rs r - - PowerPoint PPT Presentation
rs r t rt
✶ ✴ ✺✷
m c
k ❚✇❡❛❦✿ ✢❡①✐❜✐❧✐t② t♦ t❤❡ ❝✐♣❤❡r ❊❛❝❤ t✇❡❛❦ ❣✐✈❡s ❞✐✛❡r❡♥t ♣❡r♠✉t❛t✐♦♥
✷ ✴ ✺✷
m t c k
✷ ✴ ✺✷
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T ˜ EN,A1
k
˜ EN,A2
k
˜ EN,Aa
k
˜ EN,M⊕
k
˜ EN,M1
k
˜ EN,M2
k
˜ EN,Md
k
✸ ✴ ✺✷
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T ˜ EN,A1
k
˜ EN,A2
k
˜ EN,Aa
k
˜ EN,M⊕
k
˜ EN,M1
k
˜ EN,M2
k
˜ EN,Md
k
✸ ✴ ✺✷
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T ˜ EN,A1
k
˜ EN,A2
k
˜ EN,Aa
k
˜ EN,M⊕
k
˜ EN,M1
k
˜ EN,M2
k
˜ EN,Md
k
✸ ✴ ✺✷
M1 M2 Md C1 C2 Cd ˜ E i,1
k
˜ E i,2
k
˜ E i,d
k
✹ ✴ ✺✷
M1 M2 Md C1 C2 Cd ˜ E i,1
k
˜ E i,2
k
˜ E i,d
k
✹ ✴ ✺✷
M1 M′
2 = M2
Md C1 C′
2
Cd ˜ E i,1
k
˜ E i,2
k
˜ E i,d
k
✹ ✴ ✺✷
M1 M′
2 = M2
Md C1 C′
2
Cd ˜ E i,1
k
˜ E i,2
k
˜ E i,d
k
✹ ✴ ✺✷
config M1 Mℓ iv h
· · · · · · ˜ Econ ˜ Emsg ˜ Emsg ˜ Eout
✺ ✴ ✺✷
config M1 Mℓ iv h
· · · · · · ˜ Econ ˜ Emsg ˜ Emsg ˜ Eout
✺ ✴ ✺✷
✻ ✴ ✺✷
✻ ✴ ✺✷
✼ ✴ ✺✷
✽ ✴ ✺✷
E
P
✾ ✴ ✺✷
m c t
k k m c h(t) h(t)
k
✶✵ ✴ ✺✷
m c 2α3β7γEk(N)
k m c 2α3β7γEk(N) 2α3β7γEk(N)
k
❈❤❛❦r❛❜♦rt② ❛♥❞ ❙❛r❦❛r ❬❈❙✵✻❪✿ ❢♦r ▲❋❙❘
✶✶ ✴ ✺✷
m c 2α3β7γEk(N)
k m c 2α3β7γEk(N) 2α3β7γEk(N)
k
❈❤❛❦r❛❜♦rt② ❛♥❞ ❙❛r❦❛r ❬❈❙✵✻❪✿ ❢♦r ▲❋❙❘
✶✶ ✴ ✺✷
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T ˜ EN,A1
k
˜ EN,A2
k
˜ EN,Aa
k
˜ EN,M⊕
k
˜ EN,M1
k
˜ EN,M2
k
˜ EN,Md
k
✶✷ ✴ ✺✷
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
✶✷ ✴ ✺✷
L = EK(N)
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
✶✷ ✴ ✺✷
L = EK(N)
