16
6.857 Computer and Network Security Lecture 13 Today: Pedersen Commitment PK Encryption El Gamal PK encryption Semantic security DDH (Decision Diffie-Hellman) IND-CCA2 Cramer-Shoup PK encryption Readings: Paar and Pelzl, Chapters 6,7,8 Katz and Lindell, Chapter 10 1

Network and Computer Security, Lecture 13 Computer and Network Security Lecture 13 Today: Pedersen Commitment PK Encryption El Gamal PK encryption Semantic security

Embed Size (px)

Citation preview

6.857 Computer and Network Security Lecture 13

Today:

Pedersen Commitment PK Encryption El Gamal PK encryption Semantic security DDH (Decision Diffie-Hellman) IND-CCA2 Cramer-Shoup PK encryption

Readings: Paar and Pelzl, Chapters 6,7,8 Katz and Lindell, Chapter 10

1

______________________________

) /1113

‘FILE UNDER:

e

I ICpvtms%.nk Czc\tmt

U

1

LI-tomm4Incw4%:3c

-i Dptn$ c&nimc4wnni) flvt4% 9

hon)yofan:nofl_ +

I C?) t Lan’+- pvDiua

t5% )C41 fws

‘C

Cmv’

&iocfl by

1cetN

S

I).

‘‘ pt;mts cit cj \pl t.kgfføc

vn°” 4: ?-c “%“P 0

1L’4Hf’ <j):&stnmJ

prC..4. F)

rqr,àorn r E

C.

x

2

izzzzzzj4_L

I}

-.,

----

-_---4

—I -----::

‘t‘C

’is

--c

t.J

.t’

-C

‘--‘

_c

_

1-

‘a

-x

+-

--

%-

6-

AA

C

--?;r

L4

c;zzzz

ICC

‘5’”

—‘

-‘

C.

JX

çflp

flt

•-—

‘-

--—

-‘

—-

-c.•-

4-t.

—z

_C

I’S

----‘

L.0

ZL

L_

-_--

C.

oC

4.:C

—z

,Lj

a

“6IaII

V

-j--_

i__

__

__

.-

iiiir

:i

-----‘-—

--•-•- e

-_x

—C

.2

ff

r-I

L1U

k15.1

If‘4C.

--7

r-

::t.

1-4-

z-,•z

‘3

r’4

Ct

3

_______

—- -

5nL-T

rzzzzzzzaz:z*z : i*zz

‘I’ ad

ii

VtI

TJi4wLkLsai

th

I

ä

i.j

1

1‘C ‘r ‘ ensiaw 10

•AE-±.

w!

.*

1

t$a 4’— a

La

.a

F lC

C’ 2-4. QS1Jr4F-F

L is

if— I I

‘!-*LL_1ZTJZZt’H —1 I

I

Ii

I L -z TiI H- -r—t

pg:: 4k$cttr:4I, I £ a

—_tjthk flyit’c44 4_4r-mmv

, I

I At’h

1-i±i4_t± imzizrz

41tLJ I—r — —- -—t tf -

I ttL h1H —:

I ‘——I -— — — I -. —t —

zi_L.J3

4

LJ5.3

BI’-&qni4) PX encrp%vs (rawr £1

Let be a

(X’eyn tm1y D..I5p.ik a*scrcpi 4 & 6_, iten A.)

A. .4 r4rJbm’am[o,,,j&)-SJ

Let 5tCt*.

Let

&LhtpQt (w) s1c (a J.settpirvn bf 6, i need4)

ncryp%n t•

?ck kèanckm 4nrn [o,,.)a)-s]

Ass.nne rress4,e m ‘iS eICWitnt t

Le€ t recpc’tnt

c =(k

, cpkn4eAt

Dc

L€t’ cs (qO :t receWecI cplwkict

Let n/a. &i4tpbd+vvI.

Cccrectwes1s4flpwssnct

5

L—

-

-

-[

-

-

--

——

-_r__i-L

__

H

-oC

rC

InU

.

‘C--

-

S6_I

Sn

*II

II

I,II

US-x0’

.1

V

1-7%

-4-3€‘S

-1--

£

-p

a-9rI‘37

’-o

IØIIa

6

1-ew it dectrie SCtL4t+’y 4tr P)< encryptron?

Wall ea two cia{cviiFons:

C $tman+CC sccutily (oUwasser &Mcc.I

“a4apka tosen cip)wrkit ‘rHc.ck’ (4Cc4) Secwrt.

(is $b we Sqw 4€ syunnic$v. enctypfr.n’)

r• Exqn’.;ner 3erer44ts (pwsw) t.ESfl5 keyenC’1)

• gqm;ner seJs PR 4krers4ry

• AAveisry crnnpAes r po)ynomci 6 a) fme, *&cn

ot*pks two mccayts m31m, of %me

0nà °S%\C [m0ni, (t1i4irtA].

?“ Ij\.

— aSt. ‘WI) 1.

