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    "summary": "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.",
    "boundary": "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.",
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        "description": "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.",
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      "statement": "# Pedersen: verify shared secret pieces without exposing the secret\n\nTwo-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.\n\n## Scientific scope\n\nThe 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.\n\n## People and systems\n\nTorben Pryds Pedersen\n\n\n\n## Original sources\n\n- [Torben Pryds Pedersen: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing (CRYPTO1991,printed1992)](https://www.cs.cornell.edu/courses/cs754/2001fa/129.PDF)\n",
      "summary": "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.",
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    "title": "Pedersen: verify shared secret pieces without exposing the secret",
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        "title": "Torben Pryds Pedersen: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing (CRYPTO 1991, printed 1992)",
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