A Comparative Performance and Scalability Analysis of Blockchain Anchoring Designs for Shamir’s Secret Sharing-Based Private Key Recovery

Private-key loss can permanently prevent access to blockchain-based assets, motivating recovery mechanisms that avoid retaining an entire key at a single location. Shamir’s Secret Sharing (SSS) distributes a secret across multiple shares, but off-chain shares require a verifiable integrity reference. This paper compares two blockchain anchoring designs under controlled inputs: Per-Share anchoring, which records one hash per share, and Merkle Root Anchoring, which commits the complete share set through a single root. Seven share settings (n = 5, 10, 20, 50, 100, 500, and 1000) were evaluated with k = ⌊n/2⌋ + 1 and 30 paired datasets per setting in a Hardhat local Ethereum environment. The evaluation consisted of 420 main runs, 420 counterbalanced recovery runs, and 510 runs of a paper-guided Pedin baseline. At n = 1000, the mean cumulative anchoring gas decreased from 47,479,746.8 for Per-Share to 46,538.8 for Merkle Root Anchoring, a 99.90% reduction, while the transaction count decreased from 1000 to 1. Merkle Root Anchoring achieved lower mean recovery times across all settings; however, the paired 95% confidence interval excluded zero only at n = 20, 50, 100, and 500. At n = 1000, mean recovery times converged to 459.29 ms for Per-Share and 453.74 ms for Merkle Root Anchoring. These results show that Merkle Root Anchoring substantially improves on-chain scalability, but the resulting savings do not translate proportionally into end-to-end recovery latency because the dominant latency source shifts from repeated blockchain queries to Merkle-proof verification.