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
✶✷ ✴ ✺✷
L = EK(N)
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
✶✷ ✴ ✺✷
L = EK(N)
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
✶✷ ✴ ✺✷
L = EK(N)
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
M1 M2 Md C1 C2 Cd ˜ E i,1
k
˜ E i,2
k
˜ E i,d
k ✶✷ ✴ ✺✷
L = EK(N)
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
M1 M2 Md C1 C2 Cd
2L 22L 2dL 2L 22L 2dL
Ek Ek Ek
✶✷ ✴ ✺✷
L = EK(N) L = EK(i)
A1 A2 Aa M1 M2 Md ⊕Mi C1 C2 Cd T
2·32L 2232L 2a32L 2d3L 2L 22L 2dL 2L 22L 2dL
Ek Ek Ek Ek Ek Ek Ek
M1 M2 Md C1 C2 Cd
2L 22L 2dL 2L 22L 2dL
Ek Ek Ek
✶✷ ✴ ✺✷
L = EK(N) L = EK(i)
m c 2α3β7γEk(N)
k m c 2α3β7γEk(N) 2α3β7γEk(N)
k
❈❤❛❦r❛❜♦rt② ❛♥❞ ❙❛r❦❛r ❬❈❙✵✻❪✿ ❢♦r ▲❋❙❘
✶✸ ✴ ✺✷
m c 2α3β7γEk(N)
k m c 2α3β7γEk(N) 2α3β7γEk(N)
k
✶✸ ✴ ✺✷
m c 2α3β7γ(kN ⊕ P(kN))
✶✹ ✴ ✺✷
m c 2α3β7γEk(0) 2α3β7γEk(0)
k
✶✺ ✴ ✺✷
m c 2α3β7γEk(0) 2α3β7γEk(0)
k
m c (2α3β7γ ⊕ 1)k ⊕ 2α3β7γP(k)
✶✺ ✴ ✺✷
m c k
t m c 2α3β7γEk(N) 2α3β7γEk(N)
E
k m c 2α3β7γ(kN ⊕ P(kN))
P
✶✻ ✴ ✺✷
♣❧❛✐♥ ❂ ✜rst r♦✉♥❞✱ ❜♦❧❞ ❂ s❡❝♦♥❞ r♦✉♥❞
m c k
t m c 2α3β7γEk(N) 2α3β7γEk(N)
E
k m c 2α3β7γ(kN ⊕ P(kN))
P
✶✻ ✴ ✺✷
♣❧❛✐♥ ❂ ✜rst r♦✉♥❞✱ ❜♦❧❞ ❂ s❡❝♦♥❞ r♦✉♥❞
✶✼ ✴ ✺✷
m c k
t m c 2α3β7γEk(N) 2α3β7γEk(N)
E
k m c 2α3β7γ(kN ⊕ P(kN))
P
✶✽ ✴ ✺✷
❬▼❡♥✶✺❜❪✱ ❣❡♥❡r❛❧✐③❛t✐♦♥ ♦❢ t❤✐s
♣❧❛✐♥ ❂ ✜rst r♦✉♥❞✱ ❜♦❧❞ ❂ s❡❝♦♥❞ r♦✉♥❞
m c k
t m c 2α3β7γEk(N) 2α3β7γEk(N)
E
k m c 2α3β7γ(kN ⊕ P(kN))
P
✶✽ ✴ ✺✷
♣❧❛✐♥ ❂ ✜rst r♦✉♥❞✱ ❜♦❧❞ ❂ s❡❝♦♥❞ r♦✉♥❞
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
