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

Mohamad Ali Mehrabi, Christophe Doche

Research output: Contribution to journalArticle

1 Citation (Scopus)
17 Downloads (Pure)

Abstract

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)
Volume10
Issue number9
DOIs
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.

Keywords

  • 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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