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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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A Complete Public-Key Cryptosystem

Dima Grigoriev1 / Edward A. Hirsch2 / Konstantin Pervyshev3

1IRMAR, Université de Rennes, Campus de Beaulieu, 35042 Rennes, France. http://perso.univ-rennes1.fr/dmitry.grigoryev/

2Steklov Institute of Mathematics at St.Petersburg, 27 Fontanka, 191023 St.Petersburg, Russia. http://logic.pdmi.ras.ru/~hirsch/

3University of California, San Diego, USA

Citation Information: Groups – Complexity – Cryptology. Volume 1, Issue 1, Pages 1–12, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/GCC.2009.1, February 2010

Publication History

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We present a cryptosystem which is complete for the class of probabilistic public-key cryptosystems with bounded error. Besides traditional encryption schemes such as RSA and El Gamal and probabilistic encryption of Goldwasser and Micali, this class contains also Ajtai-Dwork and NTRU cryptosystems. The latter two make errors with a small positive probability.

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