✶ ✏❙t✉♣✐❞✑
✐♥s❡❝✉r❡
✷ ✏◆♦r♠❛❧✑
s✐♥❣❧❡✲❦❡② s❡❝✉r❡
✸ ✏❙tr♦♥❣✑
r❡❧❛t❡❞✲❦❡② s❡❝✉r❡
✶✾ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
✶ ✏❙t✉♣✐❞✑
✐♥s❡❝✉r❡
✷ ✏◆♦r♠❛❧✑
s✐♥❣❧❡✲❦❡② s❡❝✉r❡
✸ ✏❙tr♦♥❣✑
r❡❧❛t❡❞✲❦❡② s❡❝✉r❡
✶✾ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
✶ ✏❙t✉♣✐❞✑ T
− → ✐♥s❡❝✉r❡
✷ ✏◆♦r♠❛❧✑
s✐♥❣❧❡✲❦❡② s❡❝✉r❡
✸ ✏❙tr♦♥❣✑
r❡❧❛t❡❞✲❦❡② s❡❝✉r❡
✶✾ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
✶ ✏❙t✉♣✐❞✑ T
− → ✐♥s❡❝✉r❡
✷ ✏◆♦r♠❛❧✑ T
− → s✐♥❣❧❡✲❦❡② s❡❝✉r❡
✸ ✏❙tr♦♥❣✑
r❡❧❛t❡❞✲❦❡② s❡❝✉r❡
✶✾ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
✶ ✏❙t✉♣✐❞✑ T
− → ✐♥s❡❝✉r❡
✷ ✏◆♦r♠❛❧✑ T
− → s✐♥❣❧❡✲❦❡② s❡❝✉r❡
✸ ✏❙tr♦♥❣✑ T
− → r❡❧❛t❡❞✲❦❡② s❡❝✉r❡
✶✾ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
✷✵ ✴ ✺✷
m 0k ⊕ 0P(k) 0k ⊕ 0P(k)
(0, 0, 0, 0) ∈ T
✷✵ ✴ ✺✷
m P(m) 0k ⊕ 0P(k) 0k ⊕ 0P(k)
(0, 0, 0, 0) ∈ T = ⇒ XPXk((0, 0, 0, 0), m) = P(m)
✷✵ ✴ ✺✷
k 1k ⊕ 0P(k) 1k ⊕ 1P(k)
(0, 0, 0, 0) ∈ T = ⇒ XPXk((0, 0, 0, 0), m) = P(m) (1, 0, 1, 1) ∈ T = ⇒ XPXk((1, 0, 1, 1), 0) = k
✷✵ ✴ ✺✷
3P(k) 1k ⊕ 0P(k) 0k ⊕ 2P(k)
(0, 0, 0, 0) ∈ T = ⇒ XPXk((0, 0, 0, 0), m) = P(m) (1, 0, 1, 1) ∈ T = ⇒ XPXk((1, 0, 1, 1), 0) = k (1, 0, 0, 2) ∈ T = ⇒ XPXk((1, 0, 0, 2), 0) = 3P(k)
✷✵ ✴ ✺✷
3P(k) 1k ⊕ 0P(k) 0k ⊕ 2P(k)
(0, 0, 0, 0) ∈ T = ⇒ XPXk((0, 0, 0, 0), m) = P(m) (1, 0, 1, 1) ∈ T = ⇒ XPXk((1, 0, 1, 1), 0) = k (1, 0, 0, 2) ∈ T = ⇒ XPXk((1, 0, 0, 2), 0) = 3P(k) · · · · · · · · ·
✷✵ ✴ ✺✷
3P(k) 1k ⊕ 0P(k) 0k ⊕ 2P(k)
