August 2011
Intermediate to advanced
332 pages
9h 10m
English
Content preview from Lattice Basis Reduction
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136 Lattice Basis Reduction
t
∗
.
.
.
1
.
.
.
.
.
.
.
.
.
∗
t/X
dh−1
1
M
O
.
.
.
M
h−1
7−→
C
0
O
1
∗
.
.
.
1
C 7−→ C
′
FIGURE 8.3
Row operations transforming C to C
′
By the definition of X we have |x
0
| < X and hence
|s|
2
<
dh
X
k=1
t
2
= dht
2
= 1,
since t = 1 /
√
dh.
Since p(x) is a monic polynomial, s o is q
ij
(x) for all i and j. It follows
that the bottom d(h−1) rows of the upper right block of C form an uppe r
triangular ma trix with every diag onal entry equal to 1. Therefore we c an
perform ele mentary row operations on C and obtain a new matrix C
′
in which
the upper right dh × d(h−1) block is the zero matrix and the lower right
d(h−1) × d(h−1) block is the ...
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