Details:
Title  An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography  Author(s)  JeanCharles Faugère, Ludovic Perret  Type  Article in Journal  Abstract  In this paper, we present an efficient and general algorithm for decomposing multivariate polynomials of the same arbitrary degree. This problem, also known as the Functional Decomposition Problem (FDP), is classical in computer algebra. It is the first general method addressing the decomposition of multivariate polynomials (any degree, any number of polynomials). As a byproduct, our approach can be also used to recover an ideal I from its k th power I^k . The complexity of the algorithm depends on the ratio between the number of variables ( n ) and the number of polynomials ( u ). For example, polynomials of degree four can be decomposed in O ( n^12 ) , when this ratio is smaller than 1/2 . This work was initially motivated by a cryptographic application, namely the cryptanalysis of 2 R − schemes. From a cryptographic point of view, the new algorithm is so efficient that the principle of tworound schemes, including 2 R − schemes, becomes useless. Besides, we believe that our algorithm is of independent interest.  Keywords  Multivariate polynomials decomposition, Gröbner bases, Cryptography  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108001818 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  12  Pages  1676  1689  Year  2009  Note  Gröbner Bases in Cryptography, Coding Theory, and Algebraic Combinatorics  Edition  0  Translation 
No  Refereed 
No 
