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description: Algorithmic Number Theory
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# 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!



