In A Course in Mathematical Cryptography, by Gilbert Baumslag, it is stated that

...breaking many types of cryptosystems can be reduced to solving large systems of polynomials equations over finite fields.

That is, *algebraic varieties*.

In another excerpt:

After seeing the difficulties involved in using (commutative) Gröbner bases for constructing new cryptosystems, let us turn the tables and try to use Gröbner bases to break existing cryptosystems. This topic is known as **algebraic attacks**...

#algebra

#grobner

#cryptography