ON FUNCTIONAL DECOMPOSITION OF MULTIVARIATE POLYNOMIALS WITH DIFFERENTIATION AND HOMOGENIZATION  

作　　者：Shangwei ZHAO Ruyong FENG Xiao-Shan GAO 

机构地区：[1]Beijing Electronic Science and Technology Institute [2]KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Journal of Systems Science & Complexity》2012年第2期329-347,共19页系统科学与复杂性学报（英文版）

基　　金：partially supported by a National Key Basic Research Project of China under Grant No. 2011CB302400;by a Grant from NSFC with Nos 60821002 and 10901156

摘　　要：This paper gives a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which were proposed by Ye, Dai, and Lam （1999） and were developed by Faugere, Perret （2006, 2008, 2009）. The authors show that a degree proper functional decomposition for a set of randomly decomposable quartic homoge- nous polynomials can be computed using the algorithm with high probability. This solves a conjecture proposed by Ye, Dal, and Lam （1999）. The authors also propose a conjecture which asserts that the decomposition for a set of polynomials can be computed from that of its homogenization and show that the conjecture is valid with high probability for quartic polynomials. Finally, the authors prove that the right decomposition factors for a set of polynomials can be computed from its right decomposition factor space.

关 键 词：Cryptosystem analysis functional decomposition homogeneous polynomials multivariatepolynomial right factor space. 

分 类 号：O174[理学—数学]