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

TL;DR

HyperFrog introduces a novel post-quantum KEM leveraging 3D voxel topology and high-genus structures to enhance security, with a focus on topological complexity and geometric constraints.

Contribution

It proposes a new lattice-based cryptographic scheme using topological structures as trapdoors, expanding the design space for post-quantum cryptography.

Findings

Provides a construction, parameterization, and serialization format.

Includes a reference implementation with self-tests and benchmarking.

Discusses security interactions with lattice and decoding attacks.

Abstract

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.