Improved modular multiplication for optimal prime fields

Hwajeong Seo; Zhe Liu; Yasuyuki Nogami; Jongseok Choi; Howon Kim

doi:10.1007/978-3-319-15087-1_12

Improved modular multiplication for optimal prime fields

Hwajeong Seo, Zhe Liu, Yasuyuki Nogami, Jongseok Choi, Howon Kim

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Optimal Prime Fields (OPFs) are considered to be one of the best choices for lightweight elliptic curve cryptography implementation on resource-constraint embedded processors. In this paper, we revisit efficient implementation of the modular arithmetic over the special prime fields, and present improved implementation of modular multiplication for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) method. OPF-CIOC method follows the general idea of (consecutive) operand caching technique, but has been carefully optimized and redesigned for Montgomery multiplication in an integrated fashion. We then evaluate the practical performance of proposed method on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC method outperforms the previous best known results in ACNS’14 by a factor of 5%. Furthermore, our method is implemented in a regular way which helps to reduce the leakage of side-channel information.

Original language	English
Title of host publication	Information Security Applications - 15th International Workshop, WISA 2014, Revised Selected Papers
Editors	Kyung-Hyune Rhee, Jeong Hyun Yi
Publisher	Springer Verlag
Pages	150-161
Number of pages	12
ISBN (Electronic)	9783319150864
DOIs	https://doi.org/10.1007/978-3-319-15087-1_12
Publication status	Published - 2015
Event	15th International Workshop on Information Security Applications, WISA 2014 - , Korea, Republic of Duration: Aug 25 2014 → Aug 27 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8909
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	15th International Workshop on Information Security Applications, WISA 2014
Country	Korea, Republic of
Period	8/25/14 → 8/27/14

Keywords

Consecutive operand caching
Embedded processors
Montgomery multiplication
Operand caching
Optimal prime fields
Public key cryptography

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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Seo, H., Liu, Z., Nogami, Y., Choi, J., & Kim, H. (2015). Improved modular multiplication for optimal prime fields. In K-H. Rhee, & J. H. Yi (Eds.), Information Security Applications - 15th International Workshop, WISA 2014, Revised Selected Papers (pp. 150-161). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8909). Springer Verlag. https://doi.org/10.1007/978-3-319-15087-1_12

Improved modular multiplication for optimal prime fields. / Seo, Hwajeong; Liu, Zhe; Nogami, Yasuyuki; Choi, Jongseok; Kim, Howon.

Information Security Applications - 15th International Workshop, WISA 2014, Revised Selected Papers. ed. / Kyung-Hyune Rhee; Jeong Hyun Yi. Springer Verlag, 2015. p. 150-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8909).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Seo, H, Liu, Z, Nogami, Y, Choi, J & Kim, H 2015, Improved modular multiplication for optimal prime fields. in K-H Rhee & JH Yi (eds), Information Security Applications - 15th International Workshop, WISA 2014, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8909, Springer Verlag, pp. 150-161, 15th International Workshop on Information Security Applications, WISA 2014, Korea, Republic of, 8/25/14. https://doi.org/10.1007/978-3-319-15087-1_12

Seo H, Liu Z, Nogami Y, Choi J, Kim H. Improved modular multiplication for optimal prime fields. In Rhee K-H, Yi JH, editors, Information Security Applications - 15th International Workshop, WISA 2014, Revised Selected Papers. Springer Verlag. 2015. p. 150-161. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-15087-1_12

Seo, Hwajeong ; Liu, Zhe ; Nogami, Yasuyuki ; Choi, Jongseok ; Kim, Howon. / Improved modular multiplication for optimal prime fields. Information Security Applications - 15th International Workshop, WISA 2014, Revised Selected Papers. editor / Kyung-Hyune Rhee ; Jeong Hyun Yi. Springer Verlag, 2015. pp. 150-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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keywords = "Consecutive operand caching, Embedded processors, Montgomery multiplication, Operand caching, Optimal prime fields, Public key cryptography",

author = "Hwajeong Seo and Zhe Liu and Yasuyuki Nogami and Jongseok Choi and Howon Kim",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.; 15th International Workshop on Information Security Applications, WISA 2014 ; Conference date: 25-08-2014 Through 27-08-2014",

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N2 - Optimal Prime Fields (OPFs) are considered to be one of the best choices for lightweight elliptic curve cryptography implementation on resource-constraint embedded processors. In this paper, we revisit efficient implementation of the modular arithmetic over the special prime fields, and present improved implementation of modular multiplication for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) method. OPF-CIOC method follows the general idea of (consecutive) operand caching technique, but has been carefully optimized and redesigned for Montgomery multiplication in an integrated fashion. We then evaluate the practical performance of proposed method on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC method outperforms the previous best known results in ACNS’14 by a factor of 5%. Furthermore, our method is 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 implementation on resource-constraint embedded processors. In this paper, we revisit efficient implementation of the modular arithmetic over the special prime fields, and present improved implementation of modular multiplication for OPFs, called Optimal Prime Field Coarsely Integrated Operand Caching (OPF-CIOC) method. OPF-CIOC method follows the general idea of (consecutive) operand caching technique, but has been carefully optimized and redesigned for Montgomery multiplication in an integrated fashion. We then evaluate the practical performance of proposed method on representative 8-bit AVR processor. Experimental results show that the proposed OPF-CIOC method outperforms the previous best known results in ACNS’14 by a factor of 5%. Furthermore, our method is implemented in a regular way which helps to reduce the leakage of side-channel information.

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Improved modular multiplication for optimal prime fields

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