Details:
Title  Vectorial Boolean functions and induced algebraic equations.  Author(s)  Jovan Dj. Golic  Type  Article in Journal  Abstract  A general mathematical framework behind algebraic cryptanalytic attacks is developed. The framework relates to finding algebraic equations induced by vectorial Boolean functions and, in particular, equations of low algebraic degree. The equations may involve only a subset of input variables and may or may not be conditioned on the values of output variables. In addition, the equations may have a constrained form interesting for the socalled fast algebraic attacks. A possible divideandconquer effect is pointed out and the notion of algebraic immunity order, naturally extending the notion of correlation immunity order, is defined. An application of general results to stream ciphers known as combiners with or without memory, with possibly multiple outputs, is studied in particular detail and the concept of divideandconquer algebraic attacks is introduced. Special properties of combiners with finite input memory, such as nonlinear filter generators, are also established. It is also pointed out that Groumlbner basis algorithms may be used for finding lowdegree induced algebraic equations  ISSN  00189448 
URL 
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1580793 
Language  English  Journal  IEEE Trans. Inf. Theory  Volume  52  Number  2  Pages  528537  Publisher  Institute of Electrical and Electronics Engineers (IEEE), New York, NY  Year  2006  Edition  0  Translation 
No  Refereed 
No 
