Highly efficient GF(28) inversion circuit based on redundant GF arithmetic and its application to AES design

Rei Ueno, Naofumi Homma, Yukihiro Sugawara, Yasuyuki Nogami, Takafumi Aoki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Citations (Scopus)

Abstract

This paper proposes a compact and efficient GF(28) inversion circuit design based on a combination of non-redundant and redundant Galois Field (GF) arithmetic. The proposed design utilizes redundant GF representations, called Polynomial Ring Representation (PRR) and Redundantly Represented Basis (RRB), to implement GF(28) inversion using a tower field GF((24)2). In addition to the redundant representations, we introduce a specific normal basis that makes it possible to map the former components for the 16th and 17th powers of input onto logic gates in an efficient manner. The latter components for GF(24) inversion and GF(24) multiplication are then implemented by PRR and RRB, respectively. The flexibility of the redundant representations provides efficient mappings from/to the GF(28). This paper also evaluates the efficacy of the proposed circuit by means of gate counts and logic synthesis with a 65 nm CMOS standard cell library and comparisons with conventional circuits, including those with tower fields GF(((22)2)2). Consequently, we show that the proposed circuit achieves approximately 40% higher efficiency in terms of area-time product than the conventional best GF(((22)2)2) circuit excluding isomorphic mappings. We also demonstrate that the proposed circuit achieves the best efficiency (i. e., area-time product) for an AES encryption S-Box circuit including isomorphic mappings.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages63-80
Number of pages18
Volume9293
ISBN (Print)9783662483237
DOIs
Publication statusPublished - 2015
EventInternational Workshop on Cryptographic Hardware and Embedded Systems, CHES 2015 - Saint-Malo, France
Duration: Sep 13 2015Sep 16 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9293
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

OtherInternational Workshop on Cryptographic Hardware and Embedded Systems, CHES 2015
CountryFrance
CitySaint-Malo
Period9/13/159/16/15

Fingerprint

Galois field
Inversion
Networks (circuits)
Towers
Polynomial ring
Polynomials
Logic gates
Isomorphic
Design
Logic Synthesis
Normal Basis
Cryptography
S-box
Circuit Design
Encryption
High Efficiency
Efficacy
Multiplication
Count
Flexibility

Keywords

  • AES
  • Compact hardware implementation
  • GF(2) inversion
  • S-Box

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ueno, R., Homma, N., Sugawara, Y., Nogami, Y., & Aoki, T. (2015). Highly efficient GF(28) inversion circuit based on redundant GF arithmetic and its application to AES design. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9293, pp. 63-80). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9293). Springer Verlag. https://doi.org/10.1007/978-3-662-48324-4_4

Highly efficient GF(28) inversion circuit based on redundant GF arithmetic and its application to AES design. / Ueno, Rei; Homma, Naofumi; Sugawara, Yukihiro; Nogami, Yasuyuki; Aoki, Takafumi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9293 Springer Verlag, 2015. p. 63-80 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9293).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ueno, R, Homma, N, Sugawara, Y, Nogami, Y & Aoki, T 2015, Highly efficient GF(28) inversion circuit based on redundant GF arithmetic and its application to AES design. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 9293, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9293, Springer Verlag, pp. 63-80, International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2015, Saint-Malo, France, 9/13/15. https://doi.org/10.1007/978-3-662-48324-4_4
Ueno R, Homma N, Sugawara Y, Nogami Y, Aoki T. Highly efficient GF(28) inversion circuit based on redundant GF arithmetic and its application to AES design. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9293. Springer Verlag. 2015. p. 63-80. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-48324-4_4
Ueno, Rei ; Homma, Naofumi ; Sugawara, Yukihiro ; Nogami, Yasuyuki ; Aoki, Takafumi. / Highly efficient GF(28) inversion circuit based on redundant GF arithmetic and its application to AES design. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9293 Springer Verlag, 2015. pp. 63-80 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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