AWhat changed
Uniform random polynomial coefficients over a finite field make any k valid shares sufficient to recover a secret, while fewer shares have secret-independent distributions.
Scientific scope
Uniform random polynomial coefficients over a finite field make any k valid shares sufficient to recover a secret, while fewer shares have secret-independent distributions. The secret is encoded in a finite field, with distinct nonzero participant indices and independently uniform polynomial coefficients. Any k consistent shares reconstruct it; fewer than k reveal no information under that randomization model. The original prime-field construction requires a modulus large enough for the secret and participant indices. Reconstruction assumes honest, intact shares. Detecting a malicious dealer, authenticating shares and verifiable secret sharing are later/separate mechanisms. Blakley developed a different threshold construction independently. WRS has not performed an implementation/security audit.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Adi Shamir · SCIENCE: Original scientific author of this polynomial threshold construction, distinct from all threshold-sharing methods.
- G.R.Blakley; prior interpolation and mechanicalthreshold sources · SCIENCE: The original paper acknowledges a distinct contemporary scheme and antecedents, without making them coauthors.
- R.Rivest / Office of Naval Research · PARTICIPATION: Source-listed editor and funding roles, distinct from original scientific byline credit.
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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