Journal of Cryptographic Engineering

, Volume 8, Issue 4, pp 271–283 | Cite as

A class of safe and efficient binary Edwards curves

  • Luckas A. FariasEmail author
  • Bruno C. Albertini
  • Paulo S. L. M. Barreto
Regular Paper


This work describes a family of binary Edwards curves that admit modular reductions (an operation that can be responsible for up to 30% of the processing time in point arithmetic) twice as fast than the best usual settings, while essentially being as secure as a binary elliptic curve can be (in terms of being rigid and twist safe). Moreover, we present a hardware architecture with a generic VHDL description that can be synthesized to any FPGA with enough area to support the circuit. For this architecture, we are able to execute a point multiplication by scalar on \(\mathbb {F}_{562}\) in 2.28 ms on Cyclone IV GX, in 1.23 ms on Virtex-7 and in 1.01 ms on Zynq 7020.


Elliptic curve cryptosystems Binary Edwards curves Efficient arithmetic Hardware implementation Side-channel protection 

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Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Escola PolitécnicaUniversidade de São PauloSão PauloBrazil

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