On hashing into elliptic curves

Reza R. Farashahi 1 , Igor E. Shparlinski 2 ,  and José Felipe Voloch 3
  • 1 Department of Computing, Macquarie University, Sydney, NSW 2109, Australia. Email: reza@ics.mq.edu.au
  • 2 Department of Computing, Macquarie University, Sydney, NSW 2109, Australia. Email: igor@ics.mq.edu.au
  • 3 Department of Mathematics, University of Texas, Austin TX 78712, USA. Email: voloch@math.utexas.edu

Abstract

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.

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JMC is a forum for original research articles in the area of mathematical cryptology. Works in the theory of cryptology and articles linking mathematics with cryptology are welcome. Submissions from all areas of mathematics significant for cryptology are published, including but not limited to, algebra, algebraic geometry, coding theory, combinatorics, number theory, probability and stochastic processes.

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