HFE Polynomial
The private polynomial with degree over is an element of . If the terms of polynomial have at most quadratic terms over then it will keep the public polynomial small. The case that consists of monomials of the form, i.e. with 2 powers of in the exponent is the basic version of HFE, i.e. is chosen as
The degree of the polynomial is also known as security parameter and the bigger its value the better for security since the resulting set of quadratic equations resembles a randomly chosen set of quadratic equations. On the other side large slows down the deciphering. Since is a polynomial of degree at most the inverse of, denoted by can be computed in operations.
Read more about this topic: Hidden Field Equations