Pedersen: verify shared secret pieces without exposing the secret

What changed

Two-generator perfectly hiding commitments combine with polynomial shares so recipients verify consistency non-interactively; secret privacy is information-theoretic while share consistency relies on the dealer not knowing the generator discrete-log relation.

Scientific scope

Two-generator perfectly hiding commitments combine with polynomial shares so recipients verify consistency non-interactively; secret privacy is information-theoretic while share consistency relies on the dealer not knowing the generator discrete-log relation. The construction combines threshold sharing with commitments in a prime-order group. Perfect hiding uses uniformly random blinding; computational binding assumes that the discrete-log relationship between the two generators is unknown to the committing party. Share verification and reconstruction use the stated participant indices, threshold and broadcast/private-channel model. Information-theoretic privacy does not mean unconditional resistance to malicious inconsistent openings. The work was presented at CRYPTO 1991 and printed in 1992. WRS has not independently reconstructed the full security proof or certified the exact formula transcription.

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

• Torben Pryds Pedersen · SCIENCE: Complete soleoriginalbyline;1991/1992samefamily.
• Shamir; Blakley; Feldman; Bos–Chaum–Purdy · SCIENCE: Explicitly credited threshold-sharing, noninteractive verifiable-secret-sharing and commitment antecedents, distinct from this paper's coauthors.
• Earlier Pedersen; Ingemarsson–Simmons; earlier interactive-MPC authors · SCIENCE: Acknowledged precursors and contrasted protocols; their scoped credit is retained.

• Torben Pryds Pedersen: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing (CRYPTO 1991, printed 1992)

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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