We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovasz [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximat

We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovasz [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2exp(O(n)), SLLL-reduction runs in O(n.exp(5+epsilon)) bit operations for every epsilon > 0, compared to O(exp(n7+epsilon)) for the original LLL and to O(exp(n6+epsilon)) for the LLL-algorithms of Schnorr (1988) and Storjohann (1996). We present an even faster algorithm for SLLL-reduction via iterated subsegments running in O(n*exp(3)*log n) arithmetic steps.

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