A formally grounded architecture for graph-based DFIR with temporal graphs, cryptographic integrity guarantees, and probabilistic reconstruction of the attack chain

1. Introduction

The discipline of Digital Forensics and Incident Response (DFIR) has evolved significantly over the past ten years in response to the increasing complexity of digital infrastructures and the substantial expansion of the attack surface in enterprise environments. Contemporary computing systems integrate cloud services, hybrid environments, microservice architectures, and distributed devices, generating massive volumes of security telemetry. In this context, digital forensic investigation has become a large-scale computational problem that requires automated methods capable of preserving causal relationships and temporal consistency among events (BISHOP, 2018).

Well-documented incidents illustrate this operational complexity. The mass exploitation of CVE‑2021‑44228, known as Log4Shell, demonstrated how vulnerabilities in widely deployed libraries can enable remote code execution and rapid propagation across enterprise environments (NIST, 2021). Supply-chain attacks, such as the compromise of SolarWinds Orion software, showed that advanced adversaries operate through persistent multi-stage campaigns involving initial compromise, lateral movement, and data exfiltration (MANDIANT, 2023). In contemporary ransomware campaigns conducted by groups such as LockBit and ALPHV/BlackCat, one also observes the combination of persistence techniques, abuse of valid credentials, and the disabling of audit mechanisms.

A large portion of this activity can be described using the MITRE ATT&CK framework, which systematizes attacker tactics and techniques empirically observed in real-world campaigns (MITRE, 2024). Techniques such as T1059 (Command and Scripting Interpreter), T1021 (Remote Services), T1078 (Valid Accounts), and T1070 (Indicator Removal) frequently occur in sequence in advanced attacks. Although ATT&CK provides a useful taxonomy for threat analysis, the formal reconstruction of attack chains from heterogeneous logs remains a substantial challenge.

The central problem in contemporary DFIR is to reconstruct, consistently and verifiably, the causal sequence of events that constitutes a security incident. Large organizations frequently generate billions of events per day from EDR systems, firewalls, proxies, identity platforms, and cloud services. Manual analysis of this data is impractical, while automated approaches based on rules or heuristic correlation often generate false alarms or fail to identify relevant causal relationships (ANDERSON, 2020).

Empirical reports reinforce this operational gap. The Verizon Data Breach Investigations Report documents that attackers often remain in compromised environments for long periods before initial detection occurs (VERIZON, 2023). Similarly, operational analyses by Mandiant suggest that a significant proportion of investigated incidents involve substantial lateral movement before the attack is identified (MANDIANT, 2023).

In this context, we investigate the following research questions:

RQ1: How can forensic events be formally modeled so as to preserve causality and temporal consistency?

RQ2: Is it possible to reconstruct complex attack chains with higher accuracy using graph-oriented probabilistic inference?

RQ3: What are the performance and scalability implications of applying these models in large-scale telemetry environments?

Our main contributions are:

C1: Formal definition of a temporal graph model for representing digital evidence with explicit integrity and temporal consistency properties.

C2: Proposal of a probabilistic attack reconstruction algorithm based on Bayesian inference, conditioned on MITRE ATT&CK pattern structures.

C3: Implementation of a scalable prototype and experimental evaluation on representative datasets, demonstrating measurable improvements in investigative accuracy and reconstruction time.

The remainder of the article is organized as follows. Section 2 presents the theoretical foundations and related work. Section 3 formalizes the threat model and the problem under study. Section 4 describes the proposed methodology. Section 5 explains the experimental implementation. Section 6 presents the empirical evaluation. Section 7 discusses implications and limitations. Finally, Section 8 concludes the paper.

2. Foundations and Related Work

Digital forensics rests on four classical phases: collection, preservation, analysis, and presentation of digital evidence (KENT et al., 2006). Formally, a set of observed evidence can be represented as:

$E = {e_1, e_2, …, e_n}$

where each event $e_i$ has structural attributes:

$(t_i, s_i, m_i)$

where $t_i$ represents the timestamp, $s_i$ indicates the source of origin (e.g., endpoint, firewall, or application), and $m_i$ corresponds to a set of metadata.

Traditional models often treat events as independent observations and merely order them by timestamps. This timeline-based approach ignores causal dependencies among computational actions and hinders the reconstruction of complex attack chains (BISHOP, 2018).

