Paper 2026/195

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

Abstract

We present HyperFrog, a lattice-based Key Encapsulation Mechanism (KEM) targeting post-quantum security levels. The construction instantiates a variant of the Learning With Errors (LWE) problem in which the secret vector is derived from high-genus topological structures embedded in a three-dimensional grid. Unlike standard LWE schemes that draw secrets from uniform or Gaussian distributions, HyperFrog uses a topology-mining procedure to generate sparse binary secret keys corresponding to connected subgraphs with cyclomatic number (genus) >= 8, introducing geometric constraints while preserving combinatorial hardness. To achieve practical robustness, the scheme applies the Fujisaki-Okamoto (FO) transform, attaining IND-CCA2 security under standard assumptions. The reference implementation, internally codenamed "Topological Obsidian", includes a constant-time decoding routine based on branchless arithmetic to eliminate secret-dependent control flow during decryption and re-encryption. We provide benchmark results on an AMD Ryzen 9 5950X implementation using AVX2 vectorization for polynomial arithmetic, and demonstrate the integration of the KEM into a high-performance AES-256-GCM hybrid encryption pipeline.

Note: This report provides the complete specification and reference implementation of HyperFrog, an experimental post quantum Key Encapsulation Mechanism based on voxel topology and a topology mined LWE secret distribution. The document includes the full construction, correctness arguments, security rationale, benchmark methodology, constant time implementation notes, serialization format, and a Fujisaki Okamoto style CCA transform. Source code, test vectors, and implementation artifacts are released under the MIT license.