Constructing Boolean functions with potentially optimal algebraic immunity based on additive decompositions of finite fields (extended abstract) | IEEE Conference Publication | IEEE Xplore

Constructing Boolean functions with potentially optimal algebraic immunity based on additive decompositions of finite fields (extended abstract)


Abstract:

We propose a general approach to construct cryptographic significant Boolean functions of (r + 1)m variables based on the additive decomposition F2rm × F2m of the finite ...Show More

Abstract:

We propose a general approach to construct cryptographic significant Boolean functions of (r + 1)m variables based on the additive decomposition F2rm × F2m of the finite field F2(r+1)m, where r ≥ 1 is odd and m ≥ 3. A class of unbalanced functions is constructed first via this approach, which coincides with a variant of the unbalanced class of generalized Tu-Deng functions in the case r = 1. Functions belonging to this class have high algebraic degree, but their algebraic immunity does not exceed m, which is impossible to be optimal when r > 1. By modifying these unbalanced functions, we obtain a class of balanced functions which have optimal algebraic degree and high nonlinearity (shown by a lower bound we prove). These functions have optimal algebraic immunity provided a combinatorial conjecture on binary strings which generalizes the Tu-Deng conjecture is true. Computer investigations show that, at least for small values of number of variables, functions from this class also behave well against fast algebraic attacks.
Date of Conference: 29 June 2014 - 04 July 2014
Date Added to IEEE Xplore: 11 August 2014
Electronic ISBN:978-1-4799-5186-4

ISSN Information:

Conference Location: Honolulu, HI, USA

References

References is not available for this document.