A note on some algebraic trapdoors for block ciphers

Marco Calderini

doi:10.3934/amc.2018030

Article Contents

2018, Volume 12, Issue 3: 515-524. Doi: 10.3934/amc.2018030

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A note on some algebraic trapdoors for block ciphers

Marco Calderini

Department of Informatics, University of Bergen, Norway

Received: June 2017

Revised: March 2018

Published: July 2018

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Abstract

We provide sufficient conditions to guarantee that a translation based cipher is not vulnerable with respect to the partition-based trapdoor. This trapdoor has been introduced, recently, by Bannier et al. (2016) and it generalizes that introduced by Paterson in 1999. Moreover, we discuss the fact that studying the group generated by the round functions of a block cipher may not be sufficient to guarantee security against these trapdoors for the cipher.

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Mathematics Subject Classification: Primary: 94A60, 20B15; Secondary: 20B35.

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Table 1. AES state

$V_1$	$V_2$	$V_3$	$V_4$
$V_5$	$V_6$	$V_7$	$V_8$
$V_9$	$V_{10}$	$V_{11}$	$V_{12}$
$V_{13}$	$V_{14}$	$V_{15}$	$V_{16}$

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Table 2. AES wall

$ \color{orange}{V_1}$	$V_2$	$V_3$	$V_4$		$\color{orange}{V_1}$	$V_2$	$V_3$	$V_4$		$\color{orange}{V_1}$	$V_2$	$V_3$	$V_4$
$V_5$	$\color{orange}{V_6}$	$V_7$	$V_8$	$\mathop {SR}\limits_ \mapsto $	$\color{orange}{V_5}$	$V_6$	$V_7$	$V_8$	$\mathop {MC}\limits_ \mapsto $	$\color{orange}{V_5}$	$V_6$	$V_7$	$V_8$
$V_9$	$V_{10}$	$\color{orange}{V_{11}}$	$V_{12}$		$\color{orange}{V_9}$	$V_{10}$	$V_{11}$	$V_{12}$		$\color{orange}{V_9}$	$V_{10}$	$V_{11}$	$V_{12}$
$V_{13}$	$V_{14}$	$V_{15}$	$\color{orange}{V_{16}}$		$\color{orange}{V_{13}}$	$V_{14}$	$V_{15}$	$V_{16}$		$\color{orange}{V_{13}}$	$V_{14}$	$V_{15}$	$V_{16}$

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References

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