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A Course in Mathematical Cryptography by Gerhard Rosenberger, Martin Kreuzer, Benjamin Fine, Gilbert Baumslag

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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 ...

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