TY  - CHAP
U1  - Konferenzveröffentlichung
A1  - Safieh, Malek
A1  - Freudenberger, Jürgen
T1  - Montgomery Modular Arithmetic over Gaussian Integers
T2  - 24th International Conference on Information Technology (IT), 18-22 February 2020, Zabljak, Montenegro
N2  - The Montgomery multiplication is an efficient method for modular arithmetic. Typically, it is used for modular arithmetic over integer rings to prevent the expensive inversion for the modulo reduction. In this work, we consider modular arithmetic over rings of Gaussian integers. Gaussian integers are subset of the complex numbers such that the real and imaginary parts are integers. In many cases Gaussian integer rings are isomorphic to ordinary integer rings. We demonstrate that the concept of the Montgomery multiplication can be extended to Gaussian integers. Due to independent calculation of the real and imaginary parts, the computation complexity of the multiplication is reduced compared with ordinary integer modular arithmetic. This concept is suitable for coding applications as well as for asymmetric key cryptographic systems, such as elliptic curve cryptography or the Rivest-Shamir-Adleman system.
KW  - Computational complexity
KW  - Digital arithmetic
KW  - Encoding
KW  - Public key cryptography
Y1  - 2020
UR  - https://ieeexplore.ieee.org/document/9070297
SN  - 978-1-7281-5136-6
SB  - 978-1-7281-5136-6
U6  - https://doi.org/10.1109/IT48810.2020.9070297
DO  - https://doi.org/10.1109/IT48810.2020.9070297
N1  - Volltextzugriff für Angehörige der Hochschule Konstanz via Datenbank IEEE Xplore möglich
SP  - 4
S1  - 4
PB  - IEEE
ER  -