The HyperFrog Cryptosystem: High-Genus Voxel Topology as a Trapdoor for Post-Quantum KEMs

Computer Science > Cryptography and Security [Submitted on 6 Feb 2026] The HyperFrog Cryptosystem: High-Genus Voxel Topology as a Trapdoor for Post-Quantum KEMs Victor Duarte Melo HyperFrog is an experimental post-quantum Key Encapsulation Mechanism that explores a variant of the Learning With Errors (LWE) design space in which the secret is not sampled from an independent product distribution, but is deterministically derived from discrete topological structure. The scheme embeds a voxel grid in three dimensions and uses a topology mining procedure to search for connected subgraphs with prescribed complexity, measured by cyclomatic number (high genus). The resulting structure is encoded as a sparse binary secret vector, inducing strong geometric constraints on the secret distribution while retaining a large combinatorial search space. Encapsulation produces noisy linear relations over public parameters and derives the shared key via hashing; a Fujisaki-Okamoto style transform is used to target IND-CCA security in the random oracle model. We present the construction, parameterization, and serialization format, together with a reference implementation featuring self-tests and benchmarking on commodity CPUs. We also discuss how topology-derived secrets interact with known lattice and decoding attacks, and we outline open problems required for conservative parameter selection and for a full security analysis. HyperFrog is intended as a research vehicle rather than a production-ready KEM. Comments: Experimental post-quantum KEM using high-genus voxel topology. Includes full specification, code, benchmarks, and security discussion Subjects: Cryptography and Security (cs.CR); Quantum Physics (quant-ph) Cite as: arXiv:2603.23505 [cs.CR]   (or arXiv:2603.23505v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2603.23505 Focus to learn more Related DOI: https://doi.org/10.5281/zenodo.18502099 Focus to learn more Submission history From: Víctor Duarte [view email] [v1] Fri, 6 Feb 2026 12:48:01 UTC (1,938 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-03 Change to browse by: cs quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)