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Open AccessArticle

Low-Cost, Low-Power FPGA Implementation of ED25519 and CURVE25519 Point Multiplication

1
Department of computing, Macquarie University, Sydney 2109, Australia
2
Optus Macquarie University Cyber Security Hub, Sydney 2109, Australia
*
Author to whom correspondence should be addressed.
Information 2019, 10(9), 285; https://doi.org/10.3390/info10090285
Received: 13 August 2019 / Revised: 2 September 2019 / Accepted: 9 September 2019 / Published: 14 September 2019
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 2 255 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. View Full-Text
Keywords: interleaved modular reduction; elliptic curve cryptography (ECC); twisted Edwards curves; Montgomery curve; Montgomery ladder algorithm; Edwards-curve Digital Signature Algorithm (EdDSA); ED25519; CURVE25519; X25519 interleaved modular reduction; elliptic curve cryptography (ECC); twisted Edwards curves; Montgomery curve; Montgomery ladder algorithm; Edwards-curve Digital Signature Algorithm (EdDSA); ED25519; CURVE25519; X25519
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Mehrabi, M.A.; Doche, C. Low-Cost, Low-Power FPGA Implementation of ED25519 and CURVE25519 Point Multiplication. Information 2019, 10, 285.

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