Information-Theoretic Privacy for Long-Term Share Storage on Noisy Media

Many secret-sharing schemes often require permanent storage of shares in robust media. This includes threshold keys generated by DKG protocols and state fragments produced by oblivious databases using multiparty computation. These shares are stored on heterogeneous and uncontrolled devices, where they may persist for years or even decades under unknown conditions. Confidentiality based on computational encryption can be weakened by changes in hardware, cryptanalysis, or new quantum capabilities. In addition, storage hardware can accumulate bit-level corruption owing to retention errors, wear and drift. Many existing approaches handle only one side of the story. Information-theoretic secret sharing assumes symbol-perfect retrieval, whereas erasure-coded storage tolerates node loss or failure under internal noise and offers no confidentiality by itself. We present Robust Noise-aware Ramp Polar Codes (RobustNRPC), a storage construction designed for the long-term, decentralised retention of cryptographic shares. The system combines a linear ramp secret-sharing layer with a polar-based sanitisation layer reinforced by a key-dependent interleaver and syndrome-based coset mask. The mask hides the frozen bit structure of finite-length polar codes and forces adversarial corruption to appear symmetric, thereby avoiding the targeted noise vulnerabilities documented in previous studies. The interleaver hides the physical positions of the frozen bits. The sanitised symbols are then fed into a ramp scheme, preserving information-theoretic confidentiality even if the computational assumptions are degraded in the future. We conducted a theoretical analysis of confidentiality, integrity, and reliability, including an explicit reconstruction failure bound using the binary KL divergence. We implemented our protocol as a proof of concept and demonstrated reliable decoding with bit-error rates of up to \(5.4\%\) , burst corruption affecting up to \(14.1\%\) of payload bytes (with a soft-decision tail extending to 18– \(23\%\) ), and simultaneous corruption or erasure of multiple shares. Our results show that RobustNRPC is practical for noisy long-term storage in DKG/MPC deployments and large distributed archival systems.