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 two-round schemes, including 2 R − schemes, becomes useless. Besides, we believe that our algorithm is of independent interest.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.