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Concurrent Error Detection in Montgomery Multiplication over Binary Extension Fields
September 2011 (vol. 60 no. 9)
pp. 1341-1353
ASCII Text
x 
 
Arash Hariri, Arash Reyhani-Masoleh, "Concurrent Error Detection in Montgomery Multiplication over Binary Extension Fields," IEEE Transactions on Computers, vol. 60, no. 9, pp. 1341-1353, September, 2011.
 
 
BibTex
x
 
@article{ 10.1109/TC.2010.258,
author = {Arash Hariri and Arash Reyhani-Masoleh},
title = {Concurrent Error Detection in Montgomery Multiplication over Binary Extension Fields},
journal ={IEEE Transactions on Computers},
volume = {60},
number = {9},
issn = {0018-9340},
year = {2011},
pages = {1341-1353},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2010.258},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Concurrent Error Detection in Montgomery Multiplication over Binary Extension Fields
IS - 9
SN - 0018-9340
SP1341
EP1353
EPD - 1341-1353
A1 - Arash Hariri,
A1 - Arash Reyhani-Masoleh,
PY - 2011
KW - Montgomery multiplication
KW - concurrent error detection
KW - finite fields
KW - elliptic curve cryptography.
VL - 60
JA - IEEE Transactions on Computers
ER -
 
Arash Hariri, The University of Western Ontario, London
Arash Reyhani-Masoleh, The University of Western Ontario, London
Multiplication is one of the most important operations in finite field arithmetic. It is used in cryptographic and coding applications, such as elliptic curve cryptography and Reed-Solomon codes. In this paper, we consider the finite field multiplication used in elliptic curve cryptography and design concurrent error detection circuits. It is shown in the literature that the Montgomery multiplication can be used in cryptography to accelerate the scalar multiplication. Here, we use a parity-based concurrent error detection approach to increase the reliability of different Montgomery multipliers available in the literature. First, we consider bit-serial Montgomery multiplication and propose an error detection circuit. Then, we apply the same technique on the digit-serial Montgomery multiplication. Finally, we consider low time-complexity bit-parallel Montgomery multiplication and design the required components to implement the concurrent error detection circuits. ASIC implementations have been completed to analyze the time and area overheads of the proposed schemes. Also, the error detection capability is investigated by software simulations. We show that our approach results in efficient error detection schemes with small time and area overheads.

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Index Terms:
Montgomery multiplication, concurrent error detection, finite fields, elliptic curve cryptography.
Citation:
Arash Hariri, Arash Reyhani-Masoleh, "Concurrent Error Detection in Montgomery Multiplication over Binary Extension Fields," IEEE Transactions on Computers, vol. 60, no. 9, pp. 1341-1353, Sept. 2011, doi:10.1109/TC.2010.258
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