Thesis

Homological Cryptography (HC) is a new cryptographic paradigm where topological invariants, such as nontrivial cycles in simplicial complexes, replace traditional algebraic objects as the foundation of security. Instead of relying on number theory or lattices, HC leverages the computational hardness of problems like Cycle Non-Triviality (CNT), Short Homology Representatives, and Noisy Homology Equivalence, offering native post-quantum resistance, efficient homomorphic operations, and topology-driven threshold protocols for next-generation secure systems.