thrift ,D→* - Princeton Universitycuff/ele538/files/lecture_24.pdf · agile because it Z gets a...

Securesoureodinfk . unifknlh)

⇒thrift,D→*→ DE Objective

tzn EL di ( x,nxY]< D

min Etddxiz"D >bz

zn.fm

{ ( R,

Re,

D, ,k ) ) achievable ones

.

1211512076

Rate Distortion Theory for Seaney systems : Thursday

K (rate Re )← →

Italy,D→E_Distytyoxnameasurdb

$-23 -

Distortion measured by

ddx ,xT

* *

Let dilxn,xY=÷¥,d:C in ;)

Performance : E[ d. ( X,nxY]{ D,

REngufbaaunmismdeeofwkjenq.amigktddxn.ElHD3DftnFamzyElddXiiZilmDTheoremicbsneotaohieranengi.n.fr.qp.pd.YePYaYx.sjtjg@TfHdisYtetiLykTdzX.x

)]3D<

t.HN#12¥ Gladysatisfied

of ↳ bear this is the cloveHow ?

-(weakly need Raso )

Examp# X~Bern(Yd

Lossless at intended receiver : (17--0)

de Hammingdistance

|

Encoderusing

1 bit of Key told for anyn

.

Let 12=1 bitlsymbd Xorkey

with entire source

RE lnkgtms AKEY

.

MENG.

Etddxielnl )]=42

+ But thissecrecy

1although best we an hope for ) is

veryf-agile because it

Zgets a

tinyside information and

get 1- bit of X"

,then Z

'

knows X "

! ! !

Ingeneral,

construct different random codebook for each key Value

If Rk is big enough , effectively one- time pad

↳Not our case ! !

With LE, consequence is obvious !

It;Ifa±kD*¥nIII¥"I:→

Eavesdropper cares about Pxiln

Causal Disclosure:

ftp.T#pD-inZilmEx" 1 for each i

[HE

extra information .

¥ txiy

→

"

Real - time"

pessimistic assumption .

→ Applies to reputedgo.me

→ Has nice special case

* Solution : Sanitize pastoutput (using secure Dcs )

thmi Rateregion

:

( $, ,Re

,

D, ,Dz ) : F Pura st . Intuition Split description into

×jfu±YxjuY, | two parts .

send U in the dear

Rk3IH,

I ;HU) Secure V,

Pz? Et d. IX. XD

{mzin

E[dz(X,

Hud ]

Nifty : Superposition code :

U is base layer

Vlayer indexed by KY

( dyf for each kg )

€¥°⇐Ei÷iµ"

Ignore U far the moment 4=0 , use secure DCS

Pxnxnlm . ITBIN

Speed case whenyou

have hytoq dist . fnot.

seoeyprkmmmai,EµnEd{x ,;zlm,x"D]Ziayxitj

1nF,

Hlxiln ,xY= 'ah( xnln )