## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

# 13    Commutative Gröbner Basis Methods

## 13.1    Commutative Gröbner Bases

Besides numbers and group elements, polynomials are natural objects to use in algebraic cryptography. Recall that a polynomial f is a formal linear combination f = c1t1 + ··· + csts whose coefficients ci are taken in a field K and where the elements ti are terms, that is power products of indeterminates xi. The set of all polynomials of this form is called the polynomial ring P = K[x1,..., xn]. This set is a commutative ring with identity. In other words, polynomials can be added and multiplied in a natural way and the usual rules such as the associative and distributive ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required