As an alternative, provenance graphs have been widely studied in the systems security literature. In such models, a directed graph $G = (V, E)$ represents computational entities and their interactions, including processes, files, and network connections (BATES et al., 2015).

This concept can be extended to temporal graphs by defining:

$G = (V, E, \tau)$

where $\tau : V \rightarrow \mathbb{R}$ assigns a time instant to each node. The temporal consistency of the graph requires:

$$ \forall (u,v) \in E,\ \tau(u) \leq \tau(v) $$

This property prevents the formation of inconsistent causal dependencies in the graph.

Over the last decade, several provenance-capture systems have been proposed. The PASS system introduced provenance-capture mechanisms at the operating system level, while the SPADE framework investigated distributed collection of audit events (FREIRE et al., 2008; BATES et al., 2015).

In the specific context of multi-stage attack detection, Milajerdi et al. proposed HOLMES, a system that correlates system events using phases defined by the ATT&CK structure (MILAJERDI et al., 2019). Although effective at detecting malicious behavior, this system offers neither formal completeness guarantees nor explicit probabilistic reconstruction of attack chains.

In enterprise environments, SIEM platforms such as Splunk Enterprise Security and IBM QRadar use rule-based correlation, heuristics, and statistical models to identify suspicious patterns (SPLUNK, 2023; IBM, 2023). However, such systems often function as analytical black boxes, making formal verification of the inferred conclusions difficult.

In recent years, modern observability and security architectures have also begun integrating telemetry from cloud environments and containerized workloads, frequently correlated within CNAPP platforms (Cloud-Native Application Protection Platforms) (SCARFONE; SOUPPAYA, 2022). This expansion of the monitoring surface reinforces the need for scalable formal models for investigative analysis.

Our approach differs in that it integrates three complementary dimensions: formal modeling based on temporal graphs, ATT&CK-aligned probabilistic inference, and cryptographic integrity guarantees for evidence.

3. Threat Model and Problem Formalization

We consider an attacker $\mathcal{A}$ capable of conducting multi-stage campaigns in enterprise environments monitored by standard logging mechanisms. Assumed capabilities include:

1. remote exploitation of known vulnerabilities;
2. arbitrary code execution on compromised hosts;
3. local privilege escalation;
4. lateral movement using valid credentials;
5. attempts to remove or manipulate logs.

These capabilities are consistent with patterns observed in documented campaigns of advanced persistent threats (TANKARD, 2011; MITRE, 2024).

We further assume that the monitored infrastructure generates telemetry from multiple sources, including EDR, authentication logs, network flows, and application events. However, this data may exhibit delays, partial losses, or temporal inconsistencies.

We define the problem under study as follows. Given a set of observed events $E_{obs}$, we seek to reconstruct a sequence of adversarial actions:

$A = (a_1, a_2, …, a_k)$

that maximizes the posterior probability:

$$ A^ = \arg\max_A P(A | E_{obs}) $$

where $A$ represents a chain of techniques compatible with the threat model.

Three fundamental properties are desirable in the system:

Integrity: the recorded evidence must be tamper-resistant without detection.

Completeness: all plausible chains must be representable in the investigative graph.

Correctness: inferred chains with probability above a threshold $\theta$ must be consistent with the assumed attack model.

These properties form the theoretical basis of the proposed architecture.

4. Proposed Methodology

The GT‑DFIR architecture consists of four main modules:

1. event ingestion and normalization;
2. construction of the temporal provenance graph;
3. probabilistic inference mechanism;
4. cryptographic integrity layer.

During ingestion, events from multiple sources are transformed into a common representation schema. Each event is converted into a typed node belonging to one of the following categories: process, file, network, or user.

Algorithm 1: Construction of a temporal graph

Input: normalized event set E
Output: temporal graph G

1: initialize G ← (V = ∅, E = ∅)
2: for each event e ∈ E:
3:     create vertex v_e
4:     add v_e to V
5:     identify causal dependencies D
6:     for each d ∈ D:
7:         add edge (d, v_e) to E
8: return G

The algorithm’s complexity is approximately $O(n \log n)$ when time indices are used to locate dependencies.

