How to share a secret
Open accessAbstract
In this paper we show how to divide data D into n pieces in such a way that D is easily reconstructable from any k pieces, but even complete knowledge of k - 1 pieces reveals absolutely no information about D . This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
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The scheme proposed by Shamir relies on standard Lagrange polynomial interpolation, while Blakley's proposal, also known as vector scheme, relies on the geometric concept of intersecting hyperplanes.
“The scheme proposed by Shamir relies on standard Lagrange polynomial interpolation, while Blakley's proposal, also known as vector scheme, relies on the geometric concept of intersecting hyperplanes.”
From A Survey of Self-Sovereign Identity Ecosystem (2021) · cites this paper as [123]
In “A Simple (k, n) Threshold Scheme” (p. 612), Shamir says his scheme is based on polynomial interpolation and reconstructs the secret by interpolating from k shares. The paper mentions Blakley’s different scheme on p. 612 but does not describe it as a vector scheme or explain it through intersecting hyperplanes. It also does not name Lagrange interpolation specifically. (LLM, conf=0.88)
Experimental — accuracy not yet measuredIn 1979, Shamir and Blakely proposed two variations of threshold-based secret sharing schemes.
“In 1979, Shamir [123] and Blakely [124] proposed two variations of threshold-based secret sharing schemes.”
From A Survey of Self-Sovereign Identity Ecosystem (2021) · cites this paper as [123]
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- Authors
- Shamir, A.
- Affiliations
- Massachusetts Institute of Technology, Cambridge
- Venue
- Communications of the ACM
- Published
- 1979-11
- Volume
- 22
- Issue
- 11
- Pages
- 612-613
- ISSN
- 0001-0782 (ISSN-L)
- 1557-7317
- OpenAlex
- W2141420453
- Cited by
- 13,756
- References
- 7
- Citations by year
- 2026: 467 · 2025: 758 · 2024: 675 · 2023: 713 · 2022: 643 · 2021: 719 · 2020: 697 · 2019: 670 · 2018: 602 · 2017: 545 · 2016: 563 · 2015: 606 · 2014: 586 · 2013: 617 · 2012: 562
- FWCI
- 7.12
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Communications of the ACM (publishedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- Defense Technical Information Center (DTIC) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptography and Data Security
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Physical Sciences › Computer Science › Information Systems › Cloud Data Security Solutions
- Keywords
- secret sharing, information-theoretic security, key management, cryptographic key distribution, data redundancy, fault tolerance, security breaches
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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