Low-cost, low-power FPGA implementation of ED25519 and CURVE25519 point multiplication

Mohamad Ali Mehrabi, Christophe Doche

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
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Twisted Edwards curves have been at the center of attention since their introduction by Bernstein et al. in 2007. The curve ED25519, used for Edwards-curve Digital Signature Algorithm (EdDSA), provides faster digital signatures than existing schemes without sacrificing security. The CURVE25519 is a Montgomery curve that is closely related to ED25519. It provides a simple, constant time, and fast point multiplication, which is used by the key exchange protocol X25519. Software implementations of EdDSA and X25519 are used in many web-based PC and Mobile applications. In this paper, we introduce a low-power, low-area FPGA implementation of the ED25519 and CURVE25519 scalar multiplication that is particularly relevant for Internet of Things (IoT) applications. The efficiency of the arithmetic modulo the prime number 2255−19 , in particular the modular reduction and modular multiplication, are key to the efficiency of both EdDSA and X25519. To reduce the complexity of the hardware implementation, we propose a high-radix interleaved modular multiplication algorithm. One benefit of this architecture is to avoid the use of large-integer multipliers relying on FPGA DSP modules
Original languageEnglish
Article number285
Pages (from-to)1-16
Number of pages16
JournalInformation (Switzerland)
Issue number9
Publication statusPublished - Sep 2019

Bibliographical note

Copyright the Author(s) 2019. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • interleaved modular reduction
  • elliptic curve cryptography (ECC)
  • twisted Edwards curves
  • Montgomery curve
  • Montgomery ladder algorithm
  • dwards-curve Digital Signature Algorithm (EdDSA)
  • ED25519
  • CURVE25519
  • X25519


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