A Leakage-Resistant Digital Inheritance Distribution Scheme Based on Sparse-Matrix Secret Sharing

With digital assets increasingly comprising a significant portion of personal wealth, the secure management and transfer of digital legacies have emerged as a pressing concern. Secret sharing offers a solution to this problem. However, distributing shares containing the unique private key for digital assets poses significant risks of theft or tampering, potentially leading to the illegal appropriation of user assets. This paper presents a leakage-resistant digital inheritance distribution scheme based on sparse-matrix secret sharing. It employs an efficient thresholding scheme that uses sparse matrices, achieving near-linear complexity for share reconstruction via a random striped matrix. Reconstruction time is significantly reduced compared to traditional polynomial interpolation methods. To address the realistic scenario where an asset owner holds multiple independent digital accounts, we propose a multi-account blinding and aggregation mechanism. This mechanism allows the dealer to establish isolated group keys for each account in a single round of communication, while preventing adversaries from linking different accounts to the same owner. A key-derivation and encrypted-transmission mechanism is then designed based on the aggregated group keys. Group keys are established by consensus among heirs, from which each heir derives a unique session key. Authenticated encryption ensures the confidentiality, integrity, and identity-bound transmission of shares. Through security proofs and experimental performance evaluation, it is demonstrated that the proposed scheme satisfies adaptive security requirements with the hash function H modeled as a random oracle, while all other cryptographic primitives (PRF, AES-GCM, HMAC) are assumed to be secure under standard computational assumptions.