Chapter

Cryptographic Hardware and Embedded Systems, CHES 2010

Volume 6225 of the series Lecture Notes in Computer Science pp 234-247

Mixed Bases for Efficient Inversion in \({{\mathbb F}{((2^2)^2)}{2}}\) and Conversion Matrices of SubBytes of AES

  • Yasuyuki NogamiAffiliated withGraduate School of Natural Science and Technology, Okayama University
  • , Kenta NekadoAffiliated withGraduate School of Natural Science and Technology, Okayama University
  • , Tetsumi ToyotaAffiliated withGraduate School of Natural Science and Technology, Okayama University
  • , Naoto HongoAffiliated withGraduate School of Natural Science and Technology, Okayama University
  • , Yoshitaka MorikawaAffiliated withGraduate School of Natural Science and Technology, Okayama University

Abstract

A lot of improvements and optimizations for the hardware implementation of SubBytes of Rijndael, in detail inversion in \({\mathbb F}_{2^8}\) have been reported. Instead of the Rijndael original \({\mathbb F}_{2^8}\), it is known that its isomorphic tower field \({{\mathbb F}{((2^2)^2)}{2}}\) has a more efficient inversion. For the towerings, several kinds of bases such as polynomial and normal bases can be used in mixture. Different from the meaning of this mixture of bases, this paper proposes another mixture that contributes to the reduction of the critical path delay of SubBytes. To the \({{\mathbb F}{(2^2)}{2}}\)–inversion architecture, for example, the proposed mixture inputs and outputs elements represented with normal and polynomial bases, respectively.