Tatsuya Nakano
We introduce a reversible 2×2 matrix encoding for DNA sequences, the M¨obius-Compatible Transform (MCT), which maps each base to a pair of signed linear update operators whose product yields a final matrix from which the original sequence can be exactly recovered. To capture global structural properties, we further define an 8-dimensional structural signature vector. Combining matrix-level and signature-level deviations, we construct a hybrid distance metric that is biologically meaningful, mutation-stable, and fully linearizable. All matrix and signature components are projected into a finite field and committed using Pedersen commitments. We design an R1CS formulation that expresses the hybrid distance D using absolute-value decomposition and non-negativity constraints, enabling a zero-knowledge proof that D ≤ T without revealing any DNA information. We implement a complete end-to-end Python prototype integrating reversible encoding, commitment generation, R1CS verification, and large-scale distance evaluation. In a blind analysis of 10,000 randomly generated sequences, the system classifies individuals into high-, medium-, and low-similarity groups relative to a reference sequence without accessing any raw genomic data. Our results demonstrate a lightweight, algebraically structured alternative to MPC- and HE-based approaches for privacy-preserving genomics, providing a practical foundation for zero- knowledge genomic similarity proofs.