TY - RPRT
A1 - Schnorr, Claus Peter
T1 - Fast LLL-type lattice reduction
N2 - 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.
KW - LLL-reduction
KW - SLLL-reduction
KW - length defect
KW - segments
KW - local LLLreduction
KW - Householder reflection
KW - floating point errors
KW - error bounds
Y1 - 2004
UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4284
UR - https://nbn-resolving.org/urn:nbn:de:hebis:30-12071
UR - http://www.mi.informatik.uni-frankfurt.de/research/papers.html
ER -