1 Tables de hachage

n
0p−1p
m m ≤p
H={ha,b |0< a < p ∧0≤b<p}
ha,b(x) = (((ax +b)modp)modm)+1
i i0ha,b ∈H
ai +b6≡ ai0+b(modp)
i i0
∀0≤u6=v≤p∃!ha,b ∈H, ai +b≡u(modp)∧ai0+b≡v(modp)
q=Pi<i0|{(a, b)|ha,b(i) = ha,b(i0)}|
q≤n(n−1)
2
p(p−1)
m
m=n2|H0|<1
2|H|H0
n2

•
•
hii
mii
•id i=h(id )
j=hi(id )
i
•
H00 ⊆H
n m =n|H00 | ≤ 1
2|H|
f∈H00
niid h(id ) = i
Pini(ni−1)/2< n
p0< a < p
ap−1≡1 mod p
x2≡1 mod p p
x∈ {1,−1}mod p
n n −1=2st s > 1t
bt≡1 mod n
∃0≤r < s, b2rt≡ −1 mod n
∀b∈ {1, . . . , n −1}
n
|B|<1
4|{1, . . . , n −1}|
B={b∈ {1. . . n −1} | }

d=gcd(k, m)d{g, g2, . . . , gm= 1}
xk= 1
p p = 2s0t0t0
x∈ {1, . . . , p −1}
x2st≡ −1 mod p
t
•0r≥s0
•2rgcd(t, t0)r < s0
n f b
f < 1
4
•p2|n p
•n=pq p q
p−1=2s0t0t0p−1=2s00 t00 t00 s0≤s00
x≡1 mod pq x ≡1 mod p x ≡1 mod q
f≤t0t00 +t0t00 + 4t0t00 + 42t0t00 +. . . + 4s0−1t0t00
n−1
f≤t0t00 +t0t00 + 4t0t00 + 42t0t00 +. . . + 4s0−1t0t00
2s0+s00 t0t00 = 2−s0−s00 (1+4s0−1 4−1)
s0< s00
s0=s00 gcd(t, t0)gcd(t, t00 )<1
3t0t00
s0=s00
•n=p1p2. . . pkk≥3
Ax =b x ≥0A
m×n b m x
a= maxi,j (|ai,j |,|bi|)
•
Aixiyixi+yi= 1

•
xmaxixi≤2n2(ma)2m+1
maxixi
M= (ma)mmaxixi≤M
k x
M v1, . . . , vkk A
αi≤MΣiαivi= 0
k×k V vi
tV u = 1 h
m h
•