Binary-Ternary Plus-Minus Modular Inversion in RNS

A fast RNS modular inversion for finite fields arithmetic has been published at CHES 2013 conference. It is based on the binary version of the plus-minus Euclidean algorithm. In the context of elliptic curve cryptography (i.e., 160-550 bits finite fields), it significantly speeds-up modular inversio...

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Bibliographic Details
Published in:IEEE transactions on computers 2016-11, Vol.65 (11), p.3495-3501
Main Authors: Bigou, Karim, Tisserand, Arnaud
Format: Article
Language:English
Subjects:
Approximation algorithms
Computer Arithmetic
Computer Science
Cryptography and Security
ECC
Elliptic curve cryptography
Engineering Sciences
Euclidean algorithms
extended Euclidean algorithm
Field programmable gate arrays
FPGA
Micro and nanotechnologies
Microelectronics
modular arithmetic
Residue number system
Signal processing algorithms
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Summary:A fast RNS modular inversion for finite fields arithmetic has been published at CHES 2013 conference. It is based on the binary version of the plus-minus Euclidean algorithm. In the context of elliptic curve cryptography (i.e., 160-550 bits finite fields), it significantly speeds-up modular inversions. In this paper, we propose an improved version based on both radix 2 and radix 3. This new algorithm leads to 30 percent speed-up for a maximal area overhead about 4 percent on Virtex 5 FPGAs.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2016.2529625