The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Laisser nous f être une fonction booléenne dans n variables. La transformée de Möbius et son inverse de f peut décrire les comportements de transformation entre la table de vérité de f et les coefficients des monômes dans la représentation algébrique sous forme normale de f. Dans cette lettre, nous développons la transformée de Möbius et son inverse sous une forme plus généralisée, qui inclut également le résultat connu donné par Reed en 1954. Nous espérons que notre nouveau résultat pourra être utilisé dans la conception de schémas de décodage pour les codes linéaires et le cryptanalyse pour la cryptographie symétrique. Nous appliquons également notre nouveau résultat pour vérifier l’idée de base de l’attaque cube d’une manière très simple, dans laquelle l’attaque cube est une technique puissante de cryptanalyse pour la cryptographie symétrique.
Jianchao ZHANG
Shanghai Jiao Tong University
Deng TANG
Shanghai Jiao Tong University
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Jianchao ZHANG, Deng TANG, "A Note on the Transformation Behaviors between Truth Tables and Algebraic Normal Forms of Boolean Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 7, pp. 1007-1010, July 2023, doi: 10.1587/transfun.2022EAL2095.
Abstract: Let f be a Boolean function in n variables. The Möbius transform and its converse of f can describe the transformation behaviors between the truth table of f and the coefficients of the monomials in the algebraic normal form representation of f. In this letter, we develop the Möbius transform and its converse into a more generalized form, which also includes the known result given by Reed in 1954. We hope that our new result can be used in the design of decoding schemes for linear codes and the cryptanalysis for symmetric cryptography. We also apply our new result to verify the basic idea of the cube attack in a very simple way, in which the cube attack is a powerful technique on the cryptanalysis for symmetric cryptography.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAL2095/_p
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@ARTICLE{e106-a_7_1007,
author={Jianchao ZHANG, Deng TANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Note on the Transformation Behaviors between Truth Tables and Algebraic Normal Forms of Boolean Functions},
year={2023},
volume={E106-A},
number={7},
pages={1007-1010},
abstract={Let f be a Boolean function in n variables. The Möbius transform and its converse of f can describe the transformation behaviors between the truth table of f and the coefficients of the monomials in the algebraic normal form representation of f. In this letter, we develop the Möbius transform and its converse into a more generalized form, which also includes the known result given by Reed in 1954. We hope that our new result can be used in the design of decoding schemes for linear codes and the cryptanalysis for symmetric cryptography. We also apply our new result to verify the basic idea of the cube attack in a very simple way, in which the cube attack is a powerful technique on the cryptanalysis for symmetric cryptography.},
keywords={},
doi={10.1587/transfun.2022EAL2095},
ISSN={1745-1337},
month={July},}
Copier
TY - JOUR
TI - A Note on the Transformation Behaviors between Truth Tables and Algebraic Normal Forms of Boolean Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1007
EP - 1010
AU - Jianchao ZHANG
AU - Deng TANG
PY - 2023
DO - 10.1587/transfun.2022EAL2095
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2023
AB - Let f be a Boolean function in n variables. The Möbius transform and its converse of f can describe the transformation behaviors between the truth table of f and the coefficients of the monomials in the algebraic normal form representation of f. In this letter, we develop the Möbius transform and its converse into a more generalized form, which also includes the known result given by Reed in 1954. We hope that our new result can be used in the design of decoding schemes for linear codes and the cryptanalysis for symmetric cryptography. We also apply our new result to verify the basic idea of the cube attack in a very simple way, in which the cube attack is a powerful technique on the cryptanalysis for symmetric cryptography.
ER -