A Systematic Review of Graph-Theoretic Approaches to Post-Quantum Cryptographic Protocols: Methods, Architectures, and Future Research Directions
Bibliographic record
Abstract
The rapid advancement of quantum computing poses a significant threat to classical cryptographic systems, necessitating the development of robust post-quantum cryptographic (PQC) protocols. Among emerging approaches, graph-theoretic techniques have gained prominence due to their computational hardness, structural flexibility, and applicability in designing secure cryptographic primitives. This paper presents a systematic review of graph-theoretic approaches to post-quantum cryptographic protocols, focusing on methods, architectures, and future research directions. The study analyzes recent developments from 2018 to 2025, examining how graph-based constructs such as expander graphs, isogeny graphs, lattice graphs, and combinatorial structures contribute to secure key exchange, encryption, and authentication mechanisms. Additionally, the integration of chaotic systems and generative artificial intelligence is explored to enhance entropy generation and adaptive security mechanisms. The review identifies key trends, including hybrid graph-chaotic models, optimization of graph traversal algorithms for cryptographic efficiency, and AI-assisted cryptanalysis resistance. Contributions of this work include a structured synthesis of 30 studies, identification of research gaps in scalability and standardization, and a comprehensive evaluation of graph-theoretic PQC within secure software engineering frameworks. The findings emphasize the potential of graph-based cryptography as a resilient paradigm in the quantum era while highlighting the need for further interdisciplinary research.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".