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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

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Volume 8, Issue 2


The distribution of quadratic residues and non-residues in the Goldwasser–Micali type of cryptosystem

Benjamin Justus
  • Labor für IT-Sicherheit, Stegerwaldstr. 39, 48565 Steinfurt, Germany; and Lab-STICC, Télécom Bretagne, Cesson Sévigné Cedex, France
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Published Online: 2014-01-14 | DOI: https://doi.org/10.1515/jmc-2013-0001


We provide unconditional results and conditional ones under the assumption of GRH (Generalized Riemann Hypothesis) on the distribution of quadratic residues and quadratic non-residues in /N, where N=pq is an RSA modulus used in the Goldwasser–Micali cryptosystem. The paper also discusses cryptographic implications of the results obtained.

Keywords: Quadratic residuosity problem; Goldwasser–Micali cryptosystem; quadratic residues distribution

MSC: 94A60; 11A15

About the article

Received: 2013-01-05

Revised: 2013-11-29

Accepted: 2013-12-20

Published Online: 2014-01-14

Published in Print: 2014-06-01

Citation Information: Journal of Mathematical Cryptology, Volume 8, Issue 2, Pages 115–140, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2013-0001.

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