Polynomial
Random degree-(t-1) polynomial f with f(0) = S. Share i = f(i). t points determine polynomial via Lagrange interpolation.
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Reconstruction
Given t shares, compute f(0) via Lagrange. O(t²) or O(t log² t) with FFT-based interpolation.
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Verifiable SSS
Add commitments so shareholders detect malicious dealer. Feldman VSS + Pedersen VSS.
Applications
Multi-signature wallets. HSM key backup. Threshold decryption. Distributed key generation.