On the (Fast) Algebraic Immunity of Boolean Power Functions

Yusong Du; Baodian Wei; Fangguo Zhang; Huang Zhang

Paper 2015/435

On the (Fast) Algebraic Immunity of Boolean Power Functions

Yusong Du, Baodian Wei, Fangguo Zhang, and Huang Zhang

Abstract

The (fast) algebraic immunity, including (standard) algebraic immunity and the resistance against fast algebraic attacks, has been considered as an important cryptographic property for Boolean functions used in stream ciphers. This paper is on the determination of the (fast) algebraic immunity of a special class of Boolean functions, called Boolean power functions. An n-variable Boolean power function f can be represented as a monomial trace function over finite field GF(2^n). To determine the (fast) algebraic immunity of Boolean power functions one may need the arithmetic in GF(2^n), which may be not computationally efficient compared with the operations over GF(2). We provide two sufficient conditions for Boolean power functions such that their immunities can determined only by the computations in GF(2). We show that Niho functions and a number of odd variables Kasami functions can satisfy the conditions.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Boolean functions
Contact author(s): duyusong @ mail sysu edu cn
History: 2015-05-07: received
Short URL: https://ia.cr/2015/435
License: CC BY

BibTeX

@misc{cryptoeprint:2015/435,
      author = {Yusong Du and Baodian Wei and Fangguo Zhang and Huang Zhang},
      title = {On the (Fast) Algebraic Immunity of Boolean Power Functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/435},
      year = {2015},
      url = {https://eprint.iacr.org/2015/435}
}