Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Grobner bases
Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Grobner bases
复制标题
DOI：
10.1007/978-3-540-45146-4_3
复制
发表时间：
2003-01-01
期刊：
影响因子：
--
通讯作者：
Joux, A
中科院分区：
文献类型：
--
作者：
Faugère, JC;Joux, A
In this paper, we review and explain the existing algebraic cryptanalysis of multivariate cryptosystems from the hidden field equation (HFE) family. These cryptanalysis break cryptosystems in the HFE family by solving multivariate systems of equations. In this paper we present a new and efficient attack of this cryptosystem based on fast algorithms for computing Grobner basis. In particular it was was possible to break the first HFE challenge (80 bits) in only two days of CPU time by using the new algorithm F5 implemented in C.From a theoretical point of view we study the algebraic properties of the equations produced by instance of the HFE cryptosystems and show why they yield systems of equations easier to solve than random systems of quadratic equations of the same sizes. Moreover we are able to bound the maximal degree occuring in the Grobner basis computation.As a consequence, we gain a deeper understanding of the algebraic cryptanalysis against these cryptosystems. We use this understanding to devise a specific algorithm based on sparse linear algebra. In general, we conclude that the cryptanalysis of HFE can be performed in polynomial time. We also revisit the security estimates for existing schemes in the HFE family.
