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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.7 pp.1007-1010

- Publication Date
- 2023/07/01

- Publicized
- 2023/01/18

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2022EAL2095

- Type of Manuscript
- LETTER

- Category
- Cryptography and Information Security

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},}

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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 -