> For the complete documentation index, see [llms.txt](https://cryptohack.gitbook.io/cryptobook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cryptohack.gitbook.io/cryptobook/polynomials-with-shared-roots.md).

# Polynomials With Shared Roots

* Polynomial GCD
  * Euclidean GCD
  * Half-GCD for speed when e=0x10001
  * demo application for that one RSA related message attack?
* Resultant
  * eliminate multivariate polynomials at the expense of increasing polynomial degree
  * demo application for that one RSA Coppersmith short padding related message attack?
* Groebner Basis
  * what if you did GCD and Resultants at the same time, like whoa
  * and what if it took forever to run!