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International Conference on Cryptology and Network Security

CANS 2012: Cryptology and Network Security pp 296–309Cite as

Some Representations of the S-Box of Camellia in GF(((22)2)2)

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7712))

Abstract

Substitution Box (S-box) is usually the most complex module in some block ciphers. Some prominent ciphers such as AES and Camellia use S-boxes, which are affine equivalents of a multiplicative inverse in small finite fields. This manuscript describes mathematical representations of the Camellia S-box by using composite fields such as polynomial, normal or mixed. An optimized hardware implementation typically aims to reduce the number of gates to be used. Our theoretical design with composite normal bases allows saving gates in the critical path by using 19 XOR gates, 4 AND gates and 2 NOT gates. With composite mixed bases, the critical path has 2 XOR gates more than the representation with composite normal bases. Redundancies found in the affine transformation matrix that form the composite fields were eliminated. For mixed bases, new Algebraic Normal Form identities were obtained to compute the inner composite multiplicative inverse, reducing the critical path of the complete implementation of the Camellia S-box. These constructions were translated into transistor-gate architectures for hardware representations by using Electric VLSI [29] under MOSIS C5 process [17], [18], thus obtaining the corresponding schematic models.

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Authors and Affiliations

  1. Tecnológico de Monterrey, Monterrey Campus, 2501, Garza Sada Sur, Tecnológico, Monterrey, Mexico

    Alberto F. Martínez-Herrera, J. Carlos Mex-Perera & Juan A. Nolazco-Flores

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  1. Alberto F. Martínez-Herrera
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  2. J. Carlos Mex-Perera
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  3. Juan A. Nolazco-Flores
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Editors and Affiliations

  1. Department of Computing, Macquarie University, 2109, Sydney, NSW, Australia

    Josef Pieprzyk

  2. System Security Lab., Technische Universität Darmstadt, Darmstadt, Germany

    Ahmad-Reza Sadeghi

  3. Department of Computing, University of Surrey, GU2 7XH, Guildford, UK

    Mark Manulis

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Martínez-Herrera, A.F., Mex-Perera, J.C., Nolazco-Flores, J.A. (2012). Some Representations of the S-Box of Camellia in GF(((22)2)2). In: Pieprzyk, J., Sadeghi, AR., Manulis, M. (eds) Cryptology and Network Security. CANS 2012. Lecture Notes in Computer Science, vol 7712. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35404-5_22

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  • DOI: https://doi.org/10.1007/978-3-642-35404-5_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35403-8

  • Online ISBN: 978-3-642-35404-5

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