(0, 0, 0, 0) ∈ T = ⇒ XPXk((0, 0, 0, 0), m) = P(m) (1, 0, 1, 1) ∈ T = ⇒ XPXk((1, 0, 1, 1), 0) = k (1, 0, 0, 2) ∈ T = ⇒ XPXk((1, 0, 0, 2), 0) = 3P(k) · · · · · · · · ·
✷✵ ✴ ✺✷
3P(k) 1k ⊕ 0P(k) 0k ⊕ 2P(k)
(0, 0, 0, 0) ∈ T = ⇒ XPXk((0, 0, 0, 0), m) = P(m) (1, 0, 1, 1) ∈ T = ⇒ XPXk((1, 0, 1, 1), 0) = k (1, 0, 0, 2) ∈ T = ⇒ XPXk((1, 0, 0, 2), 0) = 3P(k) · · · · · · · · ·
✷✵ ✴ ✺✷
✐❢ ✐s ✈❛❧✐❞✱ ❛♥❞ ❢♦r ❛❧❧ t✇❡❛❦s✿ s❡❝✉r✐t② ❛♥❞ ✲r❦✲❙❚P❘P ✲r❦✲❙❚P❘P
✷✶ ✴ ✺✷
✐❢ ✐s ✈❛❧✐❞✱ ❛♥❞ ❢♦r ❛❧❧ t✇❡❛❦s✿ s❡❝✉r✐t② ❛♥❞ ✲r❦✲❙❚P❘P ✲r❦✲❙❚P❘P
✷✶ ✴ ✺✷
✐❢ ✐s ✈❛❧✐❞✱ ❛♥❞ ❢♦r ❛❧❧ t✇❡❛❦s✿ s❡❝✉r✐t② ❛♥❞ ✲r❦✲❙❚P❘P ✲r❦✲❙❚P❘P
✷✶ ✴ ✺✷
✐❢ T ✐s ✈❛❧✐❞✱ ❛♥❞ ❢♦r ❛❧❧ t✇❡❛❦s✿ s❡❝✉r✐t② t12, t22 = 0 ❛♥❞ (t21, t22) = (0, 1) Φ⊕✲r❦✲❙❚P❘P t11, t12, t21, t22 = 0 ΦP ⊕✲r❦✲❙❚P❘P
✷✶ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
m c k k
✷✷ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
m c k k
✷✷ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
m c k k
✷✷ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
m c (2α3β7γ ⊕ 1)k ⊕ 2α3β7γP(k)
✷✸ ✴ ✺✷
m c t11k ⊕ t12P(k) t21k ⊕ t22P(k)
m c (2α3β7γ ⊕ 1)k ⊕ 2α3β7γP(k)
✷✸ ✴ ✺✷
A1 A2 Aa−1 Aa M1 M2 Md M1⊕···⊕Md C1 C2 Cd T
33L 2·33L 2a-233L 2a-134L L 3L 2·3L 2d-13L 2d-132L 2L 22L 2dL 2d-17L
Ek Ek Ek Ek Ek Ek Ek Ek Ek Ek Ek Ek
✷✹ ✴ ✺✷
L = EK(0)
A1 A2 Aa−1 Aa M1 M2 Md M1⊕···⊕Md C1 C2 Cd T
33L 2·33L 2a-233L 2a-134L L 3L 2·3L 2d-13L 2d-132L 2L 22L 2dL 2d-17L
Ek Ek Ek Ek Ek Ek Ek Ek Ek Ek Ek Ek
✷✹ ✴ ✺✷
L = EK(0)
O
2n
s❦
O
2n
s❦
s❦
✲r❦
✲r❦
✲r❦
✷✺ ✴ ✺✷
O
2n
s❦
O
2n
s❦
s❦
O
2n
Φ✲r❦
O
2n
