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On Equivalence Classes of Boolean Functions

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Information Security and Cryptology - ICISC 2010 (ICISC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6829))

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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 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.

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Author information

Authors and Affiliations

  1. The Shanghai Key Lab of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, 200433, P.R. China

    Qichun Wang

  2. Dept. of Electrical and Information Technology, Lund University, P.O. Box 118, 221 00, Lund, Sweden

    Qichun Wang & Thomas Johansson

Authors
  1. Qichun Wang
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  2. Thomas Johansson
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Editor information

Editors and Affiliations

  1. Department of IT Convergence Application Engineering, Pukyong National University, 599-1 Daeyeon 3-Dong Namgu, 608-737, Busan, Republic of Korea

    Kyung-Hyune Rhee

  2. Department of Computer Science and Information Technology, INHA University, 253 Yonghyun-dong, Nam-gu, 402-751, Incheon, Republic of Korea

    DaeHun Nyang

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Wang, Q., Johansson, T. (2011). On Equivalence Classes of Boolean Functions. In: Rhee, KH., Nyang, D. (eds) Information Security and Cryptology - ICISC 2010. ICISC 2010. Lecture Notes in Computer Science, vol 6829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24209-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-24209-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24208-3

  • Online ISBN: 978-3-642-24209-0

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