A Two-Component Distributed Data Storage Scheme

We propose M4, a keyed two-component matrix decomposition for split storage of digital dataover Zq. The scheme transforms an input matrix A ∈ Zm×nq into a low-rank spectral componentand a key-masked, permuted modular residue. Reconstruction requires access to both componentstogether with a secret key. At the mathematical level, M4 applies a deterministic low-rank transformto obtain an approximation B of rank at most k and computes the residue R = (A−B) mod q. Thespectral component share encodes the low-rank structure, while the residue share stores a maskedand pseudorandomly permuted version of R derived from a KDF and PRNG keyed by a mastersecret. This enables split storage of the two shares across independent security domains, targetingdata-at-rest scenarios rather than online authenticated encryption.We formalize the syntax, threat model, security goals and non-goals of the construction, anddiscuss leakage properties of both shares as a function of the rank parameter k. An experimentalevaluation on synthetic and random data confirms exact reconstruction, near-uniform statistics ofthe residue share, strong visual scrambling of the stored spectral component representation, andplausible scaling behavior of the Protect/Recover algorithms. The scheme is designed to serve as acandidate building block for hardware-accelerated secure NAS appliances and other high-assurancearchival storage systems. For questions or to request the Python proof-of-concept, contact me at: [email protected]