Φ✲r❦
✲r❦
✷✺ ✴ ✺✷
O
2n
s❦
O
2n
s❦
s❦
✲r❦
✲r❦
✲r❦
✷✻ ✴ ✺✷
✲r❦
O
2n
s❦
O
2n
s❦
O
2n
s❦
✲r❦
✲r❦
✲r❦
✷✻ ✴ ✺✷
✲r❦
O
2n
s❦
O
2n
s❦
O
2n
s❦
O
2n
Φ✲r❦
O
2n
Φ✲r❦
✲r❦
✷✻ ✴ ✺✷
✲r❦
O
2n
s❦
O
2n
s❦
O
2n
s❦
O
2n
Φ✲r❦
O
2n
Φ✲r❦
Ω
Φ✲r❦
✷✻ ✴ ✺✷
✲r❦
O
2n
s❦
O
2n
s❦
O
2n
s❦
O
2n
Φ✲r❦
O
2n
Φ✲r❦
Ω
Φ✲r❦
✷✻ ✴ ✺✷
O
2n
A1 A2 Aa−1 Aa M1 M2 Md−1 Md C1 C2 Cd−1 Cd T
2L′ 2L′ 22L′ 22L′ 2a-1L′ 2a-1L′ 2a-13L′ 2a-13L′ 2L 2L 23L 23L 22d-3L 22d-3L 22d-1L 22d-1L 22L 22L 24L 24L 22d-2L 22d-2L 22d-13L 22d-13L
P P P P P P P P P P P P
✲r❦
✲r❦
✷✼ ✴ ✺✷
L′ = kflag0 ⊕ P(kflag0) L = kflagN ⊕ P(kflagN)
A1 A2 Aa−1 Aa M1 M2 Md−1 Md C1 C2 Cd−1 Cd T
2L′ 2L′ 22L′ 22L′ 2a-1L′ 2a-1L′ 2a-13L′ 2a-13L′ 2L 2L 23L 23L 22d-3L 22d-3L 22d-1L 22d-1L 22L 22L 24L 24L 22d-2L 22d-2L 22d-13L 22d-13L
P P P P P P P P P P P P
✲r❦
✲r❦
✷✼ ✴ ✺✷
L′ = kflag0 ⊕ P(kflag0) L = kflagN ⊕ P(kflagN)
A1 A2 Aa−1 Aa M1 M2 Md−1 Md C1 C2 Cd−1 Cd T
2L′ 2L′ 22L′ 22L′ 2a-1L′ 2a-1L′ 2a-13L′ 2a-13L′ 2L 2L 23L 23L 22d-3L 22d-3L 22d-1L 22d-1L 22L 22L 24L 24L 22d-2L 22d-2L 22d-13L 22d-13L
P P P P P P P P P P P P
O
2n
Φ✲r❦
✲r❦
✷✼ ✴ ✺✷
L′ = kflag0 ⊕ P(kflag0) L = kflagN ⊕ P(kflagN)
A1 A2 Aa−1 Aa M1 M2 Md−1 Md C1 C2 Cd−1 Cd T
2L′ 2L′ 22L′ 22L′ 2a-1L′ 2a-1L′ 2a-13L′ 2a-13L′ 2L 2L 23L 23L 22d-3L 22d-3L 22d-1L 22d-1L 22L 22L 24L 24L 22d-2L 22d-2L 22d-13L 22d-13L
P P P P P P P P P P P P
O
2n
Φ✲r❦
O
2n
ΦP ⊕✲r❦
✷✼ ✴ ✺✷
L′ = kflag0 ⊕ P(kflag0) L = kflagN ⊕ P(kflagN)
k 2k 2k M1 M2 Md T P P P k M1 M2 T P P P Md10∗ 4k 4k
s❦
s❦
✷✽ ✴ ✺✷
