Abstract
In this article, we present a hybrid method to improve the performance of the Montgomery reduction by taking advantage of the Karatsuba technique. We divide the Montgomery reduction into two sub-parts, including one for the conventional Montgomery reduction and the other one for Karatsuba-aided multiplication. This approach reduces the multiplication complexity of n-limb Montgomery reduction from θ(n2 + n) to asymptotic complexity θ(7n2/8 + n). Our practical implementation results over an 8-bit microcontroller also show performance enhancements by 11%.
| Original language | English |
|---|---|
| Article number | 58 |
| Journal | Transactions on Embedded Computing Systems |
| Volume | 15 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - May 1 2016 |
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Keywords
- Karatsuba multiplication
- Montgomery reduction
- Public key cryptography
- Software implementation
ASJC Scopus subject areas
- Hardware and Architecture
- Software
Cite this
Hybrid Montgomery reduction. / Seo, Hwajeong; Liu, Zhe; Nogami, Yasuyuki; Choi, Jongseok; Kim, Howon.
In: Transactions on Embedded Computing Systems, Vol. 15, No. 3, 58, 01.05.2016.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Hybrid Montgomery reduction
AU - Seo, Hwajeong
AU - Liu, Zhe
AU - Nogami, Yasuyuki
AU - Choi, Jongseok
AU - Kim, Howon
PY - 2016/5/1
Y1 - 2016/5/1
N2 - In this article, we present a hybrid method to improve the performance of the Montgomery reduction by taking advantage of the Karatsuba technique. We divide the Montgomery reduction into two sub-parts, including one for the conventional Montgomery reduction and the other one for Karatsuba-aided multiplication. This approach reduces the multiplication complexity of n-limb Montgomery reduction from θ(n2 + n) to asymptotic complexity θ(7n2/8 + n). Our practical implementation results over an 8-bit microcontroller also show performance enhancements by 11%.
AB - In this article, we present a hybrid method to improve the performance of the Montgomery reduction by taking advantage of the Karatsuba technique. We divide the Montgomery reduction into two sub-parts, including one for the conventional Montgomery reduction and the other one for Karatsuba-aided multiplication. This approach reduces the multiplication complexity of n-limb Montgomery reduction from θ(n2 + n) to asymptotic complexity θ(7n2/8 + n). Our practical implementation results over an 8-bit microcontroller also show performance enhancements by 11%.
KW - Karatsuba multiplication
KW - Montgomery reduction
KW - Public key cryptography
KW - Software implementation
UR - http://www.scopus.com/inward/record.url?scp=84974559415&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84974559415&partnerID=8YFLogxK
U2 - 10.1145/2890502
DO - 10.1145/2890502
M3 - Article
VL - 15
JO - Transactions on Embedded Computing Systems
JF - Transactions on Embedded Computing Systems
SN - 1539-9087
IS - 3
M1 - 58
ER -