TY - JOUR
T1 - Montgomery multiplication and squaring for Optimal Prime Fields
AU - Seo, Hwajeong
AU - Liu, Zhe
AU - Nogami, Yasuyuki
AU - Choi, Jongseok
AU - Kim, Howon
N1 - Funding Information:
This work was partly supported by the ICT R&D program of MSIP/IITP [10043907, Development of high performance IoT device and Open Platform with Intelligent Software] and the MSIP (Ministry of Science, ICT and Future Planning) , Korea, under the ITRC (Information Technology Research Center) support program ( NIPA-2014-H0301-14-1048 ) supervised by the NIPA (National IT Industry Promotion Agency) .
Publisher Copyright:
© 2015 Elsevier Ltd
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2015/7/1
Y1 - 2015/7/1
N2 - Optimal Prime Fields (OPFs) are considered to be one of the best choices for lightweight elliptic curve cryptography implementations on resource-constraint embedded processors. In this paper, we revisit the efficient modular arithmetic over the special prime fields, and present improved implementations of modular multiplication and squaring for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) and Coarsely Integrated Sliding Block Doubling (OPF-CISBD) methods. The OPF-CIOC and OPF-CISBD methods follow the general ideas of (consecutive) operand caching and sliding block doubling techniques, respectively. The methods have been carefully optimized and redesigned for Montgomery multiplication and squaring in an integrated fashion. We then evaluate the practical performance of proposed methods on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC and OPF-CISBD methods outperform the previous best known results in ACNS'14 by a factor of 8% and 32%. Furthermore, our methods are implemented in a regular way which helps to reduce the leakage of side-channel information.
AB - Optimal Prime Fields (OPFs) are considered to be one of the best choices for lightweight elliptic curve cryptography implementations on resource-constraint embedded processors. In this paper, we revisit the efficient modular arithmetic over the special prime fields, and present improved implementations of modular multiplication and squaring for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) and Coarsely Integrated Sliding Block Doubling (OPF-CISBD) methods. The OPF-CIOC and OPF-CISBD methods follow the general ideas of (consecutive) operand caching and sliding block doubling techniques, respectively. The methods have been carefully optimized and redesigned for Montgomery multiplication and squaring in an integrated fashion. We then evaluate the practical performance of proposed methods on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC and OPF-CISBD methods outperform the previous best known results in ACNS'14 by a factor of 8% and 32%. Furthermore, our methods are implemented in a regular way which helps to reduce the leakage of side-channel information.
KW - Consecutive operand caching
KW - Embedded processors
KW - Montgomery multiplication
KW - Operand caching
KW - Optimal Prime Fields
KW - Public key cryptography
KW - Sliding block doubling
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U2 - 10.1016/j.cose.2015.03.005
DO - 10.1016/j.cose.2015.03.005
M3 - Article
AN - SCOPUS:84926481872
SN - 0167-4048
VL - 52
SP - 276
EP - 291
JO - Computers and Security
JF - Computers and Security
ER -