• Eitaminer prtiu qL3o1i Gmp.a+u ct E(P1c, m)

• X4hlCntr ‘seAs c,s to Ahie6ary

• Acversrny ccvnru%s c poiynon’;. C:r’ )i” 4;:nse,

4wn o.4ees t (his “ics? fir

Avenstywnsla qy,e

-j !I)AT

-1 eAGL155

7

I .E P

5 P 91< enttpkon S&MC is

_____

f ?mz[A4i w;ns] 4B4t Zn orAer ‘Sir a W tncøipt:øn cAnt to

bt 5eeur€.1 if mwi flecesS4flIy

- ‘oc r ow1ed.t(RanJomqeA encrtron i’S

bui yosac1jcent .Cor senittc cecwr;>’

El 64nt) PK encypfovi .em4nfrtJly cecwcl

* mott. :b cc.rf bc sRit’%

W9 6c rcfl4o*,PC.J1)rtJ)Ot s0L

i H- L

—iip

HpztHt

H

I: . .. ..-

- - I -

F

L 1 —

H1_li I_i_4 j I il_i

8

r

‘I,

-i

a-P

S.

4..C.

4L-a

-t’

F

4<1

L_

jt—

JL

4.

3—

c—

.S

a.

11t

So

il*3

I5

-‘

-4-

Sj

-a-

-r

t:

44

0.’-

•a-1—

—5

0

ca0

._c,0

.‘S

—._

s-—

I’-4...

IV

o...4

,j:

WJ.

—I

3C

ve.

.C-

0

a°-.

.‘-

3r>4—

v—

—U

4.)

-‘

---

.1

.

Hc

ifZ

?c

I

t-

-n‘J

S

-t.r

•—

QJ

‘4C-p

-n-s

r2

—-_F

C$3)

t

Xc£

‘.4.

UF.’

am

uI

a.

L?

iii;-

9

InI

0-‘

-

I ‘44.

r

-—

-----

—S

Tr

—-I

Lt-fJr4j

14

wI

I;.

fzC

:rL

JL:

Z3._

oL

L:

i:a:

ft

F EIE

EHRE

’!1EJ

tFtF

JHW

EF7’

.E

EE

-—j-

-—r

t:flr

1c:r

irJz:I

iiiz

!r:z

;z:r

rK

:;sm

-.

5—

--

--

IlL

1

3..

-:z

rS

., tr-”r-1-r

a,

tt

r”

—:

—‘--—

flI

JJJt

‘.1‘a

..1.

$4 a.

II-I

I I

‘1

rr

T’T

h’T

tt.

fj

t4j

f 1, 4:

‘el

S

LiS

I.1

it

rw

¶4

—j

ti

13.

b .4

I;

It

±

HI

.

LA

$4

s-

:tsjz

tzt

II

a —a

‘I1—

ti

—_

_

WE

In wE .ff

-

10

L1S,9

• W%k Srbner eiótThn f Stcurify 4r Pk encviph>n?o,c i, .exci.J.s e1cec);Iy..’)

.“,DJD—CcAa. seeurt1’ (ACLA SCture* Setat

rnkr o4apwt ckoe cpvrxt acQ)‘ flJb-CCA sectaMn we Sqiv r 5ymnwtfl ent

• Stmlqr lv Sem.nrt secal, JAn, ex4- tL44j,j i\4 % kttfl*)bn ec4t, fio•

( H bus P1< So QCC2CS 40 tYlCt)iThfl oraclt arn4

• *±

1•

L..

L .L

Ac beftct, flqy f4 ake ornt!t 40 decrypt

k4i’t1 cp\’n4tt è.wrj ss”pie’)

1•

. 1

HH ..

[ZZZZH:Hf h

I

11

3

4=—v

4=

CEQVS!1

___________

3CJNfl

L___

_______

12

ririP

13

-

UI

zzzzz*ç

7p

__

__

__

__

__

__

_

IJ

I-’

I

-JIi

H

C’

Ua0H

I

14

Iopjc:

IL.E UNDER—

1 L_I 5, 13

The jw .t .1 t ir iei ‘ LI’ . ib-ttfl.

CtE tlt!. 4 tt’it. 4 ti t4 jOlta

I

V

1— — —

cur

iis cc_

Zii;[r:f!?![-::EE

lb

• --F -

—TfuE;4i5c* ct rj’ jfrii$ S

!

;Di-EL:i. ‘Pt’V

4-

--I-.——.

1.

-1-————.—

——-—.——-.-I.-----—-—-+——--—————

—— 4——-—-—-H—’-i-———f———-—t- .

zzz:4z zzRzZEzEtZzIzzzz±tz±zzLZZEZEE±iZZZ-.--.-.---i-----zizzzz:zt4z4- .zz

z Hizzzt z ::: iz

15

MIT OpenCourseWarehttp://ocw.mit.edu

6.857 Network and Computer SecuritySpring 2014

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.