k 2k 2k M1 M2 Md T P P P k M1 M2 T P P P Md10∗ 4k 4k
s❦
s❦
✷✽ ✴ ✺✷
k 2k 2k M1 M2 Md T P P P k M1 M2 T P P P Md10∗ 4k 4k
O
2n
s❦
O
2n
s❦
✷✽ ✴ ✺✷
k 2k 2k M1 M2 Md T P P P P k M1 M2 T P P P P Md10∗ 4k 4k
✲r❦
✲r❦
✷✾ ✴ ✺✷
k 2k 2k M1 M2 Md T P P P P k M1 M2 T P P P P Md10∗ 4k 4k
O
2n
Φ✲r❦
O
2n
Φ⊕✲r❦
✷✾ ✴ ✺✷
k 2k 2k M1 M2 Md T P P P P k M1 M2 T P P P P Md10∗ 4k 4k
O
2n
Φ✲r❦
O
2n
Φ⊕✲r❦
✷✾ ✴ ✺✷
✸✵ ✴ ✺✷
m c ϕγ
2 ◦ ϕβ 1 ◦ ϕα 0 ◦ P(Nk)
P♦✇❡r✐♥❣✲✉♣ ♠❛s❦✐♥❣ ▲❋❙❘ ♠❛s❦✐♥❣
✸✶ ✴ ✺✷
m c ϕγ
2 ◦ ϕβ 1 ◦ ϕα 0 ◦ P(Nk)
✸✶ ✴ ✺✷
m c ϕγ
2 ◦ ϕβ 1 ◦ ϕα 0 ◦ P(Nk)
✸✶ ✴ ✺✷
A0 A1 Aa–1 M0 M1 Md–1 ⊕Mi C1 C2 Cd T
ϕ0(L) ϕ0(L) ϕ1(L) ϕ1(L) ϕa–1(L) ϕa–1(L) ϕ2
1◦ϕa–1(L)
ϕ2
1◦ϕa–1(L)
ϕ2◦ϕ0(L) ϕ2◦ϕ1(L) ϕ2◦ϕd–1(L) ϕ2◦ϕ0(L) ϕ2◦ϕ1(L) ϕ2◦ϕd–1(L)
P P P P P P P
✸✷ ✴ ✺✷
L = P(Nk) ϕ1 = ϕ ⊕ id, ϕ2 = ϕ2 ⊕ ϕ ⊕ id
A0 A1 Aa–1 M0 M1 Md–1 ⊕Mi C1 C2 Cd T
ϕ0(L) ϕ0(L) ϕ1(L) ϕ1(L) ϕa–1(L) ϕa–1(L) ϕ2
1◦ϕa–1(L)
ϕ2
1◦ϕa–1(L)
ϕ2◦ϕ0(L) ϕ2◦ϕ1(L) ϕ2◦ϕd–1(L) ϕ2◦ϕ0(L) ϕ2◦ϕ1(L) ϕ2◦ϕd–1(L)
P P P P P P P
✸✷ ✴ ✺✷
L = P(Nk) ϕ1 = ϕ ⊕ id, ϕ2 = ϕ2 ⊕ ϕ ⊕ id
A0 Aa–1 T0 Td–1 M0 Md–1
|A||M|
C1 Cd T
ϕ0(L) ϕ0(L) ϕa–1(L) ϕa–1(L) ϕ1◦ϕ0(L) ϕ1◦ϕ0(L) ϕ1◦ϕd–1(L) ϕ1◦ϕd–1(L) ϕ2
1(L)
ϕ2
1(L)
ϕ2(L) ϕ2(L) ϕ2(L)⊕M0 ϕ2(L)⊕Md–1
P P P P P P P
✸✸ ✴ ✺✷
L = P(Nk) ϕ1 = ϕ ⊕ id, ϕ2 = ϕ2 ⊕ ϕ ⊕ id
A0 Aa–1 T0 Td–1 M0 Md–1
|A||M|
C1 Cd T
ϕ0(L) ϕ0(L) ϕa–1(L) ϕa–1(L) ϕ1◦ϕ0(L) ϕ1◦ϕ0(L) ϕ1◦ϕd–1(L) ϕ1◦ϕd–1(L) ϕ2
1(L)
ϕ2
1(L)
ϕ2(L) ϕ2(L) ϕ2(L)⊕M0 ϕ2(L)⊕Md–1
P P P P P P P
✸✸ ✴ ✺✷
L = P(Nk) ϕ1 = ϕ ⊕ id, ϕ2 = ϕ2 ⊕ ϕ ⊕ id
✸✹ ✴ ✺✷
✸✺ ✴ ✺✷
✸✺ ✴ ✺✷
O
2n
O
2n
