LLL_lt.h File Reference

Static functions that are slightly modified versions of the LLL and BKZ functions of NTL. More...

Namespaces
namespace	NTL
	These functions are in the NTL namespace.

Functions
long	NTL::LLL_FP_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_double *sqlen=0)
	This function is similar to LLL_FP in NTL, but only the first r rows and first c columns of the matrix B are considered, a basis is built for the lattice generated by these (partial) rows, and the square lengths of the returned basis vectors are returned in sqlen.
long	NTL::BKZ_FP_lt (mat_ZZ &BB, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_double *sqlen=0)
	This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FPInt above.
long	NTL::LLL_XD_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_xdouble *sqlen=0)
long	NTL::BKZ_XD_lt (mat_ZZ &BB, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_xdouble *sqlen=0)
	This function is similar to BKZ_XD in NTL, with the same modifications as in LLL_FPInt above.
long	NTL::LLL_QP_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_quad_float *sqlen=0)
long	NTL::BKZ_QP_lt (mat_ZZ &BB, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_quad_float *sqlen=0)
	This function is similar to BKZ_FP in NTL, with the same modifications as in LLL_FPInt above.
long	NTL::LLL_RR_lt (mat_ZZ &B, double delta=0.99, long r=0, long c=0, vec_RR *sqlen=0)
long	NTL::BKZ_RR_lt (mat_ZZ &B, double delta=0.99, long blocksize=10, long prune=0, long r=0, long c=0, vec_RR *sqlen=0)
	These two functions are wrappers of BKZ_RR in NTL, with the same modifications as in LLL_RR_lt above.

Detailed Description

Static functions that are slightly modified versions of the LLL and BKZ functions of NTL.

With the modified functions, it is possible to apply the reductions only to an upper-left corner of the basis matrix, i.e., only the first r rows and first c columns of the matrix B. The other elements of B are ignored. The basis is returned in the upper left corner of B, with the shortest basis vector always in the first row. This differs from the LLL_FP functions, which returns the zero vectors at the top. If r=0, then all the rows of the IntMat object are taken. If c=0, then all the columns are taken. With this added flexibility the same block of memory can be reused for millions of lattices even if their bases have different dimensions. The square lengths of the returned basis vectors are also returned in the double vector sqlen, in sqlen[0],..., sqlen[d-1] if this vector given. The indices of B and sqlen start at 0. Each function returns the dimension of the computed basis (number of independent rows).