Matrix Cryptographic Tree: A Reversible, Structure-Preserving Cryptographic Primitive with Unified Zero-Knowledge Proofs

Abstract

This repository/dataset presents the Matrix Cryptographic Tree (MCT), a novel cryptographic primitive based on the special linear group SL(2, \mathbb{Z}). Unlike traditional hash-based Merkle Trees, MCT is fully reversible and structure-preserving, allowing for unique algebraic verification without information loss. The core of this research is the integration of Unified Zero-Knowledge Proofs (ZKP). MCT enables advanced privacy-preserving operations, such as proving data similarity (L1 norm distance), prefix/suffix matching, and existence proofs, all without revealing the underlying data.