TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Safieh, Malek
A1  - Thiers, Johann-Philipp
A1  - Freudenberger, Jürgen
T1  - A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers
JF  - Electronics
N2  - 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.
KW  - Elliptic curve cryptography
KW  - Elliptic curve point multiplication
KW  - Gaussian integers
KW  - Montgomery modular reduction
KW  - Processor
KW  - Resource-constrained systems
Y1  - 2020
UN  - https://nbn-resolving.org/urn:nbn:de:bsz:kon4-opus4-26609
SN  - 2079-9292
SS  - 2079-9292
U6  - https://doi.org/10.3390/electronics9122050
DO  - https://doi.org/10.3390/electronics9122050
N1  - Corresponding author: Jürgen Freudenberger
VL  - 9
IS  - 12
SP  - 21
S1  - 21
PB  - MDPI
CY  - Basel
ER  -