<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Modular reduction in extended finite fields and polynomial rings is presented, which once implemented works for any random reduction polynomial without changes of the hardware. It is possible to reduce polynomials of whatever degree. Based on the principal defined, two example RTL architectures are designed, and some useful features are noted furthermore. The first architecture is sequential and reduce whatever degree polynomials, taking 2 cycles per term. The second one is Parallel and designed for reduction of polynomials of 2(<italic>t</italic> −1) degree at most, taking 1 cycle for the whole reduction.</p></abstract>

Modular reduction in extended finite fields and polynomial rings is presented, which once implemented works for any random reduction polynomial without changes of the hardware. It is possible to reduce polynomials of whatever degree. Based on the principal defined, two example RTL architectures are designed, and some useful features are noted furthermore. The first architecture is sequential and reduce whatever degree polynomials, taking 2 cycles per term. The second one is Parallel and designed for reduction of polynomials of 2(t −1) degree at most, taking 1 cycle for the whole reduction.

Note on Modular Reduction in Extended Finite Fields and Polynomial Rings for Simple Hardware

Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Technology, Ilkovičova 3, Bratislava, SK-812 19, Slovakia

Journal of Electrical Engineering

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Modular reduction in extended finite fields and polynomial rings is presented, which once implemented works for any random reduction polynomial without changes...

Note on Modular Reduction in Extended Finite Fields and Polynomial Rings for Simple Hardware

Published Online: Mar 17, 2016

Page range: 56 - 60

Received: Oct 08, 2015

DOI: https://doi.org/10.1515/jee-2016-0008

Keywords
modular reduction, extended finite fields, extended polynomial rings, algebraic codes, McEliece PKC, Niederreiter PKC

© 2016 Faculty of Electrical Engineering and Information Technology, Slovak University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Note on Modular Reduction in Extended Finite Fields and Polynomial Rings for Simple Hardware

Published Online: Mar 17, 2016

Page range: 56 - 60

Received: Oct 08, 2015

DOI: https://doi.org/10.1515/jee-2016-0008

Keywordsmodular reduction, extended finite fields, extended polynomial rings, algebraic codes, McEliece PKC, Niederreiter PKC

© 2016 Faculty of Electrical Engineering and Information Technology, Slovak University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
modular reduction, extended finite fields, extended polynomial rings, algebraic codes, McEliece PKC, Niederreiter PKC