Acta Metallurgica Sinica(English letters) ›› 2013, Vol. 20 ›› Issue (3): 73-77.doi: 10.1016/S1005-8885(13)60052-7

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On the construction of odd-variable boolean functions with optimal algebraic immunity

  

  1. 1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 2. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • Received:2012-11-03 Revised:2013-02-03 Online:2013-06-30 Published:2013-06-26
  • Supported by:

    This work was supported by the National Natural Science Foundation of China (61102093, 61170270, 61121061), The Fundamental Research for the Central Universities (BUPT 2012RC0710).

Abstract:

Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.

Key words:

algebraic immunity, Boolean functions, algebraic attacks, annihilators