On Indifferentiable Deterministic Hashing into Elliptic Curves

Authors

  • Nafissatou Diarra Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal
  • Djiby Sow Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal
  • Ahmed Youssef Ould Cheikh Khlil Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal

Keywords:

deterministic encodings, elliptic curves, random oracle, indifferentiable hashing

Abstract

In this paper, we give new deterministic encodings based on Elligator`s model, for some families of elliptic curves. These encodings are almost-injective and easily invertible. This allows to make points in the image set of the encoding indistinguishable from uniform string of bits, which is useful for applications in censorship circumvention. Following the idea of Farashahi et al., we show that our encodings are well-distributed. And thus they give rise to hash functions constructions indifferentiable from random oracles.

Author Biographies

  • Nafissatou Diarra, Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal

    Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal

  • Djiby Sow, Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal

    Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal

  • Ahmed Youssef Ould Cheikh Khlil, Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal

    Laboratoire d’Alg`ebre, de Cryptographie, de G´eom´etrie Alg´ebrique et Aplications (LACGAA, Cheikh Anta Diop University, Dakar, Senegal

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Published

2017-02-03

Issue

Vol. 10 No. 2: (January 2017)

Section

Coding Theory and Cryptology

License

Copyright (c) 2017 European Journal of Pure and Applied Mathematics

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How to Cite

On Indifferentiable Deterministic Hashing into Elliptic Curves. (2017). European Journal of Pure and Applied Mathematics, 10(2), 363-391. https://www.ejpam.com/index.php/ejpam/article/view/2623