Generation of Elliptic Curve Points in Tandem

Abstract

A hash to curve function H, mapping bit strings to points on an elliptic curve, is often required in cryptographic schemes based on elliptic curves. Its construction is based on a deterministic encoding and a cryptographic hash function, which complementarily dominate its execution time. To improve the performance of H, we propose a parallel strategy where two units execute in tandem the internal operations of H. We instantiate this approach with a parallel software implementation of a hash to curve function that outputs points on a twisted Edwards curve. A performance benchmark on Haswell and Skylake micro-architectures shows that our parallel implementation is 1.4 times faster than its sequential implementation.

Citation

@inproceedings{faz_sbseg2020,
  author = {Armando Faz-Hernández and Julio López},
  title = {Generation of Elliptic Curve Points in Tandem},
  booktitle = {Anais do XX Simpósio Brasileiro em Segurança da Informação e de Sistemas Computacionais},
  location = {Petrópolis, RJ, Brazil},
  editor = {Igor Monteiro Moraes and Luis Kowada},
  address = {Porto Alegre, RS, Brasil},
  year = {2020},
  month = {oct},
  pages = {1--9},
  publisher = {Sociedade Brasileira de Computação},
  doi = {10.5753/sbseg.2020.19230}
}