TD: le problème des pannes byzantines.

n n
n−1
n f
`0`1`n−1
h i h i
δ
P0
`0
`0, . . . , `3`2
L
v
0
1
2
v =v
vv
v
v
v
0v
v
0
1
3
2
3
v =v v = v
0
L
L
1
3
L
2
v
v
00
1
3
2
3
v =v v = v
0
L
L
1
3
L
2
L
v =v
0
1
2
v =v
v =v
v =v
v =v
v =y
v =z
yz
v
v

`0hvi`1`2`3
`2`3`1hvi
`2hvi`3`1v=majorite(v, v, v)
`1hvi`3hyi`2v=majorite(v, y, v)
`3hvi`1hxi`2v=majorite(v, x, v)
`1`2v `0
n m n > 3m
m= 0
`0hvi
`jhvivj=v vj=DEF
m m > 0n > 3m > 0
`0hvi
`j
hvivj=v vj=DEF
vj
n−2
`ij6=i
vjhvi`i`jvj=DEF
δ
val =majorite(v0, . . . , vn−1)
majorite(v0, . . . , vn−1) = v v
DEF
val
n m 3n>m)
m k n > 2k+m k
n m n > 3m
P0
`0
`0

n
f n ≤3f+ 1
20 1
u
valeur
nn+f
2
f
2f+ 1
n= 4 f= 1
p q