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 language | English |
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Article number | 285 |
Pages (from-to) | 1-16 |
Number of pages | 16 |
Journal | Information (Switzerland) |
Volume | 10 |
Issue number | 9 |
DOIs | |
Publication status | Published - Sept 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