✸✺ ✴ ✺✷
O
2n
O
2n
✸✺ ✴ ✺✷
m c
· · · · · ·
h1(t) h1(t)⊕h2(t) hρ−1(t)⊕hρ(t) hρ(t)
k1 k2 kρ
✸✻ ✴ ✺✷
m c
· · · · · ·
h1(t) h1(t)⊕h2(t) hρ−1(t)⊕hρ(t) hρ(t)
k1 k2 kρ
✸✻ ✴ ✺✷
m c
· · · · · ·
h1(t) h1(t)⊕h2(t) hρ−1(t)⊕hρ(t) hρ(t)
✸✼ ✴ ✺✷
m c
· · · · · ·
h1(t) h1(t)⊕h2(t) hρ−1(t)⊕hρ(t) hρ(t)
✸✼ ✴ ✺✷
s❝❤❡♠❡ s❡❝✉r✐t② ✭log2✮ ❦❡② ❧❡♥❣t❤ ❝♦st E ⊗/h LRW1 n/2 n ✷ ✵ LRW2 n/2 2n ✶ ✶ XEX n/2 n ✷ ✵ LRW2[2] 2n/3 4n ✷ ✷ LRW2[ρ] ρn/(ρ+2) 2ρn ρ ρ max{n/2, n−|t|}
✸✽ ✴ ✺✷
✸✾ ✴ ✺✷
✸✾ ✴ ✺✷
✸✾ ✴ ✺✷
✸✾ ✴ ✺✷
m c
k t0n−|t|
✹✵ ✴ ✺✷
m c
k t2 t2 t10n−|t1|
t t1t2
✹✵ ✴ ✺✷
s❝❤❡♠❡ s❡❝✉r✐t② ✭log2✮ ❦❡② ❧❡♥❣t❤ ❝♦st E ⊗/h t❞❦ LRW1 n/2 n ✷ ✵ ✵ LRW2 n/2 2n ✶ ✶ ✵ XEX n/2 n ✷ ✵ ✵ LRW2[2] 2n/3 4n ✷ ✷ ✵ LRW2[ρ] ρn/(ρ+2) 2ρn ρ ρ ✵ Min max{n/2, n−|t|} n ✷ ✵ ✶ Min✲❳❚❳ 2n/3 7n/3 ✷ ✶ ✶
✹✶ ✴ ✺✷
✹✷ ✴ ✺✷
m m m m c
E E E A1 A2 A3 A4 B1 B2 B3
k, t k, t k, t, y1 k, t, y1, y2 l1 x1 y1 l2 x2 y2 l3 x3 y3
s❤♦✉❧❞ ❜❡ s✉❝❤ t❤❛t ✐s ✐♥✈❡rt✐❜❧❡ ❜✉t ❝❛♥ ❜❡ ❛♥②t❤✐♥❣ ♦t❤❡r✇✐s❡
✹✸ ✴ ✺✷
m m m m c
E E E A1 A2 A3 A4 B1 B2 B3
k, t k, t k, t, y1 k, t, y1, y2 l1 x1 y1 l2 x2 y2 l3 x3 y3
E[ρ] ✐s ✐♥✈❡rt✐❜❧❡
✹✸ ✴ ✺✷
m m c
E A1 A2 B1
k, t l1 x1 y1
✹✹ ✴ ✺✷
m m c
E A1 A2 B1
k, t l1 x1 y1
✹✹ ✴ ✺✷
m c k t z
✹✺ ✴ ✺✷
m c k t z
✹✺ ✴ ✺✷
m c k t z
✹✺ ✴ ✺✷
k
✹✻ ✴ ✺✷
k
m c t
✹✻ ✴ ✺✷
k
m c t m ⊕ k ⊗ t c ⊕ k ⊗ t k ⊕ t
✹✻ ✴ ✺✷
k
m c t m ⊕ k ⊗ t c ⊕ k ⊗ t k ⊕ t x y l
✹✻ ✴ ✺✷
k
m c t m ⊕ k ⊗ t c ⊕ k ⊗ t k ⊕ t x y l
✹✻ ✴ ✺✷
k
m c t m ⊕ k ⊗ t c ⊕ k ⊗ t k ⊕ t x y l
✹✻ ✴ ✺✷
k
m c t m ⊕ k ⊗ t c ⊕ k ⊗ t k ⊕ t x y l
✹✻ ✴ ✺✷
k
