Title: Hashing into Hessian curves

Authors: Reza Rezaeian Farashahi

Addresses: Department of Mathematical Sciences, Isfahan University of Technology, P.O. Box 85145, Isfahan, Iran; School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

Abstract: We propose an encoding function from the elements of the finite field F_q into points on a Hessian curve. Next, we present an injective encoding function from the set of all positive integers less than or equal to l into points on a Hessian curve over F_q with odd q and l = (q - 1)/2. We also present an injective encoding function from the bit strings of length k = 1 into points on a Hessian curve over the binary finite field F_2k.

Keywords: elliptic curve cryptography; Hessian curves; hashing; injective encoding; security.

DOI: 10.1504/IJACT.2014.062737

International Journal of Applied Cryptography, 2014 Vol.3 No.2, pp.139 - 147

Published online: 16 Aug 2014 *

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