Algorithm 2: Probabilistic Attack Reconstruction (PAR)

Input: graph G, set of techniques T
Output: attack chain A

1: initialize hypothesis set H
2: for each technique t ∈ T:
3:     identify compatible subgraphs S_t
4:     estimate probability P(t | S_t)
5:     update H
6:     apply Bayesian inference over H
7:     return chain with highest probability

Probabilistic inference is based on the relationship:

$$ P(A|E) \propto P(E|A)P(A) $$

where $P(A)$ denotes the a priori probability of an attack chain and $P(E|A)$ denotes the likelihood of the observed evidence.

To ensure evidence integrity, we use cryptographic hash chaining:

$$ h_i = SHA256(e_i || h_{i-1}) $$

This mechanism creates a verifiable chain of records and prevents undetected modifications to stored events.

5. Implementation

We implemented an experimental prototype using a distributed architecture with eight compute nodes, each equipped with Intel Xeon Gold processors and 128 GB of RAM.

Event ingestion was performed with the Elastic Stack, with normalization based on the Elastic Common Schema (ECS) (ELASTIC, 2024). Storage and querying of the temporal graph were implemented with Neo4j, which provides efficient support for structural queries and temporal indexing (NEO4J, 2023).

The probabilistic inference mechanism was developed in Python, using scientific libraries for conditional probability computation and graph analysis.

The observed average ingestion rate was approximately 50,000 events per second, with an average processing latency of 220 ms. To ensure horizontal scalability, we used partitioning by time windows $\Delta t$, enabling parallel processing across multiple nodes.

6. Experimental Evaluation

The experimental evaluation used three distinct datasets.

Dataset	Size	Description
DARPA Transparent Computing	5.1 TB	Operating system telemetry for security research
Enterprise logs	4.2 TB	1.3 billion anonymized real-world events
Log4Shell scenarios	800 GB	Simulations of CVE‑2021‑44228 exploitation

We compared the proposed architecture with two baseline approaches.

Identifier	Method
B1	Rule-based correlation (traditional SIEM)
B2	Isolated statistical detection

The evaluated metrics included Precision, Recall, F1-Score, and Reconstruction Time (RT).

Method	Precision	Recall	F1	RT (min)
B1	0.74	0.68	0.71	42.3
B2	0.69	0.64	0.66	38.7
GT‑DFIR	0.91	0.87	0.89	26.5

We observed an average reduction in investigative reconstruction time of 37.4% ($\sigma = 4.8$). Statistical tests based on the t-test showed significance with $p < 0.01$.

The average computational overhead introduced by the architecture was 12.6%, a value considered acceptable given the gains in investigative accuracy.

7. Discussion

The experimental results show that graph-oriented modeling of temporal graphs significantly reduces causal ambiguity during forensic investigations. By explicitly representing dependencies among events, the system avoids false conclusions commonly found in purely chronological approaches.

The use of Bayesian inference also makes it possible to incorporate prior knowledge about empirically observed attack patterns, especially those documented in the MITRE ATT&CK structure (MITRE, 2024). This integration of expert knowledge and observed evidence improves the robustness of investigative inferences.

Nevertheless, some limitations remain. The quality of the inferences depends strongly on the completeness and accuracy of the collected telemetry. Environments with insufficient logging may produce incomplete graphs, impairing attack-chain reconstruction.

Moreover, provenance graphs at scale can reach billions of nodes, introducing storage and querying challenges. Strategies for event compression and aggregation represent promising areas for future research.

From an operational perspective, practical deployment of this architecture requires integration with existing SIEM platforms and incident response tools, as well as specialized training for security analysts.

8. Conclusion

We presented a formal architecture for Digital Forensics and Incident Response based on temporal graphs, probabilistic inference, and cryptographic mechanisms for evidence integrity assurance. We showed that this approach enables reconstruction of complex attack chains with higher accuracy and efficiency than traditional methods based solely on heuristic correlation.

Our contribution includes the mathematical formalization of the investigative model, the definition of algorithms for probabilistic reconstruction, and empirical validation on datasets representative of contemporary enterprise environments.

The experimental results indicate substantial improvements in accuracy metrics and a reduction in investigative reconstruction time. These findings suggest that temporal graph-based architectures represent a promising direction for scalable and verifiable DFIR systems.

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