m c t m ⊕ k ⊗ t c ⊕ k ⊗ t k ⊕ t x y l
✹✻ ✴ ✺✷
❈♦♥s✐❞❡r ❛ ✜♥✐t❡ ✜❡❧❞ ✳ ▲❡t ❜❡ ❛ s❡t ♦❢ ❧✐♥❡s ❜❡ ❛ s❡t ♦❢ ♣♦✐♥ts ★ ♣♦✐♥t✲❧✐♥❡ ✐♥❝✐❞❡♥❝❡s
✹✼ ✴ ✺✷
❈♦♥s✐❞❡r ❛ ✜♥✐t❡ ✜❡❧❞ F✳ ▲❡t
★ ♣♦✐♥t✲❧✐♥❡ ✐♥❝✐❞❡♥❝❡s ≤ min{|L|1/2|P|+|L|, |L||P|1/2 +|P|}
✹✼ ✴ ✺✷
❈♦♥s✐❞❡r ❛ ✜♥✐t❡ ✜❡❧❞ F✳ ▲❡t
★ ♣♦✐♥t✲❧✐♥❡ ✐♥❝✐❞❡♥❝❡s ≤ min{|L|1/2|P|+|L|, |L||P|1/2 +|P|}
✹✼ ✴ ✺✷
❈♦♥s✐❞❡r ❛ ✜♥✐t❡ ✜❡❧❞ F✳ ▲❡t
★ ♣♦✐♥t✲❧✐♥❡ ✐♥❝✐❞❡♥❝❡s ≤ min{|L|1/2|P|+|L|, |L||P|1/2 +|P|}
✹✼ ✴ ✺✷
❈♦♥s✐❞❡r ❛ ✜♥✐t❡ ✜❡❧❞ F✳ ▲❡t
★ ♣♦✐♥t✲❧✐♥❡ ✐♥❝✐❞❡♥❝❡s ≤ min{|L|1/2|P|+|L|, |L||P|1/2 +|P|}
✹✼ ✴ ✺✷
❈♦♥s✐❞❡r ❛ ✜♥✐t❡ ✜❡❧❞ F✳ ▲❡t
★ ♣♦✐♥t✲❧✐♥❡ ✐♥❝✐❞❡♥❝❡s ≤ min{|L|1/2|P|+|L|, |L||P|1/2 +|P|}
✹✼ ✴ ✺✷
m c k
2
t z
✹✽ ✴ ✺✷
◆❡✇ ❛❢t❡r ♦❜s❡r✈❛t✐♦♥ ❜② ●✉♦ ❡t ❛❧✳ ✭♦r✐❣✐♥❛❧ ♣r♦♦❢ ♦♥❧② ❢♦r ✮
m c k
2
t z
✹✽ ✴ ✺✷
◆❡✇ ❛❢t❡r ♦❜s❡r✈❛t✐♦♥ ❜② ●✉♦ ❡t ❛❧✳ ✭♦r✐❣✐♥❛❧ ♣r♦♦❢ ♦♥❧② ❢♦r ✮
m c k
2
t z
✹✽ ✴ ✺✷
◆❡✇ ❛❢t❡r ♦❜s❡r✈❛t✐♦♥ ❜② ●✉♦ ❡t ❛❧✳ ✭♦r✐❣✐♥❛❧ ♣r♦♦❢ ♦♥❧② ❢♦r ✮
m c k
2
t z
✹✽ ✴ ✺✷
◆❡✇ ❛❢t❡r ♦❜s❡r✈❛t✐♦♥ ❜② ●✉♦ ❡t ❛❧✳ ✭♦r✐❣✐♥❛❧ ♣r♦♦❢ ♦♥❧② ❢♦r t = 0✮
k
2
✹✾ ✴ ✺✷
k
2
z m c t z ⊕ m z ⊕ c k ⊕ t x y l
✹✾ ✴ ✺✷
k
2
z m c t z ⊕ m z ⊕ c k ⊕ t x y l
✹✾ ✴ ✺✷
s❝❤❡♠❡ s❡❝✉r✐t② ✭log2✮ ❦❡② ❧❡♥❣t❤ ❝♦st E ⊗/h t❞❦ LRW1 n/2 n ✷ ✵ ✵ LRW2 n/2 2n ✶ ✶ ✵ XEX n/2 n ✷ ✵ ✵ LRW2[2] 2n/3 4n ✷ ✷ ✵ LRW2[ρ] ρn/(ρ+2) 2ρn ρ ρ ✵ Min max{n/2, n−|t|} n ✷ ✵ ✶ Min✲❳❚❳ 2n/3 7n/3 ✷ ✶ ✶ Men1 2n/3 ⋆ n ✶ ✶ ✶ Men2 n ⋆ n ✷ ✵ ✶
✺✵ ✴ ✺✷
⋆ ■♥❢♦r♠❛t✐♦♥✲t❤❡♦r❡t✐❝ ♠♦❞❡❧
✺✶ ✴ ✺✷
✺✷ ✴ ✺✷
✺✷ ✴ ✺✷
✺✷ ✴ ✺✷
✺✸ ✴ ✺✷
m c
E E E
A-1
2
3
4
B1 B2
k, t k, t k, t, y1 k, t, y1 l1 x1 y1 l2 x2 y2 l3 x3 y3
✺✹ ✴ ✺✷