Hidden Field Equations ||This article may require cleanup to
meet Wikipedia's quality standards. (January 2009)| Hidden
Fields Equations (HFE) is a public key cryptosystem which was
introduced at Eurocrypt in 1996 and proposed by (French) Jacques
Patarin following the idea of the Matsumoto and Imai system. HFE
is also known as HFE trapdoor function. It is based on
polynomials over finite fields of different size to disguise the
relationship between the private key and public key. HFE is in
fact a family which consists of basic HFE and combinatorial
versions of HFE. The HFE family of cryptosystems is based on the
hardness of the problem of finding solutions to a system of
multivariate quadratic equations (the so called MQ problem)
since it uses private affine transformations to hide the
extension field and the private polynomials. Hidden Field
Equations also have been used to construct digital signature
schemes, e.g. Quartz and Sflash. One of the central notions to
understand how Hidden Field Equations work is