The Extended Euclidean algorithm calculates an associated factor at each step. It is the final value of this factor, the modular multiplicative inverse, that is the private key—29 in this case.

Les procédés usuels de réduction, et en particulier l'algorithme LLL, deviennent plus performants lorsqu'on les adapte à ces structures, Numerous important lattices (𝔻₄, 𝔼₈, the Coxeter-Todd lattice ...