Lucas-PoST: A Secure, Efficient, and Robust Proof of Storage-Time Protocol Based on Lucas Sequences

Proof of Storage-Time (PoST) is the core verification mechanism for blockchain data storage, ensuring the integrity and continuous availability of data throughout the storage period. Although the current mainstream Compact Proofs of Storage-Time (cPoST) and Practical and Client-Friendly Proof of Storage-Time (ePoST) solutions have seen significant progress in engineering implementation, their security fundamentally relies on the algebraic structure assumptions underlying their verifiable delay function (VDF) components. In addition, if there are small-order elements that can be efficiently calculated in the underlying group structure, it will directly lead to the failure of the soundness properties of the VDF; thus, the entire PoST system will face systemic security risks. To address the above issues, we propose an innovative PoST protocol based on the modular Lucas sequence. By constructing a delay function through the modular Lucas sequence, the security condition is transferred from the strong security assumption to the weak security assumption, which enhances the security of the protocol: when the protocol encounters an algorithmic breakthrough that causes the modular square security assumption to fail, the soundness of the protocol can still be guaranteed. Secondly, we map all elements to the target $\lambda$-strong groups through homomorphic mapping technology, a domain input restriction mechanism, and a non-unique representation strategy of elements, effectively avoiding the security risks caused by small-order elements in the group structure. Compared with traditional protocols, our protocol achieves significant improvements in security and reliability, providing a more robust framework for decentralized storage and data verification.