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On sharing secrets and Reed-Solomon codes

Authors:

R. J. McEliece,

D. V. SarwateAuthors Info & Claims

Communications of the ACM, Volume 24, Issue 9

Pages 583 - 584

https://doi.org/10.1145/358746.358762

Published: 01 September 1981 Publication History

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Abstract

Shamir's scheme for sharing secrets is closely related to Reed-Solomon coding schemes. Decoding algorithms for Reed-Solomon codes provide extensions and generalizations of Shamir's method.

References

[1]

Berlekamp, E.R. Algebraic Coding Theory. McGraw-Hill, New York, 1968.

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[2]

McEliece, R.J. The Theory of Information and Coding. Addison- Wesley, Reading MA, 1977.

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[3]

Reed, I.S. and Solomon, G. Polynomial codes over certain finite fields. J. SIAM 8, 2 (June 1960), 300-304.

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[4]

Sarwate, D.V. On the complexity of decoding Goppa codes. IEEE Trans. Inform. Theory 23, 4 (July 1977), 515-516.

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[5]

Shamir, A. How to share a secret. Comm. A CM, 22, 11 (Nov. 1979), 612-613.

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Sugiyama, Y., Kasahara, M., Hirasawa, S., and Namekawa, T. An erasures-and-errors decoding algorithm for Goppa codes. IEEE Trans. Inform. Theory 22, 2 (Mar. 1976), 238-241.

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Charpin P(2025)Cyclic CodesEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_343(546-551)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_343
Desmedt Y(2025)Secret Sharing and Shamir Threshold SchemeEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_1822(2212-2216)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_1822
Prouff E(2025)Masking CountermeasureEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_1697(1489-1493)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_1697
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Index Terms

On sharing secrets and Reed-Solomon codes

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Published In

Communications of the ACM Volume 24, Issue 9

Sept. 1981

72 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/358746

Editor:
Robert L. Ashenhurst
The Univ. of Chicago, IL

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 1981

Published in CACM Volume 24, Issue 9

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Charpin P(2025)Cyclic CodesEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_343(546-551)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_343
Desmedt Y(2025)Secret Sharing and Shamir Threshold SchemeEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_1822(2212-2216)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_1822
Prouff E(2025)Masking CountermeasureEncyclopedia of Cryptography, Security and Privacy10.1007/978-3-030-71522-9_1697(1489-1493)Online publication date: 8-Jan-2025
https://doi.org/10.1007/978-3-030-71522-9_1697
Eldridge HBeck GGreen MHeninger NJain ABalzarotti DXu W(2024)Abuse-resistant location trackingProceedings of the 33rd USENIX Conference on Security Symposium10.5555/3698900.3699204(5431-5448)Online publication date: 14-Aug-2024
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Liang YShan HLuo ZQi LXie Y(2024)PowerBridge: Covert Air-Gap Exfiltration/Infiltration via Smart PlugApplied Sciences10.3390/app1414632114:14(6321)Online publication date: 19-Jul-2024
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Yamanaka MKinjo SMiyamoto S(2024)A study of secure communication with secret sharing method in MIMO eigen stream parallel channelsIEICE Communications Express10.23919/comex.2023XBL014413:3(72-75)Online publication date: Mar-2024
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YAMASAKI SMATSUSHIMA TONO KTANAKA H(2024)Variable-Length Orthogonal Codes over Finite Fields Realizing Data Multiplexing and Error Correction Coding SimultaneouslyIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.2023TAP0012E107.A:3(373-383)Online publication date: 1-Mar-2024
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张玲(2024)Verifiable Multi-Secret Sharing Scheme Based on LCD CodeAdvances in Applied Mathematics10.12677/aam.2024.131249713:12(5147-5152)Online publication date: 2024
https://doi.org/10.12677/aam.2024.1312497
Smith CTabassum MDaruru SKulhare GWang AMiller EZadok E(2024)Secure Archival is Hard... Really HardProceedings of the 16th ACM Workshop on Hot Topics in Storage and File Systems10.1145/3655038.3666093(38-46)Online publication date: 8-Jul-2024
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Hayashi MKoshiba T(2024)Universal Adaptive Construction of Verifiable Secret Sharing and Its Application to Verifiable Secure Distributed Data StorageIEEE/ACM Transactions on Networking10.1109/TNET.2023.328357732:1(253-267)Online publication date: Feb-2024
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Abstract

References

Cited By

Index Terms

Recommendations

Sharing one secret vs. sharing many secrets

Efficient Generalized Minimum-distance Decoders of Reed-Solomon Codes

Efficient architecture for algebraic soft‐decision decoding of Reed–Solomon codes

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