TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Safieh, Malek
A1  - Freudenberger, Jürgen
T1  - Montgomery Reduction for Gaussian Integers
JF  - Cryptography
N2  - Modular arithmetic over integers is required for many cryptography systems. Montgomeryreduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Mont-gomery reduction is used for rings of ordinary integers.  In contrast, we investigate the modularreduction over rings of Gaussian integers. Gaussian integers are complex numbers where the real andimaginary parts are integers. Rings over Gaussian integers are isomorphic to ordinary integer rings.In this work, we show that Montgomery reduction can be applied to Gaussian integer rings. Twoalgorithms for the precision reduction are presented. We demonstrate that the proposed Montgomeryreduction enables an efficient Gaussian integer arithmetic that is suitable for elliptic curve cryptogra-phy. In particular, we consider the elliptic curve point multiplication according to the randomizedinitial point method which is protected against side-channel attacks.  The implementation of thisprotected point multiplication is significantly faster than comparable algorithms over ordinary primefields.
KW  - Public-key cryptography
KW  - Elliptic curve point multiplication
KW  - Gaussian integers
KW  - Mont-gomery modular reduction
Y1  - 2021
UN  - https://nbn-resolving.org/urn:nbn:de:bsz:kon4-opus4-28159
SN  - 2410-387X
SS  - 2410-387X
U6  - https://doi.org/10.3390/cryptography5010006
DO  - https://doi.org/10.3390/cryptography5010006
N1  - Corresponding author: Jürgen Freudenberger
VL  - 5
IS  - 1
SP  - 18
S1  - 18
PB  - MDPI
CY  - Basel
ER  -