Overview

“Cryptographic Accelerators for Digital Signature Based on Ed25519” is a peer-reviewed article by Mojtaba Bisheh-Niasar, Reza Azarderakhsh, and Mehran Mozaffari-Kermani, published in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 29, no. 7, July 2021. It presents two field-programmable gate array (FPGA) hardware implementations of the Ed25519 instance of the Edwards-curve Digital Signature Algorithm (EdDSA): an area-efficient design for constrained devices and a high-performance design for throughput. The work is notable because, despite Ed25519’s wide use in protocols like TLS and SSH, dedicated hardware implementations focused solely on EdDSA were scarce at the time.

Key points

• Two FPGA architectures target a security level comparable to AES-128 on a Xilinx Zynq-7020: an efficient (small-area) variant and a high-performance (high-throughput) variant.
• The efficient design reports more than 84% improvement in the area-time product over the best prior work, with more than 8x speedup; the high-performance design reports roughly 21x speedup, exceeding 6200 signature operations per second.
• Field arithmetic uses multi-level Karatsuba multiplication (evaluated against Schoolbook and Toom-3), redundant number representation, distributed RAM/ROM blocks, and an interleaved architecture; 255-bit add/subtract completes in a single clock cycle.
• The design computes over the Montgomery curve form of Curve25519 (restricted-X coordinate) and maps to the twisted Edwards domain, leveraging cheaper Montgomery-ladder arithmetic while producing Edwards-form signatures; it also integrates a SHA-512 hash core, which adds roughly 25% of the utilized area.
• Side-channel countermeasures are embedded against timing, simple power analysis (SPA), and differential power analysis (DPA) attacks, including Z-coordinate (point) randomization and constant-time Montgomery-ladder execution.
• The paper motivates Ed25519 as a fast, constant-time, backdoor-resistant alternative to ECDSA for embedded and IoT devices; work supported in part by NIST and NSF grants.

Relevance to Truestamp

Truestamp uses Ed25519 signatures to sign proof material, so this paper’s analysis of Ed25519 performance and side-channel resistance provides useful background on why the scheme is chosen over ECDSA and how it can be hardened and accelerated in hardware.

Citations

1. Cryptographic Accelerators for Digital Signature Based on Ed25519. Mojtaba Bisheh-Niasar, Reza Azarderakhsh, Mehran Mozaffari-Kermani; IEEE Transactions on VLSI Systems, vol. 29, no. 7, July 2021 (NSF Public Access Repository).