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XOR-Counts and Lightweight Multiplication with Fixed Elements in Binary Finite Fields

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Advances in Cryptology – EUROCRYPT 2019 (EUROCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11476))

Abstract

XOR-metrics measure the efficiency of certain arithmetic operations in binary finite fields. We prove some new results about two different XOR-metrics that have been used in the past. In particular, we disprove a conjecture from [10]. We consider implementations of multiplication with one fixed element in a binary finite field. Here we achieve a complete characterization of all elements whose multiplication matrix can be implemented using exactly 2 XOR-operations, confirming a conjecture from [2]. Further, we provide new results and examples in more general cases, showing that significant improvements in implementations are possible.

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Acknowledgments

The author wishes to thank the anonymous referees for their comments that improved especially the introduction considerably and helped to set this work into context with existing literature.

I also thank Gohar Kyureghyan for many discussions and help with structuring this paper.

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Authors and Affiliations

  1. University of Rostock, Rostock, Germany

    Lukas Kölsch

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  1. Lukas Kölsch
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Correspondence to Lukas Kölsch .

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Editors and Affiliations

  1. Technion, Haifa, Israel

    Yuval Ishai

  2. COSIC Group, KU Leuven, Heverlee, Belgium

    Vincent Rijmen

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Kölsch, L. (2019). XOR-Counts and Lightweight Multiplication with Fixed Elements in Binary Finite Fields. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11476. Springer, Cham. https://doi.org/10.1007/978-3-030-17653-2_10

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  • DOI: https://doi.org/10.1007/978-3-030-17653-2_10

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  • Online ISBN: 978-3-030-17653-2

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