rt ss s s - - PowerPoint PPT Presentation
rt ss s s rt t rt s
✶ ✴ ✶✹
t1 t2 t3 tℓ f1 f2 f3 fℓ
✷ ✴ ✶✹
✸ ✴ ✶✹
✹ ✴ ✶✹
✹ ✴ ✶✹
✹ ✴ ✶✹
✹ ✴ ✶✹
function
ideal primitive random
simulator for P
✺ ✴ ✶✹
function
ideal primitive random
simulator for P
✺ ✴ ✶✹
✻ ✴ ✶✹
(i) (i)
✻ ✴ ✶✹
(i) (i) (ii)
✻ ✴ ✶✹
(i) (i) (ii) (iii) (iii)
✻ ✴ ✶✹
(i) (i) (ii) (iii) (iii)
✻ ✴ ✶✹
✼ ✴ ✶✹
✼ ✴ ✶✹
m h h′ t f IV
\
n/2
\
n/4
\
n/4
\
n
\
n
\
n
\
2n
\
n
\
n
\
2n
\
n
\
n
✽ ✴ ✶✹
a a a a
b b b b c c c c d d d d
k k k k k k k k k k k k k k k k
a′ a′ a′ a′
b′ b′ b′ b′ c′ c′ c′ c′ d′ d′ d′ d′
2n
\
2n
\
2n
✾ ✴ ✶✹
a a a a
b b b b c c c c d d d d
k k k k k k k k k k k k k k k k
a′ a′ a′ a′
b′ b′ b′ b′ c′ c′ c′ c′ d′ d′ d′ d′
2n
\
2n
\
2n
✾ ✴ ✶✹
a a a a
b b b b c c c c d d d d
k k k k k k k k k k k k k k k k
a′ a′ a′ a′
b′ b′ b′ b′ c′ c′ c′ c′ d′ d′ d′ d′
2n
\
2n
\
2n
✾ ✴ ✶✹
a a a a
b b b b c c c c d d d d
k k k k k k k k k k k k k k k k
a′ a′ a′ a′
b′ b′ b′ b′ c′ c′ c′ c′ d′ d′ d′ d′
2n
\
2n
\
2n
✾ ✴ ✶✹
m h h′ t f IV
\
n/2
\
n/4
\
n/4
\
n
\
n
\
n
\
2n
\
n
\
n
\
2n
\
n
\
n
✐♥♣✉t ♠❛t❝❤❡s ❧❡❣✐t✐♠❛t❡ ✲❝❛❧❧❄ ❝♦♥s✉❧t ②❡s ✐♥♣✉t ✇❡❛❦❄ r❡♣❧② ❧✐❦❡ ✇❡❛❦ ♣❡r♠✉t❛t✐♦♥ ②❡s r❡♣❧② ✉♥✐❢♦r♠❧② ❛t r❛♥❞♦♠ ♥♦ ♥♦
✶✵ ✴ ✶✹
m h h′ t f IV
\
n/2
\
n/4
\
n/4
\
n
\
n
\
n
\
2n
\
n
\
n
\
2n
\
n
\
n
✐♥♣✉t ♠❛t❝❤❡s ❧❡❣✐t✐♠❛t❡ F✲❝❛❧❧❄ ❝♦♥s✉❧t R ②❡s ✐♥♣✉t ✇❡❛❦❄ r❡♣❧② ❧✐❦❡ ✇❡❛❦ ♣❡r♠✉t❛t✐♦♥ ②❡s r❡♣❧② ✉♥✐❢♦r♠❧② ❛t r❛♥❞♦♠ ♥♦ ♥♦
✶✵ ✴ ✶✹
m h h′ t f IV
\
n/2
\
n/4
\
n/4
\
n
\
n
\
n
\
2n
\
n
\
n
\
2n
\
n
\
n
✐♥♣✉t ♠❛t❝❤❡s ❧❡❣✐t✐♠❛t❡ F✲❝❛❧❧❄ ❝♦♥s✉❧t R ②❡s ✐♥♣✉t ✇❡❛❦❄ r❡♣❧② ❧✐❦❡ ✇❡❛❦ ♣❡r♠✉t❛t✐♦♥ ②❡s r❡♣❧② ✉♥✐❢♦r♠❧② ❛t r❛♥❞♦♠ ♥♦ ♥♦
✶✵ ✴ ✶✹
m h h′ t f IV
\
n/2
\
n/4
\
n/4
\
n
\
n
\
n
\
2n
\
n
\
n
\
2n
\
n
\
n
✐♥♣✉t ♠❛t❝❤❡s ❧❡❣✐t✐♠❛t❡ F✲❝❛❧❧❄ ❝♦♥s✉❧t R ②❡s ✐♥♣✉t ✇❡❛❦❄ r❡♣❧② ❧✐❦❡ ✇❡❛❦ ♣❡r♠✉t❛t✐♦♥ ②❡s r❡♣❧② ✉♥✐❢♦r♠❧② ❛t r❛♥❞♦♠ ♥♦ ♥♦
✶✵ ✴ ✶✹
m h h′ t f IV
\
n/2
\
n/4
\
n/4
\
n
\
n
\
n
\
2n
\
n
\
n
\
2n
\
n
\
n
✐♥♣✉t ♠❛t❝❤❡s ❧❡❣✐t✐♠❛t❡ F✲❝❛❧❧❄ ❝♦♥s✉❧t R ②❡s ✐♥♣✉t ✇❡❛❦❄ r❡♣❧② ❧✐❦❡ ✇❡❛❦ ♣❡r♠✉t❛t✐♦♥ ②❡s r❡♣❧② ✉♥✐❢♦r♠❧② ❛t r❛♥❞♦♠ ♥♦ ♥♦
✶✵ ✴ ✶✹
m h h′ t f IV
\
n/2
\
n/4
\
n/4
\
n
\
n
\
n
\
2n
\
n
\
n
\
2n
\
n
\
n
✐♥♣✉t ♠❛t❝❤❡s ❧❡❣✐t✐♠❛t❡ F✲❝❛❧❧❄ ❝♦♥s✉❧t R ②❡s ✐♥♣✉t ✇❡❛❦❄ r❡♣❧② ❧✐❦❡ ✇❡❛❦ ♣❡r♠✉t❛t✐♦♥ ②❡s r❡♣❧② ✉♥✐❢♦r♠❧② ❛t r❛♥❞♦♠ ♥♦ ♥♦
t1 t2 t3 tℓ f1 f2 f3 fℓ
✶✶ ✴ ✶✹
t1 t2 t3 tℓ f1 f2 f3 fℓ
✶✶ ✴ ✶✹
t1 t2 t3 tℓ f1 f2 f3 fℓ
✶✷ ✴ ✶✹
t1 t2 t3 tℓ f1 f2 f3 fℓ
✶✷ ✴ ✶✹
t1 t2 t3 tℓ f1 f2 f3 fℓ
✶✷ ✴ ✶✹
t1 t2 t3 tℓ+1 f1 f2 f3 fℓ+1
✶✸ ✴ ✶✹
t1 t2 t3 tℓ+1 f1 f2 f3 fℓ+1
2
✶✸ ✴ ✶✹
t1 t2 t3 tℓ+1 f1 f2 f3 fℓ+1
2
✶✹ ✴ ✶✹
✶✺ ✴ ✶✹
a e a e b f b f c g c g d h d h
k k k k k k k k k k k k k k k k
a′ e′ a′ e′ b′ f′ b′ f′ c′ g′ c′ g′ d′ h′ d′ h′
\
2n
\
2n
\
2n
✶✻ ✴ ✶✹