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Journal of Mathematical Cryptology

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

Editorial Board Member: 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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On hashing into elliptic curves

Reza R. Farashahi1 / Igor E. Shparlinski2 / José Felipe Voloch3

1Department of Computing, Macquarie University, Sydney, NSW 2109, Australia. Email:

2Department of Computing, Macquarie University, Sydney, NSW 2109, Australia. Email:

3Department of Mathematics, University of Texas, Austin TX 78712, USA. Email:

Citation Information: Journal of Mathematical Cryptology. Volume 3, Issue 4, Pages 353–360, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: 10.1515/JMC.2009.022, March 2010

Publication History

Published Online:


We study the hash function from a finite field 𝔽q into an elliptic curve over 𝔽q which has recently been introduced by T. Icart. In particular we slightly adjust and prove the asymptotic formula conjectured by T. Icart for the image size of this function.

Keywords.: Elliptic curve cryptography; hashing; Chebotarev density theorem

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