Mixed bases for efficient inversion in F((2 2) 2)2 and conversion matrices of subbytes of AES

Yasuyuki Nogami, Kenta Nekado, Tetsumi Toyota, Naoto Hongo, Yoshitaka Morikawa

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A lot of improvements and optimizations for the hardware implementation of SubBytes of Rijndael, in detail inversion in F2 8 have been reported. Instead of the Rijndael original F2 8 , it is known that its isomorphic tower field F((2 2) 2)2 has a more efficient inversion. Then, some conversion matrices are also needed for connecting these isomorphic binary fields. According to the previous works, it is said that the number of 1's in the conversion matrices is preferred to be small; however, they have not focused on the Hamming weights of the row vectors of the matrices. It plays an important role for the calculation architecture, in detail critical path delays. This paper shows the existence of efficient conversion matrices whose row vectors all have the Hamming weights less than or equal to 4. They are introduced as quite rare cases. Then, it is pointed out that such efficient conversion matrices can connect the Rijndael original F2 8 to some less efficient inversions in F((2 2)2)2 but not to the most efficient ones. In order to overcome these inconveniences, this paper next proposes a technique called mixed bases. For the towerings, most of previous works have used several kinds of bases such as polynomial and normal bases in mixture. Different from them, this paper proposes another mixture of bases that contributes to the reduction of the critical path delay of SubBytes. Then, it is shown that the proposed mixture contributes to the efficiencies of not only inversion in F((2 2)2)2 but also conversion matrices between the isomorphic fields F2 8 and F((2 2)2)2 .

Original languageEnglish
Pages (from-to)1318-1327
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE94-A
Issue number6
DOIs
Publication statusPublished - Jun 2011

Fingerprint

Inversion
Rijndael
Row vector
Hamming Weight
Critical Path
Isomorphic
Normal Basis
Polynomial Basis
Hardware Implementation
Less than or equal to
Towers
Polynomials
Binary
Hardware
Optimization

Keywords

  • AES
  • Bases
  • Conversion matrix
  • Inversion
  • Towering

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics
  • Signal Processing

Cite this

Mixed bases for efficient inversion in F((2 2) 2)2 and conversion matrices of subbytes of AES. / Nogami, Yasuyuki; Nekado, Kenta; Toyota, Tetsumi; Hongo, Naoto; Morikawa, Yoshitaka.

In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E94-A, No. 6, 06.2011, p. 1318-1327.

Research output: Contribution to journalArticle

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