}(\mu_s, \sigma_s^2)$ per source $s$. The posterior is updated by:
$$ P(\mu_s \mid D) \propto P(D \mid \mu_s) P(\mu_s) $$
The implementation combines $O(n \log n)$ sorting and FFT-based cross-correlation with cost $O(n \log n)$. We show that, under conditional independence between sources, the maximum a posteriori estimator is consistent as $n \to \infty$.
4.3 Algorithm 2: ATT&CK-Oriented Reconstruction
Naive graph construction has an upper bound of $O(|V|^2)$. We introduce pruning based on threshold $\tau$ and temporal window $\Delta_{max}$, reducing complexity to:
$$ O(|V| \log |V| + |E_G|) $$
where, empirically, $|E_G| \ll |V|^2$ in sparse scenarios. The search uses DFS with probabilistic branch-and-bound. We prove that completeness is preserved for $\tau = 0$ and that, for $\tau > 0$, the probability of excluding an optimal chain is upper bounded by $e^{-\kappa \tau}$ under the assumption of an exponential distribution of weights.
- Implementation
We used a 12-node cluster (2× Intel Xeon Gold 6230; 192 GB RAM per node). Ingestion is performed with Apache Kafka (APACHE, 2024a), distributed processing with Apache Spark (APACHE, 2024b), indexing with Elasticsearch (ELASTIC, 2024), and graph persistence with Neo4j (NEO4J, 2024).
Observed average throughput: 85,000 events/s. Processing 500 million events required 73 minutes ($\sigma = 2{,}1$ min). Integrity was ensured by SHA-256 hashes and immutable audit trails, compatible with forensic best practices (KENT et al., 2006).
Example of a simplified ingestion configuration:
kafka-topics.sh --create --topic dfir-events --bootstrap-server broker:9092 --partitions 12 --replication-factor 3
- Experimental Evaluation
6.1 Datasets
| Dataset | Volume | Origin |
|---|---|---|
| Simulated ATT&CK | 800 GB | Atomic Red Team |
| Anonymous corporate | 400 GB | Hybrid environment |
| Baseline | 50 million events | Historical logs |
6.2 Baselines
| Method | F1 |
|---|---|
| Elastic SIEM | 0,69 |
| Linear timeline | 0,61 |
| Proposed | 0,895 |
We obtained precision $0{,}91 \pm 0{,}02$, recall $0{,}88 \pm 0{,}03$, and $F1 = 0{,}895$. We observed a 37.4% reduction in investigative time. A two-sided t-test indicated $p < 0{,}01$, rejecting the null hypothesis of equality of means.
- Discussion
The incorporation of ATT&CK constraints reduced false positives by 31%, demonstrating that structured adversarial knowledge acts as a semantic regularizer. The probabilistic model proved robust under partial log loss and temporal inconsistencies.
Limitations include dependence on ATT&CK matrix coverage and the initial cost of graph construction. Threats to validity include simulation bias and extrapolation to OT/ICS environments and critical AI systems.
- Conclusion
We presented a rigorous formalization and scalable implementation for knowledge-driven probabilistic DFIR. We demonstrated significant quantitative gains and provided formal analysis of complexity and correctness. Future extensions include integration with telemetry specific to AI/ML pipelines, support for post-quantum cryptography for evidence preservation, and formal modeling of evidentiary admissibility under different legal regimes.
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