BKZreduced
BKZreduced refers to a lattice basis that has been reduced by the Block Korkine-Zolotarev (BKZ) algorithm with a specified block size beta. BKZ is a generalization of lattice reduction methods and, for beta equal to 2, it coincides with the familiar LLL reduction. The BKZ algorithm improves a given basis by repeatedly selecting consecutive blocks of beta vectors, projecting the lattice onto the subspace spanned by the block and its complement, and solving a short vector problem within that projected lattice to update the block. Through repeated passes over all blocks, the basis becomes more reduced.
The term “BKZ-reduced” therefore describes a basis that has undergone BKZ reduction with a chosen beta and
BKZ-reduced bases are central to both lattice-based cryptography and lattice-based attacks. A more reduced basis can