Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes)

Athmane Seghier; Jianxin Li

doi:10.1007/978-3-030-41579-2_24

Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes)

Athmane Seghier^*
, Jianxin Li

^*Corresponding author for this work

School of Computer Science and Engineering

Beihang University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Boolean functions and their generalization Vectorial Boolean functions or Substitution Boxes (S-Boxes) have attracted much attention in the domain of modern block ciphers that use only these elements to provide the necessary confusion against the cryptanalysis attacks. Thus, a significant number of research has been done to construct cryptographically strong Boolean functions and S-Boxes. Among these researches, several heuristics were applied and therefore the hill climbing heuristic was largely investigated. In this paper, we propose a new variant of Hill Climbing heuristic called Parallel Steepest Ascent Hill Climbing to construct Boolean functions and (formula presented) S-Boxes through the progressive construction and incorporation of their m coordinate Boolean functions. The obtained results demonstrate that this new variant provides solutions with high cryptographic properties.

Original language	English
Title of host publication	Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers
Editors	Jianying Zhou, Xiapu Luo, Qingni Shen, Zhen Xu
Publisher	Springer
Pages	413-429
Number of pages	17
ISBN (Print)	9783030415785
DOIs	https://doi.org/10.1007/978-3-030-41579-2_24
State	Published - 2020
Event	21st International Conference on Information and Communications Security, ICICS 2019 - Beijing, China Duration: 15 Dec 2019 → 17 Dec 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11999 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	21st International Conference on Information and Communications Security, ICICS 2019
Country/Territory	China
City	Beijing
Period	15/12/19 → 17/12/19

Keywords

Boolean functions
Cost function
Hill Climbing
S-Boxes

Access to Document

10.1007/978-3-030-41579-2_24

Cite this

Seghier, A., & Li, J. (2020). Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes). In J. Zhou, X. Luo, Q. Shen, & Z. Xu (Eds.), Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers (pp. 413-429). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11999 LNCS). Springer. https://doi.org/10.1007/978-3-030-41579-2_24

Seghier, Athmane ; Li, Jianxin. / Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes). Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers. editor / Jianying Zhou ; Xiapu Luo ; Qingni Shen ; Zhen Xu. Springer, 2020. pp. 413-429 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{82c8bb79884d438b9b9ffe8708b73ab0,

title = "Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes)",

abstract = "Boolean functions and their generalization Vectorial Boolean functions or Substitution Boxes (S-Boxes) have attracted much attention in the domain of modern block ciphers that use only these elements to provide the necessary confusion against the cryptanalysis attacks. Thus, a significant number of research has been done to construct cryptographically strong Boolean functions and S-Boxes. Among these researches, several heuristics were applied and therefore the hill climbing heuristic was largely investigated. In this paper, we propose a new variant of Hill Climbing heuristic called Parallel Steepest Ascent Hill Climbing to construct Boolean functions and (formula presented) S-Boxes through the progressive construction and incorporation of their m coordinate Boolean functions. The obtained results demonstrate that this new variant provides solutions with high cryptographic properties.",

keywords = "Boolean functions, Cost function, Hill Climbing, S-Boxes",

author = "Athmane Seghier and Jianxin Li",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 21st International Conference on Information and Communications Security, ICICS 2019 ; Conference date: 15-12-2019 Through 17-12-2019",

year = "2020",

doi = "10.1007/978-3-030-41579-2\_24",

language = "英语",

isbn = "9783030415785",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

pages = "413--429",

editor = "Jianying Zhou and Xiapu Luo and Qingni Shen and Zhen Xu",

booktitle = "Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers",

address = "德国",

}

Seghier, A & Li, J 2020, Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes). in J Zhou, X Luo, Q Shen & Z Xu (eds), Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11999 LNCS, Springer, pp. 413-429, 21st International Conference on Information and Communications Security, ICICS 2019, Beijing, China, 15/12/19. https://doi.org/10.1007/978-3-030-41579-2_24

Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes). / Seghier, Athmane; Li, Jianxin.
Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers. ed. / Jianying Zhou; Xiapu Luo; Qingni Shen; Zhen Xu. Springer, 2020. p. 413-429 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11999 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes)

AU - Seghier, Athmane

AU - Li, Jianxin

PY - 2020

Y1 - 2020

N2 - Boolean functions and their generalization Vectorial Boolean functions or Substitution Boxes (S-Boxes) have attracted much attention in the domain of modern block ciphers that use only these elements to provide the necessary confusion against the cryptanalysis attacks. Thus, a significant number of research has been done to construct cryptographically strong Boolean functions and S-Boxes. Among these researches, several heuristics were applied and therefore the hill climbing heuristic was largely investigated. In this paper, we propose a new variant of Hill Climbing heuristic called Parallel Steepest Ascent Hill Climbing to construct Boolean functions and (formula presented) S-Boxes through the progressive construction and incorporation of their m coordinate Boolean functions. The obtained results demonstrate that this new variant provides solutions with high cryptographic properties.

AB - Boolean functions and their generalization Vectorial Boolean functions or Substitution Boxes (S-Boxes) have attracted much attention in the domain of modern block ciphers that use only these elements to provide the necessary confusion against the cryptanalysis attacks. Thus, a significant number of research has been done to construct cryptographically strong Boolean functions and S-Boxes. Among these researches, several heuristics were applied and therefore the hill climbing heuristic was largely investigated. In this paper, we propose a new variant of Hill Climbing heuristic called Parallel Steepest Ascent Hill Climbing to construct Boolean functions and (formula presented) S-Boxes through the progressive construction and incorporation of their m coordinate Boolean functions. The obtained results demonstrate that this new variant provides solutions with high cryptographic properties.

KW - Boolean functions

KW - Cost function

KW - Hill Climbing

KW - S-Boxes

UR - https://www.scopus.com/pages/publications/85081170626

U2 - 10.1007/978-3-030-41579-2_24

DO - 10.1007/978-3-030-41579-2_24

M3 - 会议稿件

AN - SCOPUS:85081170626

SN - 9783030415785

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 413

EP - 429

BT - Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers

A2 - Zhou, Jianying

A2 - Luo, Xiapu

A2 - Shen, Qingni

A2 - Xu, Zhen

PB - Springer

T2 - 21st International Conference on Information and Communications Security, ICICS 2019

Y2 - 15 December 2019 through 17 December 2019

ER -

Seghier A, Li J. Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes). In Zhou J, Luo X, Shen Q, Xu Z, editors, Information and Communications Security - 21st International Conference, ICICS 2019, Revised Selected Papers. Springer. 2020. p. 413-429. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-41579-2_24

Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes)

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this