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We all know that block Korkine-Zolotarev (BKZ) algorithm is essentially a deterministic lattice reduction algorithm. However, in the actual implementation, the BKZ algorithm contains some randomization, For example, the actual algorithm will do some random unimodular transformations on the lattice basis in order to obtain a better reduced basis. I wonder if this subtle change will make a big difference to the final output. Does it?

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  • $\begingroup$ How would one quantify such difference? $\endgroup$
    – Rodrigo de Azevedo
    Commented Jul 14, 2023 at 9:43
  • $\begingroup$ one quantity is using the length of the shortest vector in the reduced basis $\endgroup$
    – constantine
    Commented Jul 14, 2023 at 11:40

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