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A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers

  • This work presents a new concept to implement the elliptic curve point multiplication (PM). This computation is based on a new modular arithmetic over Gaussian integer fields. Gaussian integers are a subset of the complex numbers such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this arithmetic is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of secure hardware implementations, which are robust against attacks. Furthermore, an area-efficient coprocessor design is proposed with an arithmetic unit that enables Montgomery modular arithmetic over Gaussian integers. The proposed architecture and the new arithmetic provide high flexibility, i.e., binary and non-binary key expansions as well as protected and unprotected PM calculations are supported. The proposed coprocessor is a competitive solution for a compact ECC processor suitable for applications in small embedded systems.

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Author:Malek Safieh, Johann-Philipp Thiers, Jürgen FreudenbergerORCiDGND
Parent Title (English):Electronics
Document Type:Article
Year of Publication:2020
Release Date:2021/01/18
Tag:Elliptic curve cryptography; Elliptic curve point multiplication; Gaussian integers; Montgomery modular reduction; Processor; Resource-constrained systems
Page Number:21
Institutes:Institut für Systemdynamik - ISD
Open Access?:Ja
Relevance:Peer reviewed Publikation in Master Journal List
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International