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Faster Interleaved Modular Multiplication Based on Barrett and Montgomery Reduction Methods
December 2010 (vol. 59 no. 12)
pp. 1715-1721
ASCII Text
x 
 
Miroslav Knežević, Frederik Vercauteren, Ingrid Verbauwhede, "Faster Interleaved Modular Multiplication Based on Barrett and Montgomery Reduction Methods," IEEE Transactions on Computers, vol. 59, no. 12, pp. 1715-1721, December, 2010.
 
 
BibTex
x
 
@article{ 10.1109/TC.2010.93,
author = {Miroslav Knežević and Frederik Vercauteren and Ingrid Verbauwhede},
title = {Faster Interleaved Modular Multiplication Based on Barrett and Montgomery Reduction Methods},
journal ={IEEE Transactions on Computers},
volume = {59},
number = {12},
issn = {0018-9340},
year = {2010},
pages = {1715-1721},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2010.93},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Faster Interleaved Modular Multiplication Based on Barrett and Montgomery Reduction Methods
IS - 12
SN - 0018-9340
SP1715
EP1721
EPD - 1715-1721
A1 - Miroslav Knežević,
A1 - Frederik Vercauteren,
A1 - Ingrid Verbauwhede,
PY - 2010
KW - Modular multiplication
KW - Barrett reduction
KW - Montgomery reduction
KW - public-key cryptography.
VL - 59
JA - IEEE Transactions on Computers
ER -
 
Miroslav Knežević, Katholieke University Leuven, Belgium
Frederik Vercauteren, Katholieke University Leuven, Belgium
Ingrid Verbauwhede, Katholieke University Leuven, Belgium
This paper proposes two improved interleaved modular multiplication algorithms based on Barrett and Montgomery modular reduction. The algorithms are simple and especially suitable for hardware implementations. Four large sets of moduli for which the proposed methods apply are given and analyzed from a security point of view. By considering state-of-the-art attacks on public-key cryptosystems, we show that the proposed sets are safe to use, in practice, for both elliptic curve cryptography and RSA cryptosystems. We propose a hardware architecture for the modular multiplier that is based on our methods. The results show that concerning the speed, our proposed architecture outperforms the modular multiplier based on standard modular multiplication by more than 50 percent. Additionally, our design consumes less area compared to the standard solutions.

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Index Terms:
Modular multiplication, Barrett reduction, Montgomery reduction, public-key cryptography.
Citation:
Miroslav Knežević, Frederik Vercauteren, Ingrid Verbauwhede, "Faster Interleaved Modular Multiplication Based on Barrett and Montgomery Reduction Methods," IEEE Transactions on Computers, vol. 59, no. 12, pp. 1715-1721, Dec. 2010, doi:10.1109/TC.2010.93
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