We present a novel secret sharing scheme based on Laurent series expansions that fundamentally extends Shamir’s Secret Sharing (SSS) for efficient key redistribution in blockchain-based multi-party computation systems. Our Laurent Series Secret Sharing (LSS) method exploits the algebraic structure of both the principal part (containing poles) and analytic part (holomorphic component) of Laurent series to enable seamless key refresh operations without requiring complete protocol restart. We provide comprehensive mathematical foundations, rigorous security proofs with formal reduction arguments, and detailed efficiency analysis demonstrating that LSS maintains identical security guarantees as SSS while achieving superior performance characteristics for dynamic key redistribution scenarios. Experimental validation confirms our theoretical predictions, showing comparable computational complexity to traditional approaches while providing enhanced operational flexibility for distributed key management in adversarial environments.
Shim et al. (Fri,) studied this question.