On equivalence classes of Boolean functions
(2011) ICISC 2010 In Lecture Notes in Computer Science 6829. p.311-324- Abstract
- In FSE 2010, Rønjom and Cid put forward a nonlinear equivalence for Boolean functions and demonstrated that many cryptographic properties are not invariant among functions within the same equivalence class by providing some special examples. Their paper presented the idea and many problems were left open.
In this paper, we investigate equivalence of Boolean functions more deeply using a new method and discuss the number of Boolean functions in each equivalence class. We investigate further the cryptographic properties including algebraic immunity, algebraic degree and nonlinearity of equivalence classes, and deduce tight bounds on them. We find that there are many equivalence classes of Boolean functions with optimum algebraic... (More) - In FSE 2010, Rønjom and Cid put forward a nonlinear equivalence for Boolean functions and demonstrated that many cryptographic properties are not invariant among functions within the same equivalence class by providing some special examples. Their paper presented the idea and many problems were left open.
In this paper, we investigate equivalence of Boolean functions more deeply using a new method and discuss the number of Boolean functions in each equivalence class. We investigate further the cryptographic properties including algebraic immunity, algebraic degree and nonlinearity of equivalence classes, and deduce tight bounds on them. We find that there are many equivalence classes of Boolean functions with optimum algebraic immunity, optimum algebraic degree and a good nonlinearity. Moreover, we discuss how to construct equivalence classes with desired properties and show that it is possible to construct practical Boolean functions such that their equivalence classes have guaranteed cryptographic properties. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1789355
- author
- Wang, Qichun and Johansson, Thomas LU
- organization
- publishing date
- 2011
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Stream ciphers, Boolean functions, Equivalence, Algebraic immunity, Nonlinearity
- host publication
- Information Security and Cryptology - ICISC 2010 : 13th International Conference, Seoul, Korea, December 1-3, 2010, Revised Selected Papers - 13th International Conference, Seoul, Korea, December 1-3, 2010, Revised Selected Papers
- series title
- Lecture Notes in Computer Science
- volume
- 6829
- pages
- 311 - 324
- publisher
- Springer
- conference name
- ICISC 2010
- conference dates
- 2010-12-01 - 2010-12-03
- ISSN
- 0302-9743
- 1611-3349
- ISBN
- 978-3-642-24209-0
- 978-3-642-24208-3
- DOI
- 10.1007/978-3-642-24209-0_21
- language
- English
- LU publication?
- yes
- id
- 836e6eaa-f351-489c-85cf-3877162572eb (old id 1789355)
- date added to LUP
- 2016-04-04 12:51:36
- date last changed
- 2023-09-23 02:53:15
@inbook{836e6eaa-f351-489c-85cf-3877162572eb, abstract = {{In FSE 2010, Rønjom and Cid put forward a nonlinear equivalence for Boolean functions and demonstrated that many cryptographic properties are not invariant among functions within the same equivalence class by providing some special examples. Their paper presented the idea and many problems were left open.<br/><br/>In this paper, we investigate equivalence of Boolean functions more deeply using a new method and discuss the number of Boolean functions in each equivalence class. We investigate further the cryptographic properties including algebraic immunity, algebraic degree and nonlinearity of equivalence classes, and deduce tight bounds on them. We find that there are many equivalence classes of Boolean functions with optimum algebraic immunity, optimum algebraic degree and a good nonlinearity. Moreover, we discuss how to construct equivalence classes with desired properties and show that it is possible to construct practical Boolean functions such that their equivalence classes have guaranteed cryptographic properties.}}, author = {{Wang, Qichun and Johansson, Thomas}}, booktitle = {{Information Security and Cryptology - ICISC 2010 : 13th International Conference, Seoul, Korea, December 1-3, 2010, Revised Selected Papers}}, isbn = {{978-3-642-24209-0}}, issn = {{0302-9743}}, keywords = {{Stream ciphers; Boolean functions; Equivalence; Algebraic immunity; Nonlinearity}}, language = {{eng}}, pages = {{311--324}}, publisher = {{Springer}}, series = {{Lecture Notes in Computer Science}}, title = {{On equivalence classes of Boolean functions}}, url = {{http://dx.doi.org/10.1007/978-3-642-24209-0_21}}, doi = {{10.1007/978-3-642-24209-0_21}}, volume = {{6829}}, year = {{2011}}, }