A Course in Mathematical Cryptography

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 + ··· + c_st_s whose coefficients c_i are taken in a field K and where the elements t_i are terms, that is power products of indeterminates x_i. The set of all polynomials of this form is called the polynomial ring P = K[x₁,..., x_n]. 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 ...